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The exponentially modified Gaussian (EMG) distribution is adopted in many fields such as psychology, chromatographic peaks, and cell biology. In this article, we focus on the test for the parameters of the EMG distribution. The primary test statistic is the classical likelihood ratio. Although the EMG distribution is an asymmetric one, we proved that the logarithm of the likelihood ratio is asymptotically distributed as χ 2 , that is, the Wilks phenomenon. We employ Q–Q plots to illustrate the sample sizes needed for the asymptotic distribution as a good approximation to the null distribution of the loglikelihood ratio for different parameters. The available approximate χ 2 distribution for the loglikelihood ratio is guaranteed by a relatively large sample size. Hence, when the sample size is small, the approximate χ 2 distribution is inapplicable, since the EMG distribution is asymmetric. For the small sample size, we propose a parametric bootstrap algorithm, which is demonstrated to be successful by the simulation studies. An application of our method to a real data example shows that the test is satisfactory. [ABSTRACT FROM AUTHOR]

Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For example, rather than providing the exact measurements of their clients, they may only provide researchers with grouped data, that is, the number of clients falling in each of a set of non-overlapping measurement intervals. The challenge is to estimate the mean and variance structure of the hidden ungrouped data based on the observed grouped data. To tackle this problem, this work considers the exact observed data likelihood and applies the Expectation-Maximization (EM) and Monte Carlo EM (MCEM) algorithms for cases where the hidden data follow a univariate, bivariate, or multivariate normal distribution. Simulation studies are conducted to evaluate the performance of the proposed EM and MCEM algorithms. The well-known Galton data set is considered as an application example. [ABSTRACT FROM AUTHOR]

Non-expert users often find it challenging to perceive the reliability of computer vision systems accurately. In human–computer decision-making applications, users' perceptions of system reliability may deviate from the probabilistic characteristics. Intuitive visualization of system recognition results within probability distributions can serve to enhance interpretability and support cognitive processes. Different visualization formats may impact users' reliability perceptions and cognitive abilities. This study first compared the mapping relationship between users' perceived values of system recognition results and the actual probabilistic characteristics of the distribution when using density strips, violin plots, and error bars to visualize normal distributions. The findings indicate that when density strips are used for visualization, users' perceptions align most closely with the probabilistic integrals, exhibiting the shortest response times and highest cognitive arousal. However, users' perceptions often exceed the actual probability density, with an average coefficient of 2.53 times, unaffected by the form of uncertainty visualization. Conversely, this perceptual bias did not appear in triangular distributions and remained consistent across symmetric and asymmetric distributions. The results of this study contribute to a better understanding of user reliability perception for interaction designers, helping to improve uncertainty visualization and thereby mitigate perceptual biases and potential trust risks. [ABSTRACT FROM AUTHOR]

Given that the Gaussianity of the observation error distribution is the fundamental principle of some data assimilation and machine learning algorithms, the error structure of radar reflectivity has become increasingly important with the development of high-resolution forecasts and nowcasts of convective systems. This study examines the error distribution of radar reflectivity and discusses what causes the non-Gaussian error distribution using 6-month observations minus backgrounds (OmBs) of composites of vertical maximum reflectivity (CVMRs) in mountainous and hilly areas. By following the symmetric error model in all-sky satellite radiance assimilation, we reveal the error structure of CVMRs as a function of symmetric rain rates, which is the average of the observed and simulated rain rates. Unlike satellite radiance, the error structure of CVMRs shows a sharper slope for light precipitation than for moderate precipitation. Thus, a three-piecewise fitting function is more suitable for CVMRs. The probability density functions of OmBs normalized by symmetric rain rates become more Gaussian than the probability density functions normalized by all samples. Moreover, the possibility of using a third-party predictor to construct the symmetric error model is also discussed in this study. The result shows that the Gaussian distribution of OmBs can be further improved via more accurate precipitation observations. According to the Jensen–Shannon divergence, a more linear predictor, the logarithmic transformation of the rain rate, can provide the most Gaussian error distribution in comparison with other predictors. [ABSTRACT FROM AUTHOR]

This paper presents a newsvendor model with backorders for customers who are willing to wait to be served. Demand follows a normal probability distribution, with the particularity that the expected value depends on the sale price and the variation coefficient is fixed. Three parameters are considered to characterize this dependence on the expected demand and the sale price: the population size of potential customers, the unit production cost of the item and an elasticity parameter with an isoelastic type. Backorders and lost sales are combined with a fixed proportion for the backorders. The quantities to be determined are the sale price and the order quantity. The goal is the maximization of the expected profit. The optimal solution is obtained in a closed form if there are no lost sales. In the case of a mixture of partial backordering and lost sales, a methodological proposal based on a numerical algorithm is given. The study reveals that the maximum expected profit and the optimal quantities to be determined are highly influenced by the unit purchasing cost and the degree of dependence of the demand concerning the sale price. Other parameters, such as the proportion of backorders and the variation coefficient of demand, are less influential. Numerical examples are used to illustrate the model, and a sensitivity analysis of the optimal solution regarding the nine initial parameters is presented. Some managerial insights deduced from the obtained results are also proposed. • A newsboy model with demand fixed partial backlogged is presented. • Demand follows a normal probability distribution with price-dependent mean. • The decision variables are the lot size and the selling price. • A numerical algorithm is given to obtain the optimal policy. [ABSTRACT FROM AUTHOR]

Empirical evidence indicates that asset returns adhere to an extended normal distribution characterized by excessive kurtosis and non-zero skewness. Consequently, option prices derived from this distribution diverge from those predicted by the Black–Scholes model. Despite the significance of option price sensitivities for risk management in investment portfolios, the existing literature lacks a thorough exploration of these sensitivities within the context of the extended normal distribution. This article addresses this research gap by deriving the Greeks for options based on the extended normal distribution. The Greeks under consideration include Vega, Delta, Theta, Gamma, Rho, Vanna, Charm, and Vera, all of which are crucial for informed financial decision-making. Furthermore, this study provides a detailed analysis of how these option price sensitivities vary with different levels of kurtosis, offering valuable insights for various market applications. This contribution not only enhances the theoretical understanding of option pricing under non-standard distributions but also presents practical implications for portfolio risk management. [ABSTRACT FROM AUTHOR]

In recent years, neural topic modeling has increasingly raised extensive attention due to its capacity on generating coherent topics and flexible deep neural structures. However, the widely used Dirichlet distribution in shallow topic models is difficult to reparameterize. Therefore, most existing neural topic models assume the Gaussian as the prior of topic proportions for reparameterization. Gaussian distribution does not have the sparsity like Dirichlet distribution, which limits the model's topic extraction ability. To address this issue, we propose a novel neural topic model approximating the Dirichlet prior with the reparameterizable Kumaraswamy distribution, namely Kumaraswamy Neural Topic Model (KNTM). Specifically, we adopted the stick-breaking process for posterior inference with the Kumaraswamy distribution as the base distribution. Besides, to capture the dependencies among topics, we propose a Kumaraswamy Recurrent Neural Topic Model (KRNTM) based on the recurrent stick-breaking construction to ensure that the model can still generate coherent topical words in high-dimensional topic space. We examined our method on five prevalent benchmark datasets over six Dirichlet-approximating neural topic models, among which KNTM has the lowest perplexity and KRNTM performance best on topic coherence and topic uniqueness. Qualitative analysis of the top topical words verifies that our proposed models can extract more semantically coherent topics compared with state-of-the-art models, further demonstrating our method's effectiveness. This work contributes to the broader application of VAEs with Dirichlet priors. [ABSTRACT FROM AUTHOR]

In this article, we study the autocorrelation function (ACF), which is a crucial element in time series analysis. We compare the distribution of the ACF, both from a theoretical and empirical point of view. We focus on white noise processes (WN), i.e., uncorrelated, centered, and identically distributed variables, whose ACFs are supposed to be asymptotically independent and converge towards the same normal distribution. But, the study of the sum of the sample ACF contradicts this property. Thus, our findings reveal a deviation of the sample ACF from normality beyond a specific lag. Note that this phenomenon is observed for white noise of varying lengths, and evenforn the residuals of an ARMA( p , q ) model. This discovery challenges traditional assumptions of normality in time series modeling. Indeed, when modeling a time series, the crucial step is to validate the estimated model by checking that the associated residuals form white noise. In this study, we show that the widely used portmanteau tests are not completely accurate. Box–Pierce appears to be too conservative, whereas Ljung–Box is too liberal. We suggest an alternative method based on the ACF for establishing the reliability of the portmanteau test and the validity of the estimated model. We illustrate our methodology using money stock data in the USA. [ABSTRACT FROM AUTHOR]

This study presents a novel approach for the optimization of genomic parental selection in breeding programs involving categorical and continuous–categorical multi-trait mixtures (CMs and CCMMs). Utilizing the Bayesian decision theory (BDT) and latent trait models within a multivariate normal distribution framework, we address the complexities of selecting new parental lines across ordinal and continuous traits for breeding. Our methodology enhances precision and flexibility in genetic selection, validated through extensive simulations. This unified approach presents significant potential for the advancement of genetic improvements in diverse breeding contexts, underscoring the importance of integrating both categorical and continuous traits in genomic selection frameworks. [ABSTRACT FROM AUTHOR]

The generation of turbulent inflow conditions is a key issue in large eddy simulation (LES) or direct numerical simulation (DNS). In this paper, an improved synthetic eddy method (SEM) is proposed to generate inflow turbulence for LES and DNS. The improvements about SEM focus on the eddy radius and eddy distributions. First, the eddy radius is improved to reduce the nonphysical vortex structure on the wall caused by overestimation of the radius. Second, a sampling method using Gaussian distribution is proposed to improve the distribution of eddies, which accurately captures the randomness of turbulent structure size and is close to the actual flow field. The improved method is applied to the direct numerical simulation of the supersonic turbulent boundary layer at Mach 2.7 and the 24° compression ramp. Results indicate that the predictions yielded by the improved method are in good agreement with both DNS and experimental data. Compared to the original method, the improved method exhibits a more rapid recovery of the friction coefficient and effectively shortens the development distances. The improved SEM has enhanced the efficiency and accuracy of generating inlet turbulence, which can provide inlet turbulence boundary conditions for LES and DNS. [ABSTRACT FROM AUTHOR]

Knowledge distillation (KD) has been one of the most potential methods to implement a lightweight detector, which plays a significant role in satellite in-orbit processing and unmanned aerial vehicle tracking. However, existing distillation paradigms exhibit limited accuracy in detecting arbitrary-oriented objects represented with rotated bounding boxes in remote sensing images. This issue is attributed to two aspects: (i) boundary discontinuity localization distillation, caused by angle periodicity of rotated bounding boxes, and (ii) spatial ossified feature distillation, induced by orientation-agnostic knowledge transitive regions, both of which contribute to ambiguous orientation estimation of objects. To address these issues, we propose an effective KD method called Orientation Distillation (OD) via anti-ambiguous spatial transformation, which consists of two modules. (i) Anti-ambiguous Location Prediction (ALP) module reformulates the regression transformation between teacher–student bounding boxes as Gaussian distributions fitting procedure. These distributions with distilled potential are optimized to accurately localize objects with the aid of boundary continuity cost. (ii) Orientation-guided Feature Calibration (OFC) module employs a learnable affine matrix to augment fixed CNN sampling grid into a spatially remapped one, which bridges between the multi-scale feature of teacher and student for effectively delivering the refined oriented awareness within adaptively distillation regions. Overall, OD customizes the spatial transformation of bounding box representation and sampling grid to transfer anti-ambiguous orientation knowledge, and significantly improves the performance of lightweight detectors upon non-axially arranged objects. Extensive experiments on multiple datasets demonstrate that our plug-and-play distillation framework achieves state-of-the-art performance. Codes are available at https://github.com/Molly6/OD. [ABSTRACT FROM AUTHOR]

We establish connections between the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert calculus for complete quadrics. We prove a conjecture by Sturmfels and Uhler on the polynomiality of the ML-degree. We also prove a conjecture by Nie, Ranestad and Sturmfels providing an explicit formula for the degree of SDP. The interactions between the three fields shed new light on the asymptotic behaviour of enumerative invariants for the variety of complete quadrics. We also extend these results to spaces of general matrices and of skew-symmetric matrices. [ABSTRACT FROM AUTHOR]

We establish a general result on the existence and uniqueness of a quasi-stationary distribution μD of a strongly Feller Markov process (Xt, t≥0) killed when it exits a domain D, under some Lyapunov function condition. Our result covers the case of hypoelliptic damped Hamiltonian systems. Our method is based on a characterization of the essential spectral radius by means of Lyapunov functions and measures of noncompactness. [ABSTRACT FROM AUTHOR]

Let 풦 + ⁢ ( σ ) = { ℙ ( ϑ , σ ) ⁢ ( d ⁢ ζ ) : ϑ ∈ ( 0 , ϑ + ⁢ ( σ ) ) } {{\mathcal{K}_{+}}(\sigma)=\{\mathbb{P}_{(\vartheta,\sigma)}(d\zeta):\vartheta% \in(0,\vartheta_{+}(\sigma))\}} be the Cauchy–Stieltjes Kernel (CSK) family generated by a probability measure σ which is non degenerate and has support bounded from above. Consider the concept of V a {V_{a}} -transformation of measures introduced in [A. D. Krystek and L. J. Wojakowski, Associative convolutions arising from conditionally free convolution, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 2005, 3, 515–545] for a ∈ ℝ {a\in\mathbb{R}} . We prove that V a ⁢ ( ℙ ( ϑ , σ ) ) ∈ 풦 + ⁢ ( σ ) {V_{a}(\mathbb{P}_{(\vartheta,\sigma)})\in{\mathcal{K}_{+}}(\sigma)} for all a ∈ ℝ ∖ { 0 } {a\in\mathbb{R}\setminus\{0\}} if and only if the measure σ is of the free Gaussian (semicircle) type law up to affinity. [ABSTRACT FROM AUTHOR]

In the presence of fixed threshold effects, the least squares (LS) estimator of the threshold parameter poses challenges for statistical inference due to its nonstandard limiting distribution, which also presents challenges for bootstrap methods. To address this issue, we propose a novel estimator: a two-step smoothed gradient least squares (SGLS) estimator. Our proposed method achieves a normal limiting distribution for the threshold parameter with minimal efficiency loss compared to the LS estimator. Furthermore, our modified bootstrap method significantly enhances computational efficiency, leading to improved bootstrap confidence intervals (CIs) for the threshold parameter compared to asymptotic CIs. Our method is validated through a small Monte Carlo study and demonstrated with an empirical application. [ABSTRACT FROM AUTHOR]

We introduce a mixture of mixtures of bounded asymmetric generalized Gaussian and uniform distributions. Based on this framework, we propose model-based classification and model-based clustering algorithms. We develop an objective function for the minimum message length (MML) model selection criterion to discover the optimal number of clusters for the unsupervised approach of our proposed model. Given the crucial attention received by Explainable AI (XAI) in recent years, we introduce a method to interpret the predictions obtained from the proposed model in both learning settings by defining their boundaries in terms of the crucial features. Integrating Explainability within our proposed algorithm increases the credibility of the algorithm's predictions since it would be explainable to the user's perspective through simple If-Then statements using a small binary decision tree. In this paper, the proposed algorithm proves its reliability and superiority to several state-of-the-art machine learning algorithms within the following real-world applications: fault detection and diagnosis (FDD) in chillers, occupancy estimation and categorization of residential energy consumers. [ABSTRACT FROM AUTHOR]

Optical bistability is investigated for optomechanical system composed of an ensemble of inhomogeneously broadened two-level atoms embedded between the two mirrors of the optical cavity, that is subjected to two input (strong and probe) fields. We consider two types of inhomogeneous broadened distributions, namely, Lorentzian and Gaussian line shapes. The first order harmonic components of the output fields (due to the presence of probe field) show reversed and knotted bistability shapes simultaneously with the standard bistable shape of the fundamental component of the field at frequency ω c . The inhomogeneous broadened line width for both Lorentzian and Gaussian distribution affects the dispersive switching of the system, as well as the bistable behavior. Locations of the maxima of photon numbers associated with higher harmonics of the output fields are identified with respect to the probe field frequency. [ABSTRACT FROM AUTHOR]

• Transformer-based multitask network is designed for spacecraft pose estimation. • Matrix Fisher & Gaussian distributions are utilized for the pose uncertainty. • The robust neural network-based network vision navigation pipeline is created. Spacecraft pose estimation (SPE) plays a vital role in the relative navigation system for on-orbit servicing and active debris removal. Current deep learning-based methods have made great achievements on object pose estimation. However, towards the challenging onboard SPE missions, most existing Convolutional Neural Network (CNN) methods failed to capture remote vision attention, leading to the reduction of accuracy and robustness. In this paper, we presented an end-to-end multi-task Pyramid Transformer SPE network (PVSPE) consisting of two novel feature extraction modules: EnhancedPVT (EnPVT) and SlimGFPN. The EnPVT module is designed to combine global spatial and channel attention, while the Slim GFPN module can fuse features more effectively. Matrix Fisher and multivariate Gaussian distributions are further employed to model the uncertainty of pose regression to increase its accuracy. Extensive experiments are carried out on challenging SPEED + and SHIRT datasets, to validate the performances on pose estimation and vision-based navigation, respectively. The results show that the proposed PVSPE model achieved high accuracy for SPE on the SPEED + dataset even under different scales and severe illumination, demonstrating its robustness and high generalization. Leveraging the insightful uncertainty model of PVSPE, the vision-based navigation pipeline, combined with Kalman filters, accurately estimated the satellite pose under challenging rendezvous scenarios on the SHIRT dataset, with degree-level attitude errors and centimeter-level translation accuracy at steady-state. [ABSTRACT FROM AUTHOR]

Clinical trials seeking to delay or prevent the onset of type 1 diabetes (T1D) face a series of pragmatic challenges. Despite more than 100 years since the discovery of insulin, teplizumab remains the only FDA‐approved therapy to delay progression from Stage 2 to Stage 3 T1D. To increase the efficiency of clinical trials seeking this goal, our project sought to inform T1D clinical trial designs by developing a disease progression model‐based clinical trial simulation tool. Using individual‐level data collected from the TrialNet Pathway to Prevention and The Environmental Determinants of Diabetes in the Young natural history studies, we previously developed a quantitative joint model to predict the time to T1D onset. We then applied trial‐specific inclusion/exclusion criteria, sample sizes in treatment and placebo arms, trial duration, assessment interval, and dropout rate. We implemented a function for presumed drug effects. To increase the size of the population pool, we generated virtual populations using multivariate normal distribution and ctree machine learning algorithms. As an output, power was calculated, which summarizes the probability of success, showing a statistically significant difference in the time distribution until the T1D diagnosis between the two arms. Using this tool, power curves can also be generated through iterations. The web‐based tool is publicly available: https://app.cop.ufl.edu/t1d/. Herein, we briefly describe the tool and provide instructions for simulating a planned clinical trial with two case studies. This tool will allow for improved clinical trial designs and accelerate efforts seeking to prevent or delay the onset of T1D. [ABSTRACT FROM AUTHOR]

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study. [ABSTRACT FROM AUTHOR]

This paper intends to model an AGC regulator for a restructured environment using Bare Bone Particle Swarm Optimization (BBPSO). The gain-controlled Proportional–Integral (PI) Controller is designed here to enhance the performance of the BBPSO algorithm along with Gaussian distribution. The practical difficulty in handling the area control error to zero is the sudden variations in load. In practice, the tremendous contribution of deregulation in the power sector causes volatility in frequency and tie-line power deviations. To ensure the robustness of the proposed controller, three different cases of power system transactions have been considered. The performance has been validated by comparing it with Real Coded Genetic Algorithm-tuned PI controller (RCGA-PI) and Differential Evolutionary Algorithm-tuned PI controller (DE-PI) for the five area Thermal-Thermal generation test system. Moreover, the dynamic performance of an extensive range of demands and disturbances of all areas like settling time and overshoot against parametric precariousness has been done on the proposed test system. [ABSTRACT FROM AUTHOR]

This paper proposes a novel multi-attribute decision-making (MADM) method for interval rough numbers (IRNs) considering different distribution types, namely uniform, exponential, and normal distributions. Upper and lower approximate interval dominance degrees are defined and aggregated using dynamic weights to obtain pairwise comparisons of IRNs. The properties of dominance are verified, and an attribute weight determination method based on the dominance balance degree is introduced. The proposed MADM method is data-driven and does not rely on the subjective preferences of decision-makers. Case analysis demonstrates the effectiveness and rationality of the proposed method, revealing that the distribution type of IRNs significantly impacts decision results, potentially leading to reversed ranking outcomes. The proposed method offers a comprehensive framework for handling MADM problems with IRNs under different distributions. [ABSTRACT FROM AUTHOR]

Copyright of Sportif Bakış: Spor ve Eğitim Bilimleri Dergisi is the property of Sportif Bakis: Spor ve Egitim Bilimleri Dergisi and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Sportif Bakış: Spor ve Eğitim Bilimleri Dergisi is the property of Sportif Bakis: Spor ve Egitim Bilimleri Dergisi and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The probabilistic prediction of monthly precipitation events, specifically more‐than‐normal (MN), normal (N), and less‐than‐normal (LN) events, holds significant importance in the field of water resource management. In this paper, we employ the Bayesian Joint Probability (BJP) modeling approach to generate monthly probabilistic forecasts for LN, N, and MN events in Northwest Iran. To model the joint distribution of observed precipitation and model precipitation, we propose the utilization of a log‐sinh transformed multivariate normal distribution. The prior distribution for the parameters of this multivariate normal distribution is established as the normal‐inverse‐Wishart, which is known to be the conjugate of the multivariate normal distribution. Bayesian inference of model parameters and associated uncertainties is conducted using STAN Markov Chain Monte Carlo (MCMC) sampling. The methodology is applied to the outputs of four North American Multi‐Model Ensemble (NMME) models, namely CanCM4i, CCSM4, NEMO, and NASA, spanning the period from 1982 to 2017 for a 4‐month forecast horizon. The accuracy of predictions is assessed through various statistical measures and graphical methods using a 12‐fold cross‐validation strategy. The results demonstrate that (a) BJP probabilistic predictions of precipitation consistently outperform raw predictions across all models, months, lead times. (b) The BJP‐NASA model exhibits superior discrimination and reliability compared to other models. (c) May and November show the least amount of discrimination. This observation may be attributed to the fact that these months serve as transitional periods in Iran. (d) Fall forecasts are the most reliable, while summer forecasts are the least reliable. Key Points: Bayesian joint probability (BJP) probabilistic predictions of precipitation have more Ranked Probability Skill Score (RPSS) than raw predictions for all models, months, and lead times, and generally outperform the raw predictionsThe BJP‐NASA models have better discrimination and higher reliability compared to othersSpring and fall have lower discrimination compared to summer and winter. On the other hand, summer is less reliable, and the fall is the most [ABSTRACT FROM AUTHOR]

This study presents a numerical investigation into the adhesion strength of micro fibrillar structures, incorporating statistical analysis and the effects of excessive pre–load leading to fibril buckling. Fibrils are modeled as soft cylinders using the Euler–Bernoulli beam theory, with buckling conditions described across three distinct states, each affecting the adhesive properties of the fibrils. Iterative simulations analyze how adhesion strength varies with pre–load, roughness, number of fibrils, and the work of adhesion. Roughness is modeled both in fibril heights and in the texture of a rigid counter surface, following a normal distribution with a single variance parameter. Results indicate that roughness and pre–load significantly influence adhesion strength, with excessive pre–load causing substantial buckling and a dramatic reduction in adhesion. This study also finds that adhesion strength decreases exponentially with increasing roughness, in line with theoretical expectations. The findings highlight the importance of buckling and roughness parameters in determining adhesion strength. This study offers valuable insights into the complex adhesive interactions of fibrillar structures, offering a scalable solution for rapid assessment of adhesion in various rough surface and loading scenarios. [ABSTRACT FROM AUTHOR]

In order to resolve the issues of low efficiency and poor precision in the traditional finishing process of hardened internal gears, a method is proposed for calculating the profile curves of a drum-shaped grinding tool suitable for mass finishing of hardened internal gears. Additionally, the impact of drum-shaped grinding tool installation errors on the tooth surface deviation of internal gears is analyzed. Firstly, the processing principle for the generation grinding of internal gears by the drum-shaped grinding tool is introduced. Based on differential geometry, meshing theory, and two-degree-of-freedom enveloping method, a mathematical model is developed for the generation grinding of internal gears. Profile curves of the drum-shaped grinding tool are obtained by solving the meshing equation between the drum-shaped grinding tool and the internal gear. Then, the tooth surface equation for the internal gear is derived in the presence of drum-shaped grinding tool installation errors. By discretizing the error tooth surface of the internal gear, the average normal deviation of the tooth surface is calculated. In the end, the distribution of normal deviation on the tooth surface of the internal gear with different drum-shaped grinding tool installation errors is acquired, and the influence of four kinds of installation errors on the tooth surface of the internal gear is analyzed. The sensitive direction is identified for drum-shaped grinding tool installation errors on the tooth surface of the internal gear. Consequently, this research provides a calculation method for the drum-shaped grinding tool fit for high-precision and high-efficiency finishing of mass-produced hardened internal gear and offers a reference for correcting deviation in the tooth surface of internal gear with installation errors of the drum-shaped grinding tool. [ABSTRACT FROM AUTHOR]

To achieve high precision and repeatability of prototyped models, work is carried out to improve existing solutions and thus expand the areas of application of 3D printers. Ways to increase the efficiency of 3D printing are being sought. The subject of the work concerns the analysis of dimensional and shape accuracy and repeatability of samples produced by a technology based on layered extrusion of thermoplastic polymers using FFF—fused filament fabrication technology. The key parameter for assessing the quality of parts is the property most expected by 3D printer users regarding the accuracy of dimensions of manufactured prototypes. As part of the research, conclusions were drawn regarding the precision of the samples as original patterns. The dimensional accuracy in the x, y, and z axes of the 3D printer was determined in terms of the design of the 3D printer's actuator system. Three-dimensional maps of deviations of the pattern surface were used in relation to the nominal 3D CAD model to test the accuracy. The analytical results obtained during the research work, together with the graphs of the normal distribution probability function, indicate a high repeatability for each of the axes, and the highest repeatability was for the z-axis. The dimensions in the remaining axes were within the assumed tolerance of 0.1 mm, except for the two extreme dimensions, which were caused by a different method of heat dissipation, proving the influence of the arrangement of samples on the working platform. [ABSTRACT FROM AUTHOR]

In bridges, monitoring data usually correspond to normal operational and environmental conditions, resulting in a lack of damage-related data. For this reason, machine learning algorithms for damage detection are typically unsupervised. Conversely, numerical models are employable as surrogates for extreme events rarely encountered during the existence of a bridge and for common damage scenarios, enabling the training of supervised machine learning algorithms. In this paper, hybrid data obtained by integrating monitoring and numerical observations from the Z-24 Bridge benchmark are used for training supervised machine learning algorithms to classify damage. Special attention is dedicated to the numerical model that, while being simple enough to be used on thousands of runs, must capture the complex nonlinear behavior that typifies damaged conditions. A model updating technique is used for the preliminary calibration of the finite-element model. Numerical data are generated in a probabilistic manner starting from the initial finite-element model, assuming the Gaussian distribution of the uncertain parameters. Three undamaged scenarios and three damaged scenarios are modeled. Subsequently, several supervised learning classifiers are trained with the same hybrid database and a comparative summary of their effectiveness is presented. The paper introduces a novel soft classification method that accounts for the overlapping of observations belonging to different structural conditions in the feature space. This study proves that data generated from probabilistic-based finite-element models can be used for structural health monitoring and damage identification in the context of bridges, therefore providing a hybrid supervised approach that can be easily applied in practice. Practical Applications: Because bridges are one-of-a-kind, expensive structures, considerable efforts are made to ensure they remain in service for as long as possible. Consequently, monitoring systems are being installed on more and more bridges. However, monitoring data are usually related to healthy states of the structure rather than damage occurrences. Therefore, digital replicas can be employed to simulate damage scenarios that may occur in the lifespan of a bridge. Hybrid data can be obtained by blending monitoring data with simulated data from the same bridge. This paper illustrates the construction of such a hybrid database, which covers a wide range of possible scenarios for a well-known bridge benchmark. This hybrid database is then used to train machine learning algorithms to distinguish between various changes in the dynamic behavior of the bridge as a way to evaluate the condition of the structure and identify damage. In practice, the hybrid approach can be implemented on monitored bridges to raise flags when flaws are detected, to localize and evaluate the severity of damage, and even to make a prognosis on the remaining life of the bridge. [ABSTRACT FROM AUTHOR]

In sandy cobble stratum, the contents of rock blocks along the tunnel line present to be different. The tunneling-induced ground deformation under different rock contents is perceived as a main concern. Considering the heterogeneity of ground material, the meso-scale numerical models of sandy cobble strata were used to simulate tunnel excavation, in which the rock blocks and soil matrix were treated as separated constituents. By comparing the ground stress of simulation results with that of theoretical values, the applicability of meso-scale models was verified. The simulation results show that the rock content has a significant effect on the ground deformation performance. With the increase of rock content from 0 to 50%, the maximum ground settlement and the expansion of plastic zone gradually decreases, and the variation rule of the maximum ground settlement with rock content can be described by a normal distribution function. Meanwhile, the tunnel deformation pattern changes from non-uniform convergence to uniform convergence. It is also found that the relationship between the maximum subsurface settlement or the width coefficient of subsurface settlement trough and subsurface depth can be described by a power function, respectively. [ABSTRACT FROM AUTHOR]

The high temperature generated by the DC pantograph-catenary arc of urban rail systems will aggravate the wear of the pantograph-catenary system. When the ablation intensifies, it will lead to disconnection accidents on the contact line. In this paper, through the establishment of a pantograph-catenary arc model and contact line arc ablation model, considering the flow of the molten pool, it is reported that the temperature distribution of the pantograph-catenary arc is axisymmetric. With the increase in the arcing time, the maximum temperature of the arc increases. The heat flux density of the arc injection contact line presents a Gaussian distribution and is positively correlated with the arcing time. The high-temperature area of the contact line and the distribution of the molten pool show an approximate arc shape. The velocity of the molten pool shows a symmetrical distribution about the center of the electrode. The area, depth, and radius of the molten pool of the contact line increase with an increase in the arcing time, and the radius of the molten pool is always greater than the depth of the molten pool. The work presented in this paper is helpful to further our understanding of the basic physical process of pantograph-catenary arc ablation of contact lines. [ABSTRACT FROM AUTHOR]

In hazard-sensitive processes, the monitoring upsets and malfunctions correctly is an important challenge to operation safely and enhance the performance. Conventional process monitoring frequently assumes that process data follow only one Gaussian distribution, which generates a constant confidence limit and hence produces a high number of false alarms. However, in fact, industrial processes usually include various operating modes. To ovoid this drawback, the suggested approach employs an adaptive confidence limit (ACL) when a substantial number of false alarms are created. The fundamental concept underlying this study is to extract internally several local linear sub-modes of the monitored variables. In typical operating circumstances, the Gaussian mixture model (GMM) is utilized to extract several local linear sub-modes, followed by fuzzy linearization using the Takagi-Sugeno model, thereafter a bank of Luenberger observers to construct the residual spaces. An abnormal event is detected when the squared prediction error (SPE) is too great or exceeds the adaptive threshold designed to prevent the false alarms. Furthermore, an enhanced contribution plots is effectively used to identify the defective variable. [ABSTRACT FROM AUTHOR]

Copyright of Arab Journal for Scientific Publishing is the property of Research & Development of Human Recourses Center (REMAH) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent studies of many-body localization in nonintegrable quantum systems, the distribution of the ratio of two consecutive energy level spacings, |$r_n=(E_{n+1}-E_n)/(E_{n}-E_{n-1})$| or |$\tilde{r}_n=\min (r_n,r_n^{-1})$|⁠ , has been used as a measure to quantify the chaoticity, alternative to the more conventional distribution of the level spacings, |$s_n=\bar{\rho }(E_n)(E_{n+1}-E_n)$|⁠ , as the former makes unnecessary the unfolding required for the latter. Based on our previous work on the Tracy–Widom approach to the Jánossy densities, we present analytic expressions for the joint probability distribution of two consecutive eigenvalue spacings and the distribution of their ratio for the Gaussian unitary ensemble (GUE) of random Hermitian |$N\times N$| matrices at |$N\rightarrow \infty$|⁠ , in terms of a system of differential equations. As a showcase of the efficacy of our results for characterizing an approach to quantum chaoticity, we contrast them to arguably the most ideal of all quantum-chaotic spectra: the zeroes of the Riemann |$\zeta$| function on the critical line at increasing heights. [ABSTRACT FROM AUTHOR]

Distributed state estimation is one of the critical technologies in the field of target tracking, where the process noise and measurement noise may have a heavy-tailed distribution. Traditionally, heavy-tailed distributions like the student-t distribution are employed, but our observation reveals that Gaussian noise predominates in many instances, with occasional outliers. This sporadic reliance on heavy-tailed distributions can degrade performances or necessitate frequent parameter adjustments. To overcome this, we introduce a novel distributed consensus multi-distribution state estimation method that combines Gaussian and student-t filters. Our approach establishes a system model using both Gaussian and student-t distributions. We derive a multi-distribution filter for a single sensor, assigning probabilities to Gaussian and student-t noise models. Parallel estimation under both distributions, utilizing Gaussian and student-t filters, allows us to calculate the likelihood of each distribution. The fusion of these results yields a mixed-state estimation and corresponding error matrix. Recognizing the increasing degrees of freedom in the student-t distribution over time, we provide an effective approximation. An information consensus strategy for multi-distribution filters is introduced, achieving global estimation through consensus on fused local filter results via interaction with neighboring nodes. This methodology is extended to the distributed case, and the recursive process of the distributed multi-distribution consensus state estimation method is presented. Simulation results demonstrate that the estimation accuracy of the proposed algorithm improved by at least 20% compared to that of the traditional algorithm in scenarios involving both Gaussian and heavy-tailed distributions. [ABSTRACT FROM AUTHOR]

Anti-sliding stability safety is a critical issue that must be given sufficient and widespread attention during the entire lifecycle of gravity dams. The calculated anti-sliding stability safety factor (ASS-SF) is usually compared with the allowable value required by the standards in the traditional method, which ignores the influence of material parameter uncertainties and leads to unreasonable safety evaluation results. Therefore, the nonlinear functional relationship between the stability safety factor (SF) and the random variable parameters is constructed based on the response surface equations, and the distribution types of SF sequences calculated by the Monte Carlo sampling are determined, then a probabilistic stability evaluation method for concrete gravity dams is proposed. Engineering application shows that the calculated SF obeys the normal distribution; the minimum guaranteed rate of different sliding paths in a gravity dam is 86.66%, and the guaranteed rate for the overload safety factor (OSF) is 36.00%. The results imply that a guaranteed rate for the allowable value of the ASS-SF should be provided when making the stability safety evaluation of the dams, especially the OSF. The outcome of this research will advance the understanding of stability evaluation of concrete dams, and reduce the potential risk of sliding instability of concrete dams. [ABSTRACT FROM AUTHOR]

Developing new features for time-series characterization is a current challenge in data science and machine learning. In this paper, we propose a new metric based on a simple and efficient algorithm, namely, the return map. The return map analysis is well established in the field of non-linear dynamics, in particular, for fitting the parameters of a chaotic system from a waveform, or to attack a chaotic communication channel. We show that our metrics work well for both non-linear dynamics and time-series feature extraction problems in the field of machine learning. In an experiment aiming to classify vibration signals of normal and damaged bearings, we compare our method with two other methods that reported to have excellent accuracy, based on entropy and statistical feature distribution, respectively. We show that our method achieves higher accuracy with almost the lowest time costs, which was confirmed in experiments with two different datasets containing three main classes of bearings: normal, with inner race faults, and with outer race faults, having different damage origins and recorded in various conditions. In particular, for the dataset supplied by Case Western Reserve University, our method reached an accuracy of 100% at signals of 5000 sample points length, with a total time of 0.4 s required for feature estimation, while the entropy-based method reached an accuracy of 95% with a time of 100 s, and a statistical feature distribution method reached an accuracy of 93% with a total time of 1.9 s. Results show that the developed method is better suited to real-time bearing condition monitoring applications than most of the methods reported to date. [ABSTRACT FROM AUTHOR]

The rudder surfaces and lifting surfaces of a missile are utilized to acquire aerodynamic forces and moments, adjust the missile's attitude, and achieve precise strike missions. However, the harsh flying conditions of missiles make the rudder surfaces and lifting surfaces susceptible to faults. In practical scenarios, there is often a scarcity of fault data, and sometimes, it is even difficult to obtain such data. Currently, data-driven fault detection and localization methods heavily rely on fault data, posing challenges for their applicability. To address this issue, this paper proposes an HBOS (Histogram-Based Outlier Score) online fault-detection method based on statistical distribution. This method generates a fault-detection model by fitting the probability distribution of normal data and incorporates an adaptive threshold to achieve real-time fault detection. Furthermore, this paper abstracts the interrelationships between the missile's flight states and the propagation mechanism of faults into a hierarchical directed graph model. By utilizing bilateral adaptive thresholds, it captures the first fault features of each sub-node and determines the fault propagation effectiveness of each layer node based on the compatibility path principle, thus establishing a fault inference and localization model. The results of semi-physical simulation experiments demonstrate that the proposed algorithm is independent of fault data and exhibits high real-time performance. In multiple sets of simulated tests with randomly parameterized deviations, the fault-detection accuracy exceeds 98% with a false-alarm rate of no more than 0.31%. The fault-localization algorithm achieves an accuracy rate of no less than 97.91%. [ABSTRACT FROM AUTHOR]

This study presents an improved comprehensive atomization model for a pressure swirl atomizer. The model integrates internal flow predictions, linear instability analysis of a swirling annular liquid sheet, primary atomization sub-model, and droplet velocity sub-model. Measurement data combined with the inviscid theory model predict the internal flow, providing liquid sheet velocity and thickness at the atomizer outlet. The dispersion relation of surface disturbances is obtained through linear instability analysis. A primary breakup predictive model for particle size distribution is constructed based on the wavelength and growth rate within the full unstable wavenumber range of the dispersion relation. Assuming uniform circumferential distribution and a normal distribution of spray angles, the droplet velocity is assigned according to the liquid sheet velocity. The model is implemented into Eulerian–Lagrangian simulations as initial conditions for discrete phase droplets to simulate the spray field. Results show the model can accurately predict the Sauter mean diameter with an error of less than 6% and effectively predicts the spray structure and spray cone angle. The dependency of the model on its parameters is also studied, determining that the values of the ligament constant and dispersion angle have an obvious impact on the prediction of Sauter mean diameter and spray structure. [ABSTRACT FROM AUTHOR]

Despite recent advances in image enhancement, it is difficult to strike a balance between improving contrast and brightness in all types of images. This paper proposes a new approach that effectively implements 2D histogram modification and utilizes evolutionary algorithms to optimize parameters to overcome this issue. The proposed method exploits the 2D histogram of the improved image in close proximity to the input image histogram and the Gaussian distribution simultaneously. Also, the parameters of the Gaussian distribution and the weighting factors are changed with the help of an optimization algorithm. In the proposed method, the krill herd algorithm initially generates two sets of optimum parameters. Next, these parameter sets are used to create two enhanced images, one with high contrast and the other with high brightness. Then, using local information, the scale for each image is estimated, and the two improved images are combined to make a new image with balanced contrast and brightness. The performance of the proposed algorithm is compared by several algorithms based on both the quality of contrast and brightness. Simulation results indicated that the proposed algorithm outperformed other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

A special-topics undergraduate course about the history of statistics which was taught in Spring 2023 at the University of South Carolina is described. We review other similar courses (past and current) and explain the discussion-based nature of this course. The conception and planning of the course are detailed, and the unique experiences (activities, guest speakers, presentations, etc.) are described. The course emphasized substantial amounts of independent reading outside of class and lively discussions during class. Topics covered in the class include the early development of probability, the normal distribution, and the central limit theorem; the development of modern statistical science by British statisticians; the rise of formal mathematical statistics; and increasing specialization and modern computational and data-analytic advances. An assessment of the course's effectiveness based on qualitative student survey data is given. Students were highly complimentary of the course, praising the in-class discussion format, the benefits of doing the outside readings, the invited guest speakers, and the in-class activities. There were occasional comments that the amount of required reading was excessive. Based on this, suggestions for future offerings of the course are presented, including developing a more carefully curated set of readings. [ABSTRACT FROM AUTHOR]

The current research aims to test the relationship and effect of sustainable leadership its dimensions (cohesive diversity, organizational justice, employee development, progress and advancement, and work-life balance) as independent variables on entrepreneurial performance with its dimensions (creativity and innovation, reputation, proactiveness, self-evaluation) as dependent variables in the Ministry of Science and Technology. Additionally, the study seeks to identify the levels of availability and utilization of sustainable leadership that are more suitable for the current conditions in the ministry. The research aims to provide a set of recommendations contributing to the enhancement of the practice and adoption of the variables within the researched organization. Adopting a descriptive-analytical approach, the research collected data from 172 respondents representing various positions within the ministry (general manager, assistant general manager, center manager, department manager and section head). The data collection methods included a questionnaire with 48 items, supplemented by personal interviews and field observations as supporting tools. The researcher utilized statistical programs (Excel, SPSS V.28), employing appropriate statistical methods such as normal distribution tests, factor analysis, exploratory and confirmatory analysis, mean, percentage, standard deviation, and relative importance to test the hypotheses. The results indicate that the Ministry of Science and Technology has embraced sustainable leadership practices, demonstrating its inclination toward adopting its dimensions, including organizational justice, cohesive diversity, employee development, progress and advancement, and quality of work life, leading to an improvement in its entrepreneurial performance. يهدف البحث الحالي الى التخمك من تاثير القيادة المستدامة بأبعادها (التنوع المتماسك، العدالة التنظيمية، طوير الموظفين، التقدو والتطوس، توازن الحياة والعمم) كمتغير مستقم مع الاداء الريادي بأبعاده (الابداع والتجديد، السمعة، الاستباقية، التقييم الذاتي) كمتغير مستجيب، في وزاره العلوم والتكنولوجيا، تسعى الدراسة إلى التعرف على مستوياث توافر واستخدام القيادة المستدامة الأكثر ملاءمة ظظروف الحالية في الوزارة. وبتهدف البحث إلى تقديم مجموعة من التوصياث التي تساْم في تعضيض ممارسة وتبني المتغيراث داخم المنظمة المبحوثة، واَطالقا من اْمية موضوع البحث للمجتمع وللمنظمة المبحوثّ وافرادْا ، اعتمد المنهج الوصفي التحليلي في اَجاز البحث الحالي وجمعج البياَاث من (172) مستجيب تمثلج عينة البحث (مدير عام، معاون مدير عام، مدير قسم ، مسؤول شعبة) ، باعتماد الاستباَة التي تضمنج (48) فقرة ورفدْا Excel,) بالمقابلاث الشخصية، والمشاْداث الميداَية كأدواث مساعدة في تعضيضْا .وقد وظفج الباحثة البرامج الاحصائية مع اعتمادْا ابرز الاساليب الاحصائية الملائمة (اختبار التوزيع الطبيعي، والتحليم العاملي ،الاستكشافي (SPSS V.28 والتوكيدي، والوسط الحسابي، والنسب المئوية، والاَحراف المعياري، والاْمية النسبية، لاختبار فرضياتّ . وقد اظهرث ابرز النتائج ان وزارة العلوم والتكنولوجيا وضفج ممارساث القيادة المستدامة ار تبين توجهها الى تبني ابعادْا وعلى التوالي (العدالة التنظيمية ،التنوع المتماسك ،تطوير الموظفين، التوجّ والتقدم ، توازن الحياة والعمم) في تحسن ادائها الريادي. [ABSTRACT FROM AUTHOR]

The objective of this paper is to assess the distribution of the Partial Autocorrelation Function (PACF), both theoretically and empirically, emphasizing its crucial role in modeling and forecasting time series data. Additionally, it evaluates the deviation of the sum of sample PACF from normality: identifying the lag at which departure occurs. Our investigation reveals that the sum of the sample PACF, and consequently its components, diverges from the expected normal distribution beyond a certain lag. This observation challenges conventional assumptions in time series modeling and forecasting, indicating a necessity for reassessment of existing methodologies. Through our analysis, we illustrate the practical implications of our findings using real-world scenarios, highlighting their significance in unraveling complex data patterns. This study delves into 185 years of monthly Bank of England Rate data, utilizing this extensive dataset to conduct an empirical analysis. Furthermore, our research paves the way for future exploration, offering insights into the complexities and potential revisions in time series analysis, modeling, and forecasting. [ABSTRACT FROM AUTHOR]

The aim is to compare the resistance to torsion between 2 implant systems with internal hexagon connection: one using screw-retained abutments (Titanium Fix) and the other using cementable abutments (ITEC) under a tangential load. An in vitro experimental study was carried out. Fourteen implants, 7 implants from each system, were included in this study. The implants were placed at a 45° angle into metal blocks to simulate their position in the maxilla. Then, implants were subjected to a resistance test on a CMT5L universal testing machine, and the maximum load was applied to each sample. The maximum force with which the torsion was achieved in each sample was analyzed. The data were tested using the Shapiro-Wilk test and showed normal distribution. Student t test was used to examine statistical significance between the two groups, and the P value was set at P <.05. There was a statistically significant difference between the two groups (P =.001). ITEC implants with a cementable abutment showed greater flexural strength compared to the Titanium Fix with a screwed abutment implant system. The cemented abutment showed more resistance to torsion against a tangential load compared with the screwed abutment. [ABSTRACT FROM AUTHOR]

Copyright of Computer Measurement & Control is the property of Magazine Agency of Computer Measurement & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Meteorological satellite data have been extensively utilized in global numerical weather prediction systems and have a positive impact to improve forecast accuracy. In order to correctly assimilate satellite radiance observations in data assimilation systems, the systematic observation biases must be corrected to conform to a Gaussian normal distribution with a mean of 0. By selecting appropriate air-mass predictors through correlation assessment, a two-step bias correction scheme (namely the scan-angle bias correction and the air-mass bias correction) is established in this paper based on radiation observations of FY-3E/ HIRAS-II from 1 to 31 January 2023. The results indicate that FY-3E/HIRAS-II O-B (observation-simulation) bias exhibits scanning angle bias dependence from nadir to limb field of view. Statistics have found that this scanning angle bias does not depend on latitude band. After scan-angle bias correction using statistical scan-angle correction coefficients, the dependence of the O-B biases on the scan angle can be eliminated. The second step is to perform air-mass correction. Our correction scheme is compared with the air-mass bias correction scheme in NCEP-GSI. Although the scan angle influence is also considered in NECP-GSI scheme, it does not account for the water vapor effect in the atmosphere. Consequently, the correction effect is not good for channels with lower peak height of weighting function, resulting in a slightly residual positive bias after correction. The combination of air-mass predictors (model surface skin temperature, model total column water vapor, thickness of 1000–300 hPa, and thickness of 200–50 hPa) selected through importance assessment in this study effectively eliminates the air-mass biases. The systematic biases between observed brightness temperature and background simulated brightness temperature from background atmospheric field for all HIRAS-II channels significantly decrease after bias correction, and the bias distribution essentially follows a Gaussian normal distribution with a mean of 0. The bias correction scheme has a significant improvement for the analysis at upper air and near surface. [ABSTRACT FROM AUTHOR]

Incorporating various elements into host shape memory alloys (SMAs) has proven to be an effective strategy for optimizing their functional properties. However, modeling the complex multi-doping effect is challenging. In the present study, we introduced a phenomenological model based on Ginzburg–Landau theory, wherein each doping element is conceptualized as an internal dilatational stress. This internal stress is represented as a spatial Gaussian distribution characterized by two influential parameters: potency (h) and range (σ). The interaction between doping elements arises from the superposition of these stresses. Utilizing a time-dependent Ginzburg–Landau simulation based on our proposed model, diverse combinations of h and σ replicate the varied experimental outcomes associated with multi-doping effects. This model offers insight into the understanding of the doping impact on martensitic transformation and may contribute to the development of SMAs with tailored properties. [ABSTRACT FROM AUTHOR]

In the era of personalized medicine, there is an increasing interest in the identification of patients who may benefit from or be sensitive to a specific type of treatment. Recently a threshold linear mixed model was proposed to identify treatment-sensitive subgroups based on a continuous covariate when longitudinal measurements are the outcomes of the study. This model assumes, however, a normal distribution for these measurements. In some studies, the longitudinal measurements are restricted in an interval and subject to floor and ceiling effects caused by a portion of subjects with measurements on the boundaries of the interval, which would violate the normality assumption. In this paper, a threshold mixed-effects Tobit model is introduced to overcome this problem. The proposed models and inference procedures are assessed through simulation studies, as well as an application to the analysis of data from a randomized clinical trial. [ABSTRACT FROM AUTHOR]

We investigate multitype subcritical Markov branching processes with immigration driven by Poisson random measures. Limiting distributions are established for various rates of the Poisson measures when they are asymptotically equivalent to exponential or regularly varying functions. Results analogous to a strong LLN are proved, and limiting normal distributions are obtained when the local intensity of the Poisson measure increases with time. When it decreases, conditional limiting distributions are established. When the intensity converges to a constant, a stationary limiting distribution is obtained. The asymptotic behavior of the first and second moments of the processes is also investigated. [ABSTRACT FROM AUTHOR]

In 1733, de Moivre, investigating the limit distribution of the binomial distribution, was the first to discover the existence of the normal distribution and the central limit theorem (CLT). In this review article, we briefly recall the history of classical CLT and martingale CLT, and introduce new directions of CLT, namely Peng's nonlinear CLT and Chen–Epstein's nonlinear CLT, as well as Chen–Epstein's nonlinear normal distribution function. [ABSTRACT FROM AUTHOR]