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We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on R Λ N , Λ N = [ - N , N ] d ∩ Z d with Hamiltonian H N (ϕ) = 1 4 d ∑ x ∼ y (ϕ (x) - ϕ (y)) 2 - ∑ x ∈ Λ N η (x) ϕ (x) and 0-boundary conditions. { η (x) } x ∈ Z d is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable η (x) when d ≥ 5 . In particular, we identify the leading order asymptotics of the maximum. [ABSTRACT FROM AUTHOR]

We propose a new, data-driven approach for efficient pricing of – fixed- and floating-strike – discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this article constitutes an extension of Perotti and Grzelak [Fast sampling from time-integrated bridges using deep learning, J. Comput. Math. Data Sci. 5 (2022)], where the problem of sampling from time-integrated stochastic bridges was addressed. The model relies on the Seven-League scheme [S. Liu et al. The seven-league scheme: Deep learning for large time step Monte Carlo simulations of stochastic differential equations, Risks 10 (2022), p. 47], where artificial neural networks are employed to 'learn' the distribution of the random variable of interest utilizing stochastic collocation points [L.A. Grzelak et al. The stochastic collocation Monte Carlo sampler: Highly efficient sampling from expensive distributions, Quant. Finance 19 (2019), pp. 339–356]. The method results in a robust procedure for Monte Carlo pricing. Furthermore, semi-analytic formulae for option pricing are provided in a simplified, yet general, framework. The model guarantees high accuracy and a reduction of the computational time up to thousands of times compared to classical Monte Carlo pricing schemes. [ABSTRACT FROM AUTHOR]

We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show how this coefficient allows identifying pairs of variables that have partially uncorrelated tails given some other variables in a random vector. Unlike other recently introduced conditional independence frameworks for extremes, our approach requires minimal modeling assumptions and can thus be used in exploratory analyses to learn the structure of extremal graphical models. Similarly to traditional Gaussian graphical models where edges correspond to the nonzero entries of the precision matrix, we can exploit classical inference methods for high-dimensional data, such as the graphical Lasso with Laplacian spectral constraints, to efficiently learn the extremal network structure via the PTCC. We apply our new method to study extreme risk networks in two different datasets (extreme river discharges and historical global currency exchange data) and show that we can extract interesting extremal structures with meaningful domain-specific interpretations. [ABSTRACT FROM AUTHOR]

Reliability analysis of the complex structural system is a popular issue due to complex failure regions and frequently time-consuming simulations. In this work, a new method based on the active learning Kriging model is proposed to solve the problem with both random and interval hybrid uncertainty. The proposed method divides the original variable space based on the proposed adaptive important exploration region (AIER), which approximates only the bounds of the failure domain. In each iteration, the proposed approach selects the optimal training point from the AIER by utilizing a predicted sign error function related to the system indicator function, which can effectively measure the uncertainty of the complex system. Subsequently, the error estimation of the failure probability is used as the convergence criterion to ensure the accuracy and efficiency of reliability analysis. Afterward, the performance of the proposed method is evaluated by investigating four examples, which show the reasonability and superiority of this method. Finally, the multibody dynamics simulation of the flap mechanism is presented, which involves the aerodynamic load analysis and the simulation modeling. Considering the two failure modes of stuck and insufficient accuracy, it is shown that the proposed method greatly reduces the number of calls for the simulation model and ensures the accuracy of the evaluation during the reliability analysis of the flap mechanism. [ABSTRACT FROM AUTHOR]

AbstractThis article is concerned with the local linear non parametric regression estimator of a right censored scalar response random variable, given a functional random covariate. First, we investigate its asymptotic normality under the concentration properties of small ball probability functions. Then, we apply the results to present the asymptotic (1−α) confidence interval of the regression function for 0<α<1. To lend further support to our theoretical results, we carry out a simulation study to illustrate the performance and the asymptotic Gaussian behavior of our estimator. Finally, an application to real data is provided. [ABSTRACT FROM AUTHOR]

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed. [ABSTRACT FROM AUTHOR]

The importance of (probability) distributions in engineering science is undeniable. They are extensively used in this sector to carry out statistical studies and draw conclusions. In this article, we construct a new trigonometric distribution with support [ 0 , 1 ] called the truncated inverted arctan power (TIAP) distribution and demonstrate its use with engineering data. The corresponding probability density function is particularly flexible in the sense that it has various decreased right-skewness and unimodal forms. The associated hazard rate function shows that the TIAP distribution may adapt data with monotonic, U-shaped, and N-shaped failure rates. To reflect the interdependence of two random variables or sets of data, a bivariate variant of the TIAP distribution is also elaborated. All these distributional tools are then applied from a statistical perspective. In particular, the involved parameters are estimated using a maximum likelihood technique. Applications to engineering data indicate that the univariate and bivariate extensions for the TIAP distribution have a better fit compared to various current distributions. [ABSTRACT FROM AUTHOR]

Defining a probability model suitable for analyzing intricate and skewed real datasets holds significant importance in statistics. Here In this study, a novel class of models using the maximum of independent identical generalized Rayleigh random variables with the number of variables that have a power series class of distributions is proposed. This novel family of distributions contain several sub-models, including Poisson-generalized Rayleigh, geometric-generalized Rayleigh, binomial-generalized Rayleigh, and logarithmic-generalized Rayleigh models. The so obtained model can be unimodal and positively skewed, and it can be applied in modeling asymmetric data. We provide numerous distributional and statistical properties of this new family of distribution, notably, probability density, cumulative function, hazard rate function, k -moment, mean, variance, and quantile function. Different techniques consider the estimation of model parameters, likely maximum likelihood estimators, Expectation–Maximization (EM) and its Modified techniques, and extensive Monte Carlo (MC) simulation studies have been employed to see the efficiency of the suggested estimation techniques. At the end, three real data sets are analyzed for illustrative purposes. The results underscore the superior performance of the proposed Geom-GR model compared to its competitors, showcasing its effectiveness in accurately representing the analyzed datasets. [ABSTRACT FROM AUTHOR]

The paper suggests a hybrid numerical method to price barrier options under Levy processes. As the main ingredient of our approach, we model the values of the Wiener-Hopf factors using artificial neural networks in the exact formula for the solution. The numerical Wiener-Hopf factorization typically reduces the problem to the factorization of the polynomial of exp(iξ), which is interpreted as the characteristic function of the random variable that approximates the Lévy process at the exponentially distributed time moment. We design and train a feedforward neural network with one hidden layer that approximates the coefficients of factors based on the input vector of the factorized polynomial coefficients. We implemented in the software a training data generator and a generalized loss function to factorize a polynomial of arbitrary degree. We demonstrate the performance of our approach using examples of factorization of second-, sixth- and 254th-degree polynomials. It takes a fraction of a second for our trained artificial neural networks to calculate the factors. [ABSTRACT FROM AUTHOR]

In this paper, a notion of non-microstate bi-free entropy with respect to completely positive maps is constructed thereby extending the notions of non-microstate bi-free entropy and free entropy with respect to a completely positive map. By extending the operator-valued bi-free structures to allow for more analytical arguments, a notion of conjugate variables is constructed using both moment and cumulant expressions. The notions of free Fisher information and entropy are then extended to this setting and used to show minima of the Fisher information and maxima of the non-microstate bi-free entropy at bi-R-diagonal elements. [ABSTRACT FROM AUTHOR]

Treated as one of the popular measures in information theory, fuzzy mutual information quantifies the amount of information that one random variable has about another one. Different from standard mutual information, fuzzy mutual information can deal with not only discrete-valued but also real-valued variables. Therefore, fuzzy mutual information has been recently used in evolutionary filter feature selection approaches to measure the correlation between the classes and the features, and the dependencies within a feature set. Typically, this way can be considered as computationally efficient but sometimes it may not contribute to the performance of a classification algorithm. To address this issue, an improved evolutionary wrapper-filter approach which integrates an initialisation scheme and a local search module based on fuzzy mutual information in differential evolution is proposed. According to a number of experiments conducted on several real-world benchmark datasets, the proposed approach does not only significantly improve the computational efficiency of an evolutionary computation technique but also the performance of a classification algorithm. [ABSTRACT FROM AUTHOR]

The geometric process has been widely studied in various disciplines and applied in reliability, maintenance and warranty cost analysis, among others. In its applications in maintenance policy optimisation, the geometric process assumes constant repair effectiveness by its process rate. Nevertheless, in practice, maintenance effectiveness may differ from time to time and can therefore be better depicted by a random variable. Motivated by this argument, this paper proposes a new variant of the geometric process, which is referred to as the rate randomized geometric process (RRGP). The probabilistic properties of the RRGP are then investigated. The maximum likelihood method is utilised to estimate the parameters of the RRGP. Numerical examples are given to show its applicability in both maintenance policy optimization and fitting real‐world failure datasets. [ABSTRACT FROM AUTHOR]

The CIR stochastic volatility model is modified to introduce nonlinear mean reversion, with the long-run volatility average as a random variable controlled by two parts being modeled through a Brownian motion and a Markov chain, respectively. This model still possesses an analytical formulation of the forward characteristic function, from which we establish variance swap prices as well as volatility swap ones with a nonlinear payoff in closed form. The numerical implementation of the two formulae demonstrates the significant impact of regime switching. [ABSTRACT FROM AUTHOR]

This research introduces min-max portfolio optimization models that incorporating transaction costs and focus on robust Entropic value-at-risk. This study offers a unified approach to handl the distribution of random parameters that affect the reward and risk aspects. Utilizing the duality theorem, the study transforms the optimization models into manageable forms, thereby accommodating the underlying random variables' discrete box and ellipsoidal distributions. The impact of transaction costs on optimal portfolio selection is examined through numerical examples under a robust return-risk framework. The results underscore the importance of the proposed model in safeguarding capital and reducing exposure to extreme risks, thus outperforming other strategies documented in the literature. This demonstrates the model's effectiveness in balancing maximizing returns and minimizing potential losses, making it a valuable tool for investors that seek to navigate uncertain financial markets. [ABSTRACT FROM AUTHOR]

In this research, we are examining the stochastic modified Korteweg-de Vries (SMKdV) equation forced in the Itô sense by multiplicative noise. We use an appropriate transformation to convert the SMKdV equation to another MKdV equation with random variable coefficients (MKdVRVCs). We use the generalizing Riccati equation mapping and Jacobi elliptic functions methods in order to acquire new trigonometric, hyperbolic, and rational solutions for MKdV-RVCs. After that, we can get the solutions to the SMKdV equation. To our knowledge, this is the first time we have assumed that the solution of the wave equation for the SMKdV equation is stochastic, since all earlier research assumed that it was deterministic. Furthermore, we provide different graphic representations to show the influence of multiplicative noise on the exact solutions of the SMKdV equation. [ABSTRACT FROM AUTHOR]

A comparative analysis between Bidirectional Evolutionary Structural Optimization (BESO) and Smoothing-ESO (SESO), simultaneously considering Reliability-Based Topology Optimization (RBTO) and the structure's self-weight in the case of three-dimensional elasticity, is presented in this study. Due to the important role of the existence of uncertainties in making the structural design more realistic, geometry, volumetric fraction, modulus of elasticity, compliance, and loading are considered random variables with normal probability distribution. When adopting the First Order Reliability Method (FORM), the failure probability is calculated based on the reliability index. Furthermore, considering the influence of self-weight in problems involving large structures in civil engineering, especially in the case of bridges, this makes the optimal configuration more reliable for design. A series of examples are covered to validate the methods presented, showing their efficiency and robustness. [ABSTRACT FROM AUTHOR]

Distributed photovoltaic (PV) output exhibits strong stochasticity and weak adjustability. After being integrated with the network, its interaction with stochastic loads increases the difficulty of assessing the distribution network's static voltage stability (SVS). In response to this issue, this article presents a probabilistic assessment method for SVS in a distribution network with distributed PV that considers the bilateral uncertainties and correlations on the source and load sides. The probabilistic models for the uncertain variables are established, with the correlation between stochastic variables described using the Copula function. The three-point estimate method (3PEM) based on the Nataf transformation is used to generate correlated samples. Continuous power flow (CPF) calculations are then performed on these samples to obtain the system's critical voltage stability state. The distribution curves of critical voltage and load margin index (LMI) are fitted using Cornish-Fisher series. Finally, the utility function is introduced to establish the degree of risk of voltage instability under different scenarios, and the SVS assessment of the distribution network is completed. The IEEE 33-node distribution system is utilized to test the method presented, and the results across various scenarios highlight the method's effectiveness. [ABSTRACT FROM AUTHOR]

Fibre-reinforced polymer (FRP) reinforcement has been employed as an alternative to conventional steel reinforcement in concrete structures, which is attributed to its excellent strength and corrosion resistance. However, one drawback is that FRP reinforcements are brittle and affect the ductility of concrete structures. One of the recent effective techniques proposed to overcome ductility issues is the compression yielding (CY) concept. The CY mechanism allows the structure to fail differently than the conventional FRP-reinforced concrete structure. Thus, the existing design recommendations as per the current codes for FRP-reinforced concrete structures are not appropriate. Hence, reliability studies are crucial for the development of a functional CY beam design in order to emphasise the structure's lifetime performance and to guarantee safety requirements. In this study, a reliability-based design approach is developed for a compression-yielded FRP-reinforced concrete beam (CY beam) using load and resistance factor design (LRFD). Firstly, the flexural failure modes of CY beams are discussed. The uncertainties involved in the development of the probabilistic model for the CY beam are defined. A case study is consequently conducted for a CY beam with random variables that are associated with the statistical characteristics of material properties and load. The reliability analysis method employed in this research is the Hasofer–Lind method. The results suggest the importance of choosing appropriate design variables and stochastic parameters for CY blocks that contribute to a higher level of reliability. The reliability index and resistance factors of a CY beam are then evaluated using the Monte Carlo Simulation computational method. The reliability index value of 3.336 is obtained from the simulation, which indicates that the CY beam demonstrates ductile behaviour. The results not only demonstrate ductile behaviour but also contribute to a possible reduction in material costs and a substantial safety margin. When compared to conventional FRP-reinforced concrete beams, for different load ratios, CY beams showed higher resistance and better reliability levels. [ABSTRACT FROM AUTHOR]

We study the competition complexity of dynamic pricing relative to the optimal auction in the fundamental single-item setting. In prophet inequality terminology, we compare the expected reward Am(F) achievable by the optimal online policy on m independent and identically distributed (i.i.d.) random variables distributed according to F to the expected maximum Mn(F) of n i.i.d. draws from F. We ask how big m has to be to ensure that (1+ε)Am(F)≥Mn(F) for all F. We resolve this question and characterize the competition complexity as a function of ε. When ε=0 , the competition complexity is unbounded. That is, for any n and m there is a distribution F such that Am(F)0 , it is sufficient and necessary to have m=ϕ(ε)n , where ϕ(ε)=Θ(log log 1/ε). Therefore, the competition complexity not only drops from unbounded to linear, it is actually linear with a very small constant. The technical core of our analysis is a lossless reduction to an infinite dimensional and nonlinear optimization problem that we solve optimally. A corollary of this reduction is a novel proof of the factor ≈0.745 i.i.d. prophet inequality, which simultaneously establishes matching upper and lower bounds. Funding: This work was supported by ANID (Anillo ICMD) [Grant ACT210005] and the Center for Mathematical Modeling [Grant FB210005]. [ABSTRACT FROM AUTHOR]

The paper contains the comparative analysis of the efficiency of different qunatile estimators for various distributions. Additionally, we show strong consistency of different quantile estimators and we study the Bahadur representation for each of the quantile estimators, when the sample is taken from NA, φ , ρ ∗ , ρ -mixing population. [ABSTRACT FROM AUTHOR]

In this paper, strong consistency of tail value-at-risk (TVaR) estimator under widely orthant dependent (WOD) samples is established, and a numerical simulation is performed to verify the validity of the theoretical results. To reveal the essence of the result, theoretical discussion on complete and complete moment convergence corresponding to the Baum–Katz law, as well as the Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for maximal weighted sums and maximal product sums of widely orthant dependent (WOD) random variables are investigated. The results obtained in the context extend the corresponding ones for independent and some dependent random variables. [ABSTRACT FROM AUTHOR]

The Nash–Sutcliffe efficiency (NSE) is now the most widely used criterion for measuring the goodness of fit between the hydrological model simulation and corresponding observation. Because there is substantial sampling uncertainty regarding hydrological simulation and observation, the NSE is a random variable. A probability density function (PDF) of NSE variable was derived based on the assumption of the simple linear regression model between the observation and simulation from the hydrological model. To avoid a subjective interpretation of the hydrological model performance, the confidence interval of the NSE variable was determined by its PDF. Because the difference in NSE variables (Φ) between two time periods or two hydrological models is often used for comparing their performances and can also be taken as a random variable, hypothesis testing should be implemented to determine whether the difference is adequate or whether the difference is a chance variation. Because the PDF of the difference can be derived based on the joint PDF of the every NSE random variables, a procedure of the hypothesis testing for the difference between two NSE variables is then proposed for comparing the performances between the hydrological models or between different time periods for a hydrological model. The proposed hypothesis testing has been applied in the abcd and dynamic water balance model (DWBM) hydrological models as case studies to illustrate the procedure of assessing the performances of a hydrological model and justifying its superiority to another model according to both the estimated NSE value and its confidence level due to the sampling uncertainty. Therefore, the proposed hypothesis testing can provide hydrological model end-users with rational model assessment. [ABSTRACT FROM AUTHOR]

In this paper, we show that a sufficient and necessary condition for that the Hoeffding concentration inequality of Banach space-valued (B -valued, for simplicity) random variables holds is that the Banach space in question admits the Rademacher type p for some 1 ≤ p ≤ 2 ; which is equivalent to that the Bernstein concentration inequality holds for such B -valued random variables. This is done by applying a refined McDiarmid inequality (stated and proved in this paper) via the entropy method. This result is also applied to the density property of induced subgraphs of random Cayley graphs generated by a finite abelian group. [ABSTRACT FROM AUTHOR]

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. For the sums of independent random variables, we obtain the Fisher information bounds without requiring the finiteness of Poincaré constant. Our method can also be used to bound the Fisher information distance in non-central limit theorems. [ABSTRACT FROM AUTHOR]

Let f be a Gaussian random field on R d and let X be the number of critical points of f contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on f, the random variable X has finite moments. So far, this has been established only for moments of order lower than three. In this paper, we prove the conjecture. Precisely, we show that X has finite moment of order p, as soon as, at any given point, the Taylor polynomial of order p of f is non-degenerate. We present a simple and general approach that is not specific to critical points and we provide various applications. In particular, we show the finiteness of moments of the nodal volumes and the number of critical points of a large class of smooth, or holomorphic, Gaussian fields, including the Bargmann-Fock ensemble. [ABSTRACT FROM AUTHOR]

Due to the inherent random variations in the engineering properties of soils and rocks, considering probabilistic analysis rather than the deterministic one is a safer option for the design of geotechnical structures. However, the probabilistic methodologies often rely on prior knowledge of probability density function (PDF) of the considered random variables (RVs). In this study, a new formulation called the fourth-moment pseudo-normal transformation (FMNT) is employed to perform the probabilistic analysis of a tunnel support system. FMNT requires only the first four statistical moments of the random variables instead of complete information about their PDF to calculate the failure probability (Pf). Further, it is an efficient technique that is demonstrated by performing analytical as well as numerical probabilistic analysis of circular and noncircular tunnels using FLAC 3D. FMNT is used in two different ways to highlight its flexibility: (1) with the first-order reliability method (FORM) called FORM-based FMNT; and (2) with point estimated method (PEM) called PEM-based FMNT. The results of the latter align adequately with the results of Monte Carlo simulation (MCS) and the analysis requires only 21 and 26 simulations for four and five random variables, respectively, instead of 100,000 simulations required by the MCS. The compatibility of this framework in actual field settings is demonstrated through an exercise using the nonnormal random variables. Practical Applications: Soil and rocks possess inherent variability. This makes it hard for engineers and scientists to predict exactly how they will behave under different situations. Therefore, they use probabilistic methods that deal with this uncertainty. One common method is called Monte Carlo simulation (MCS). It is good at handling uncertainties and giving accurate results and that is why it is commonly used as a benchmark method for comparisons. But to use it, we need to know some information about the input parameters such as their distribution. This information is generally not available when dealing with field data. To solve this, we need a method that gives us results comparable to MCS but is also efficient enough to use in the field. This study presents a new probabilistic technique named fourth-moment pseudo-normal transformation (FMNT) to do this job. It is useful and easy for assessing the safety of geotechnical structures that are demonstrated by conducting a probabilistic analysis of tunnels in the present study. This method will help the field engineers plan and deal with uncertainties in a better way. [ABSTRACT FROM AUTHOR]

The study of stress-strength reliability estimation based on phase-type distribution helps to gather results on estimation of stress-strength reliability with any probability distribution that is defined on the non negative real numbers as any discrete or continuous probability distributions on the positive real line can be represented as phase-type. The matrix representation of the parameters of phase-type distributions helps in their flexible evaluation and easy manipulation. Also in many of the experimental studies, it is very convenient and useful to apply progressive type-II right censoring mechanism in the process of data collection. In this article, we consider the estimation of stress-strength reliability (R) based on phase-type distribution under progressive type-II right censoring mechanism. Both stress and strength random variables are assumed to follow either continuous phase-type or discrete phase-type distribution. We have developed the algorithm for computing Maximum likelihood estimate (MLE) of R based on the expectation maximization (EM) method and the Bayes estimate of R using Markov Chain Monte Carlo technique. A detailed numerical illustration using simulated data/ real data sets are carried out. [ABSTRACT FROM AUTHOR]

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

We study the rank of the adjacency matrix A$$ A $$ of a random Erdős‐Rényi graph G∼픾(n,p). It is well known that when p=(log(n)−ω(1))/n$$ p=\left(\log (n)-\omega (1)\right)/n $$, with high probability, A$$ A $$ is singular. We prove that when p=ω(1/n)$$ p=\omega \left(1/n\right) $$, with high probability, the corank of A$$ A $$ is equal to the number of isolated vertices remaining in G$$ G $$ after the Karp‐Sipser leaf‐removal process, which removes vertices of degree one and their unique neighbor. We prove a similar result for the random matrix B$$ B $$, where all entries are independent Bernoulli random variables with parameter p$$ p $$. Namely, we show that if H$$ H $$ is the bipartite graph with bi‐adjacency matrix B$$ B $$, then the corank of B$$ B $$ is with high probability equal to the max of the number of left isolated vertices and the number of right isolated vertices remaining after the Karp‐Sipser leaf‐removal process on H$$ H $$. Additionally, we show that with high probability, the k$$ k $$‐core of 픾(n,p) is full rank for any k≥3$$ k\ge 3 $$ and p=ω(1/n)$$ p=\omega \left(1/n\right) $$. This partially resolves a conjecture of Van Vu for p=ω(1/n)$$ p=\omega \left(1/n\right) $$. Finally, we give an application of the techniques in this paper to gradient coding, a problem in distributed computing. [ABSTRACT FROM AUTHOR]

In response to the issues of low solution efficiency, poor path planning quality, and limited search completeness in narrow passage environments associated with Rapidly-exploring Random Tree (RRT), this paper proposes a Grid-based Variable Probability Rapidly-exploring Random Tree algorithm (GVP-RRT) for narrow passages. The algorithm introduced in this paper preprocesses the map through gridization to extract features of different path regions. Subsequently, it employs random growth with variable probability density based on the features of path regions using various strategies based on grid, probability, and guidance to enhance the probability of growth in narrow passages, thereby improving the completeness of the algorithm. Finally, the planned route is subjected to path re-optimization based on the triangle inequality principle. The simulation results demonstrate that the planning success rate of GVP-RRT in complex narrow channels is increased by 11.5–69.5% compared with other comparative algorithms, the average planning time is reduced by more than 50%, and the GVP-RRT has a shorter average planning path length. [ABSTRACT FROM AUTHOR]

Hydrologic systems are characterized by processes which may occur on, below, and above the land surface. These processes are irreversible, and the irreversibility produces entropy. In thermodynamics, entropy is a measure of the loss of heat energy which is a reflection of disorder. The entropy of a system achieves its maximum at steady state, meaning that the maximum entropy production corresponds to the most probable state. In information theory, entropy is a measure of uncertainty or disorder or information imbued in the random variable describing the hydrologic system. The maximum uncertainty corresponds to maximum entropy or the most probable distribution of the variable which leads to the principle of maximum entropy or the principle of minimum cross entropy, subject to the given constraints. The most probable or maximum entropy-based distribution is confirmed by the theorem of concentration. The form of entropy (Shannon, Tsallis, Renyi, or Kapur), principle of maximum entropy, principle of minimum cross-entropy, and the concentration theorem constitute the theory of entropy. This paper presents a general framework based on the entropy theory, and demonstrates its application for modeling a number of surface and subsurface hydrologic and water quality processes, including hydrometric network evaluation, eco-index, surface runoff, infiltration, soil moisture, velocity distribution, sediment concentration, sediment discharge, sediment yield, channel cross section, rating curve, and debris flow. [ABSTRACT FROM AUTHOR]

A novel approach to the construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to generate a new random variable in the unit interval. This approach is demonstrated using some popular choices of positive random variables, such as the exponential, Lindley, and gamma. Some existing distributions, like the uniform, the beta, and the Kummer-beta, are formulated with this method. Several new structures of density functions having potential for future applications in real-life problems are also provided. One of the new distributions, namely the LCG, is considered for detailed study along with a related distribution, namely the GCL. The moments, hazard rate, cumulative distribution function, stress-strength reliability, random sample generation using the quantile function, method of moments along with maximum likelihood estimation, and regression modeling are discussed for both the distributions. Real-life applications of the proposed models and the corresponding regression models show promising results. [ABSTRACT FROM AUTHOR]

In this article, the complete convergence for the partial sum of the moving average process { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where { Y i , − ∞ < i < ∞ } is a sequence of extended negatively dependent and identically distributed random variables that is stochastically dominated by a random variable Y under a sub-linear expectation (Ω , H , E ̂) , and { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results of moving the average process under extended negatively dependent random variables from the traditional probability space to the sub-linear expectation space. [ABSTRACT FROM AUTHOR]

Recently developed inerter-based dampers have been installed at the base layer to reduce base displacement and simultaneously improve the superstructure's performance. However, in the existing research on optimizing damper parameters, the nonlinear property of base isolation is simplified and stochastic linearization technique is introduced to approximate such nonlinearity, which would inevitably introduce errors. In this paper, an improved method is proposed for stochastic optimization of electromagnetic inertial mass dampers (EIMD) in nonlinear hybrid isolation systems subject to seismic excitations. First, a stochastic seismic excitation is represented by one elementary random variable adopting the dimension-reduction spectral representation method. Then, statistical moments of nonlinear base-isolated structural responses are estimated using two-point estimation method (2PEM). Finally, the EIMD optimal parameters are obtained via the modified directional bat algorithm (MDBA) recently proposed by the authors through minimizing base layer response moments. This proposed improved method could fully consider the base isolation nonlinearity compared with the previous stochastic linearization technique. Moreover, the proposed stochastic optimization of the EIMD only requires two dynamic analyses to achieve its efficiency. A seven-story base-isolated frame building equipped with an EIMD is investigated in the numerical simulation, and results indicate that EIMD optimized by this proposed method obviously outperforms the results by the stochastic linearization technique and the conventional viscous damper (VD) in the base layer displacement reduction. [ABSTRACT FROM AUTHOR]

Performing reliability analysis for reinforced concrete structures is a tedious and challenging task because it requires conducting a four-nested loop calculation procedure involving millions of data samples to account for the complex behaviours of the structures and multiple random variables. Therefore, the study proposes a novel, practical, and accurate reliability framework that is applicable for multi-component RC frame structures exhibiting different behaviours ranging from linear elastic and non-linear elastic to non-linear plastic. For this purpose, this study first employs a tree-based boosting ensemble model combined with quantile regression, dubbed as QR-LightGBM to calculate the structures' limit state function and the associated uncertainty estimation at the same time. Next, an active learning process is implemented to improve the computed reliability results progressively. During each active learning step, relevant data samples with potentially high impacts on the model accuracy are determined based on their uncertainty, and then QR-LightGBM is retrained utilizing these samples. By doing so, the prediction performance of the surrogate model is enhanced with a minimized number of actual data samples, thus significantly reducing overall computational resources. The viability and effectiveness of the proposed framework are validated through three case studies involving a simple 1D reinforced concrete beam, a 2D three-story frame, and a 3D five-story building structure. Furthermore, its performance is quantitatively demonstrated via comparison studies with competing methods such as Monte Carlo simulation, Kriging-based models, and an original LightGBM without active learning. [ABSTRACT FROM AUTHOR]

Let X, Y be continuous random variables with unknown distributions. The aim of this paper is to study the problem of estimating the probability θ : = P (X < Y) based on independent random samples from the distributions of X ′ , Y ′ , ζ and η , where X ′ = X + ζ , Y ′ = Y + η and X, Y, ζ , η are mutually independent random variables. In this context, ζ , η are referred to as measurement errors. We apply the ridge-parameter regularization method to derive a nonparametric estimator for θ depending on two parameters. Our estimator is shown to be consistent with respect to mean squared error if the characteristic functions of ζ , η only vanish on Lebesgue measure zero sets. Under some further assumptions on the densities of X, Y, ζ and η , we obtain some upper and lower bounds on the convergence rate of the estimator. A numerical example is also given to illustrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

The benefits of less repetitive practice schedules on motor learning are usually described in terms of greater demand for memory processes. The present study aimed to investigate the interactions between working memory and practice schedule and their effects on motor learning. Forty female participants had their WMC evaluated by the N-back test and were randomly allocated to either the variable random (VP) or the constant practice (CP) groups. In the acquisition phase, participants practiced 120 trials of a sequential key-pressing task with two goals: learning the relative and the absolute timing. Delayed retention and transfer tests occurred 24 h after the acquisition phase. Participants performed 12 trials of the motor task. Results showed that in the CP, learners with a high level of WMC presented better motor performance in the transfer test than learners with a low level of WMC. In the RP, no difference between WMC levels was found. Learners with a high level of WMC in the CP presented the same motor performance as learners in the RP regardless of the WMC level in the transfer test. In conclusion, learners with a high WMC could compensate for the poor working memory stimulation of a more repetitive practice schedule. The high WMC did not seem to exert an additional benefit when learners were well stimulated by a less repetitive practice schedule. [ABSTRACT FROM AUTHOR]

For each \alpha \in (0, 1), we construct a bounded monotone deterministic sequence (c_k)_{k \geqslant 0} of real numbers so that the number of real roots of the random polynomial f_n(z) = \sum _{k=0}^n c_k \varepsilon _k z^k is n^{\alpha + o(1)} with probability tending to one as the degree n tends to infinity, where (\varepsilon _k) is a sequence of i.i.d. (real) random variables of finite mean satisfying a mild anti-concentration assumption. In particular, this includes the case when (\varepsilon _k) is a sequence of i.i.d. standard Gaussian or Rademacher random variables. This result confirms a conjecture of O. Nguyen from 2019. More generally, our main results also describe several statistical properties for the number of real roots of f_n, including the asymptotic behavior of the variance and a central limit theorem. [ABSTRACT FROM AUTHOR]

In the analysis of a train–bridge coupled system, fuzzy uncertainty is a factor that must be considered in the prediction of coupled vibration response, but it has not been considered so far. In this work, the concept of information entropy is used to unify the fuzzy uncertainty and random variables into the train–bridge coupled system, and the fuzzy random train–bridge coupled system is established. The fuzzy dynamic response of trains and bridges with fuzzy parameters of the bridge structures and the mass of the carriage were studied, and the mean and variance of the response quantities were calculated using the new point estimation method (NPEM). The combined effect of the fuzziness is considered and the fuzzy value of the system dynamics is obtained. The feasibility of applying this method to train–bridge problems was verified. The calculation results indicated that the maximum amplitude of the fuzzy vertical displacement of the bridge exceeded the conventional vertical displacement by 25.57%, and the maximum amplitude of the fuzzy vertical acceleration of the train exceeded the conventional vertical acceleration by 23.42%. Obviously, in this case, the traditional deterministic calculation method cannot comprehensively and accurately analyze the dynamic response of the train–bridge system. The method in this paper can provide theoretical guidance for evaluating the safety of bridge structures and running safety research in the future. [ABSTRACT FROM AUTHOR]

In this paper, a model with integration of interval programming (IP), chance-constrained programming (CCP), and fuzzy random variables (FRVs), termed as an inexact fuzzy random chance-constrained programming (IFRCCP) model, was proposed to deal with the fuzzy and random uncertainties in optimization of booster cost for a water distribution system (WDS) under uncertainty. The IFRCCP model was applied to a WDS to verify the efficiency of the method. After formulating the IFRCCP model, the booster cost intervals were obtained under various violation levels and confidence levels. The results indicated that the lower and upper booster costs increased with the confidence levels of the lower limits, and decreased with the violation levels of the lower limits. Moreover, the nodal chlorine concentrations are more uniform with the increase of booster numbers. The booster costs under trapezoidal distribution FRVs are greater than that under triangular distribution FRVs. Moreover, the uniformity of nodal chlorine concentration under triangular fuzzy distributions is larger than that under trapezoidal fuzzy distributions. The results obtained can help managers to make schemes on booster optimization under fuzzy and random uncertainties. [ABSTRACT FROM AUTHOR]

Suppose X 1 ,... , X n are independent survival exponentiated location-scale random variables, and I p 1 , ... , I p n are independent Bernoulli random variables, independently of Xi's, i = 1 , ... , n. Let Y i = I p i X i , for i = 1 , ... , n. Then, in actuarial context, Yi corresponds to the claim amount in a portfolio of heterogeneous risks. In this work, we compare the largest and smallest order statistics arising from two heterogeneous portfolios in the sense of usual stochastic order. The results obtained here are based on multivariate chain majorization with heterogeneity in different parameters, and generalize some of the results known in the literature. Some examples and counterexamples are also presented for illustrating the results established here. [ABSTRACT FROM AUTHOR]

In current researches on belief rule base (BRB), input parameters are tended to be expressed in the form of quantitative values through expert knowledge combined with optimization methods. A singular quantitative value fails to capture the statistical properties, leading to irrational outcomes. Therefore, an attempt on attribute weights is made in this paper, and a new model with probability distribution attribute weights (pdw) called BRB-pdw is proposed. The combination of two attributes is in detail discussed, where attribute weights are described as random variables with specific probability distribution. To characterize the output of probability distribution attribute weight, a new concept of expectation of activation weight is proposed. In addition, the BRB-pdw is extended to multiple attributes to demonstrate its universality. Furthermore, fundamental properties and characteristics of the BRB-pdw are further validated by rigorous mathematical derivation. Finally, practicability of the BRB-pdw is validated with NASA lithium battery open dataset, and experiments show that the BRB-pdw model is more robust while maintaining precision. [ABSTRACT FROM AUTHOR]

• Reliability-based non-probabilistic multiscale topology optimization (NRBMTO) with stress constrained is proposed. • The p-norm function aggregates global unit stresses. • Mechanical and thermo-mechanical loads are considered as non-probabilistic uncertain parameters. • Ellipsoid modeling describes uncertainty in non-probabilistic random variables. • NRBMTO results in more security than the traditional deterministic multiscale topology optimization (DMTO) approach. A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β =3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method. [ABSTRACT FROM AUTHOR]

Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications. This is all the more important when elements composed of brittle materials are exposed to dynamic environments, resulting in catastrophic fatigue failures. The authors propose the application of a non-intrusive polynomial chaos expansion method for probabilistic studies on brittle materials undergoing fatigue fracture when geometrical parameters and material properties are random independent variables. Understanding the probabilistic nature of fatigue fracture in brittle materials is crucial for ensuring the reliability and safety of engineering structures subjected to cyclic loading. Crack growth is modelled using a phase-field approach within a finite element framework. For modelling fatigue, fracture resistance is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function. Number of cycles to failure is treated as the dependent variable of interest and is estimated within acceptable limits due to the randomness in independent properties. Multiple 2D benchmark problems are solved to demonstrate the ability of this approach to predict the dependent variable responses with significantly fewer simulations than the Monte Carlo method. This proposed approach can accurately predict results typically obtained through 10 5 or more runs in Monte Carlo simulations with a reduction of up to three orders of magnitude in required runs. The independent random variables' sensitivity to the system response is determined using Sobol' indices. The proposed approach has low computational overhead and can be useful for computationally intensive problems requiring rapid decision-making in sensitive applications like aerospace, nuclear and biomedical engineering. The technique does not require reformulating existing finite element code and can perform the stochastic study by direct pre/post-processing. [ABSTRACT FROM AUTHOR]

The Method of Moments (MoM) is a non-embedded uncertainty analysis method that has been widely used in Electromagnetic Compatibility (EMC) simulations in recent years due to its two major advantages of high computational efficiency and immunity from dimensional disaster. A random variable sensitivity calculation method based on the Complex Number Method of Moments (CNMoM) is proposed in this paper to improve the accuracy of the MoM in standard deviation prediction and thereby enhance the credibility of EMC simulation uncertainty analysis results. In the parallel cable crosstalk prediction example in the literature, the result of the Monte Carlo Method (MCM) is used as the standard, and the accuracy of the new method proposed in this paper is quantitatively verified using the Feature Selective Validation (FSV) method. Compared with the MoM, the proposed method can significantly improve the calculation accuracy of the standard deviation results without sacrificing simulation efficiency. [ABSTRACT FROM AUTHOR]