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• The citations of 729,515 articles fit by the generalized extreme-value distribution. • The complexity of references and citations of papers' quantiles is studied. • The macroscopic model of the citation distribution is proposed. The paper presents an in-depth study of uncited papers. For that, we explore the documents indexed in the INSPIRE database from 1970 to 2015. Uncited articles represent a complex bibliometric environment in which references are generated. The reference lists of uncited papers form a dynamic system partially responsible for the redistribution of scientific impact. Our task is to quantify the detailed structure of citations and references directly in terms of quantiles. We also study the entropy and the statistical complexity measure of references and citations of papers' quantiles. We introduce a theoretical framework in which citation distribution is considered an asymptotic distribution of the largest values in a sequence of independent identically distributed random variables. We show that this asymptotic distribution is the generalized extreme-value distribution. Furthermore, we empirically demonstrate that the asymptotic behavior of citation distribution is close to (but not quite) the generalized extreme-value distribution. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate the problem of remote state estimation for nonlinear discrete systems. Specifically, we focus on scenarios where event-triggered sensor schedules are utilized and where packet drops occur between the sensor and the estimator. In the sensor scheduler, the SOD mechanism is proposed to decrease the amount of data transmitted from the sensor to a remote estimator and the phenomena of packet drops modeled with random variables obeying the Bernoulli distribution. As a consequence of packet drops, the assumption of Gaussianity no longer holds at the estimator side. By fully considering the non-linearity and non-Gaussianity of the dynamic system, this paper develops an event-trigger particle filter algorithm to relieve the communication burden and achieve an appropriate estimation accuracy. First, we derive an explicit expression for the likelihood function when an event trigger occurs and the possible occurrence of packet dropout is taken into consideration. Then, using a special form of sequential Monte–Carlo algorithm, the posterior distribution is approximated and the corresponding minimum mean-squared error is derived. By contrasting the error covariance matrix with the posterior Cramér–Rao lower bound, the estimator's performance is assessed. An illustrative numerical example shows the effectiveness of the proposed design. [Display omitted] • Limited bandwidth networked systems require sensors scheduling algorithm design. • Event-based particle filter is designed in conjunction with scheduling algorithms and packet dropout. • With Cramér–Rao lower bound the proposed scheduling algorithms improve clearly the filter performance. • Innovation scheduling allows robustness against packet dropouts. [ABSTRACT FROM AUTHOR]

• An original centrality metric objective function for the LMRNP is introduced. • A new data-driven adaptive distributionally robust equilibrium programming method. • The DBSCAN algorithm is newly adopted to construct a data-driven ambiguity set. • The proposed model is theoretically derived into a computationally solvable form. • The performance of the deduced model is validated by two real data sets. This paper studies a variant of the two-stage last mile relief network problem by introducing a centrality metric objective including the distance centrality metric, the demand centrality value-at-risk and the residual supplies centrality metric. Under the scenario-based design, the demand in each scenario is described as a random fuzzy variable whose probability distribution is ambiguous. In order to characterize its ambiguousness, this paper designs a Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm based on sample data to construct a data-driven ambiguity set containing the support and mean, which not only realizes the visualization of the ambiguous probability distribution, but also provides a finite set of scenarios for the uncertain demand. Given the constructed data-driven ambiguity set, this paper proposes a data-driven adaptive distributionally robust equilibrium programming (DDADREP) method for the last mile relief network problem (LMRNP). In view of its computational difficulty, the safe approximation, duality technique and credibility measure theory are used to approximate it as a mixed integer second-order cone programming with significant computational advantages. Finally, the proposed model is validated with two real-world cases, and its effectiveness as well as advantages is demonstrated by comparison with the classical robust optimization and the nominal equilibrium optimization, respectively. [ABSTRACT FROM AUTHOR]

The aim of this paper is to get asymptotic deviation bounds via a Large Deviation Principle (LDP) for cumulative processes also known as compound renewal processes or renewal-reward processes. These processes cumulate independent random variables occurring in time interval given by a renewal process. Our result extends the one obtained in Lefevere et al. (2011) in the sense that we impose no specific dependency between the cumulated random variables and the renewal process and the proof uses Mariani and Zambotti (2014). In the companion paper Cattiaux et al. (2022) we apply this principle to Hawkes processes with inhibition. Under some assumptions Hawkes processes are indeed cumulative processes, but they do not enter the framework of Lefevere et al. (2011). [ABSTRACT FROM AUTHOR]

• A new nondimensional analysis of FPWM-based MEP is proposed. • The optimal order of FPWM in MEP is determined by akaike information criterion. • A new quantile function-based first order reliability method is presented. • MEQFs are applied in a case study of reliability analysis of a rock slope. The maximum entropy principle (MEP) under the constraint of fractional probability weighted moments (FPWM) is a well-developed method for a direct estimation of the quantile function of a random variable. The accuracy, unbiasedness, and efficiency of maximum entropy quantile functions (MEQFs) have been demonstrated in the literature. However, the issue of how to select an optimal order of FPWMs given a sample of data is not fully solved, and the application of this approach to reliability analysis in civil engineering has not been fully investigated. This paper presents a FPWM-based MEP with a new nondimensional analysis and proposes the Akaike information criterion to determine the optimal order of FPWM in MEP analysis. To illustrate this approach, two examples of the estimation of optimal quantile functions for soil undrained shear strength and annual maximum daily discharge are presented. The paper presents a novel approach to use the quantile function for the First Order Reliability Method, a widely used method in civil engineering. As a case study of this approach, the reliability analysis of a rock slope is included. The FPWM-based MEQFs are compared with common empirical distributions and MEQFs based on integral probability weighted moments to demonstrate the advantages and disadvantages of the developed method. [ABSTRACT FROM AUTHOR]

• Developed web openings of steel I-beams is proposed based on novel BESO method. • The novel BESO method is developed based on plastic-limit probabilistic design. • Imperfect geometrically nonlinear FE models of steel I-beam were considered. • Volume fractions and initial geometric imperfections are set to be random variables. • The load capacity of steel beams is increased when adopting the proposed algorithm. This work presents a novel geometrically nonlinear analysis with imperfections reliability-based topology optimization (RBTO) approach, considering the volume fraction and geometric imperfections as random variables due to their crucial connections to the manufacturability of web openings in steel I-beams. The objective is achieved by controlling the plastic behavior through limit analysis, which imposes a limit on the plastic ultimate load multipliers. The suggested method is developed by imposing constraints related to the available material volume. The bi-directional evolutionary structural optimization (BESO) method is utilized to fulfill the objectives of this paper. The adequacy of the proposed technique is demonstrated by comparing the results of the algorithm with benchmark steel beams that have conventional web openings. Based on the numerical examples, it appears that the selected technique has the potential to increase the load capacity of steel beams while utilizing the same quantity of material within the design domain. Moreover, the improved beams also exhibit better performance in terms of stress levels. The results of this research suggest that the proposed technique enhances the load capacity of steel beams while maintaining the same quantity of material and improving their performance in terms of stress levels. [ABSTRACT FROM AUTHOR]

• Potential induced on pipelines during geomagnetic storms by probabilistic approach. • Most probable geoelectric field direction. • Even at mid-latitudes, potentials may exceed several tens of Volts. • Risk of damage for equipment connected to the pipeline. The paper presents a probabilistic approach for the determination of the potential induced along a pipeline route during a geomagnetic storm; particular emphasis is given to intense events such as 100-year and 10-year storms. By assuming that the induced geoelectric field orientation at the ground level and at a given latitude can be treated as a random variable with normal probability distribution, by means of a Monte Carlo algorithm it is possible to build up the empirical probability distribution of the induced potential along the pipeline. The main result is that, in case of an extreme event such as a 100-year storm, even at middle latitudes, potentials of several tens of Volts have a not negligible probability of being induced, at least one time during the pipeline life, along the plant route with possible consequences of damages to apparatuses and equipment connected to the pipeline itself. [ABSTRACT FROM AUTHOR]

The study of stochastic problems is very important and there is an increasing demand for investigating the behavior of a number of sophisticated dynamical systems in different areas of science as well as in engineering and finance. In this paper, we present a method which is based on the collocation method (CM) and the operational matrix method (OMM) by using Hosoya polynomials (HPs). This mixed-method helps us to convert the stochastic problems into a system of algebraic equations to access a solution of such problems. One of the most important advantages of this method is the simulation of the noise terms at the collocation points. Finally, two types of the VO–SADEs are simulated and tested via the proposed technique to confirm the superiority and accuracy. [ABSTRACT FROM AUTHOR]

In complex security markets, uncertainty and randomness may coexist. The investors hold different risk attitudes toward different investment objectives in reality. In order to reflect this phenomenon, this paper applies mental accounts to portfolio optimization in an uncertain random environment. Firstly, considering the influence of transaction costs and diversification degree, this paper establishes an uncertain random mean-absolute semi-deviation-entropy bi-objective optimization model. Then the bi-objective model is converted to two single-objective models through three steps. Secondly, the equivalent forms of the models are deduced when the return rates of random risky securities are assumed to be normal random variables and the return rates of uncertain risky securities are assumed to be linear and zigzag uncertain variables. Furthermore, we propose an improved butterfly optimization algorithm (IBOA) to solve the two single-objective models. Finally, numerical simulations are presented to analyze the practicability and effectiveness of the models with different mental accounts and the IBOA algorithm. The results indicate that the IBOA algorithm is effective and putting money into more mental accounts may gain higher returns. • The mental accounts are considered in uncertain random portfolio optimization. • We establish a mean-absolute semi-deviation-entropy bi-objective optimization model. • An improved butterfly optimization algorithm is proposed to solve the models. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous paper (Liu and Pagès, 2020). In this paper, we establish the monotone convex order (see further (1.1)) between two R -valued McKean–Vlasov processes X = (X t) t ∈ [ 0 , T ] and Y = (Y t) t ∈ [ 0 , T ] defined on a filtered probability space (Ω , F , (F t) t ≥ 0 , P) by d X t = b (t , X t , μ t) d t + σ (t , X t , μ t) d B t , X 0 ∈ L p (P) with p ≥ 2 , d Y t = β (t , Y t , ν t) d t + θ (t , Y t , ν t) d B t , Y 0 ∈ L p (P) , where ∀ t ∈ [ 0 , T ] , μ t = P ∘ X t − 1 , ν t = P ∘ Y t − 1. If we make the convexity and monotony assumption (only) on b and | σ | and if b ≤ β and | σ | ≤ | θ | , then the monotone convex order for the initial random variable X 0 ⪯ mcv Y 0 can be propagated to the whole path of processes X and Y. That is, if we consider a non-decreasing convex functional F defined on the path space with polynomial growth, we have E F (X) ≤ E F (Y) ; for a non-decreasing convex functional G defined on the product space involving the path space and its marginal distribution space, we have E G (X , (μ t) t ∈ [ 0 , T ] ) ≤ E G (Y , (ν t) t ∈ [ 0 , T ] ) under appropriate conditions. The symmetric setting is also valid, that is, if Y 0 ⪯ mcv X 0 and | θ | ≤ | σ | , then E F (Y) ≤ E F (X) and E G (Y , (ν t) t ∈ [ 0 , T ] ) ≤ E G (X , (μ t) t ∈ [ 0 , T ] ). The proof is based on several forward and backward dynamic programming principles and the convergence of the truncated Euler scheme of the McKean–Vlasov equation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the resilient state estimation problem for a type of stochastic nonlinear systems, in which the possible dynamical bias is considered that is depicted by a dynamical equation. In pursuit of enhancing the robustness of the propagated data, a binary encoding strategy (BES) is exploited in the binary symmetric channel (BSC). While the random bit errors caused by the channel noise may take place during the propagation of the binary bit string via the memoryless BSC. To characterize the occurrence of the bit errors, a series of Bernoulli distributed random variables is adopted. More specifically, in order to deal with the possible gain fluctuation of the estimator in the execution process, a resilient state estimator is employed. This paper intends to put forward a novel resilient estimation scheme under the BES, which can assure that the estimation error dynamics is exponentially ultimately bounded in mean square. A sufficient criterion is first acquired for the existence of the expected resilient estimator and the estimator parameter is achieved by solving a convex optimization problem. Finally, an illustrative simulation example is provided to verify the validity of the theoretical results. • The resilient SEP is discussed for the bias-corrupted nonlinear system. • The distortion of the data propagation is mathematically quantified under the BES. • The state and the dynamical bias can be jointly estimated. [ABSTRACT FROM AUTHOR]

In the agri-food supply chain, the perishable nature of the commodities opens a series of challenges at all decision levels: strategical, tactical and operational. This paper presents an age-based model for the inventory-routing problem of perishable commodities with stochastic demands. To deal with this source of uncertainty, the conditional value-at-risk (CVaR) has been adopted as a risk measure, and then the model has been applied to the agri-food supply chain under investigation. The model is the core of a dynamic approach for the optimal distribution and inventory planning over a short-medium horizon. To address a problem as realistic as possible, we assume that the demand for products of each age is unknown and we model this uncertainty by means of random variables with a probability distribution that can be estimated from historical data. Computational experiments on test cases based on a real-life agri-food company located in Italy show the effectiveness of the proposed approach for evaluating different risk attitudes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the adaptive event-triggered recursive state estimation (RSE) issue for a class of nonlinear complex dynamical networks (CDNs) with random coupling parameter, missing measurements (MMs) and coding-decoding-based communication mechanism (CDBCM). First of all, a random variable uniformly distributed in a fixed interval is adopted to model the varying topologies. Then, the Bernoulli random sequence with uncertain statistical properties is considered to characterize the phenomenon of MMs subject to the uncertain occurrence probability situation. Furthermore, in order to ensure the security and reliability of the shared network channel, the adaptive event-triggered scheduling strategy (AETSS) and CDBCM are both employed to govern the data transmission thereby enhancing the communication quality. The aim of this paper is to present an RSE scheme for a class of stochastic CDNs such that for all MMs, AETSS and CDBCM, the state estimation error covariance (SEEC) is given the SEEC upper bound (SEECUB) is derived. Then, the state estimator gain matrix (SEGM) is parameterized by means of optimizing the trace of SEECUB. Moreover, the monotonicity of the trace of SEECUB with respect to the available missing probability is clarified detailed. Finally, an illustrative simulation is executed for the purpose of verifying the validity of the proposed RSE scheme. [ABSTRACT FROM AUTHOR]

This paper studies the Whittle estimation for vector autoregressive and moving average (ARMA) models with heavy-tailed noises. It is shown that the Whittle estimator is consistent with the rate of convergence n 1 / α L ̃ (n) and its limiting distribution is a function of two stable random vectors, where L ̃ (n) is a slowly varying function and α ∈ (0 , 2) is the tail index of heavy-tailed vector noise. A simulation study is carried out to assess the performance of this estimator in finite samples and a real example is given. This paper includes several limiting theorems for the general heavy-tailed vector processes, which is independent of interest. [ABSTRACT FROM AUTHOR]

In this paper, the gain-scheduled state estimation issue is investigated for a kind of complex networks subject to randomly occurring nonlinearities under bit-rate constraints. An array of random variables is introduced to govern the nonlinearities whose occurring probability is a time-varying but bounded value with known upper and lower bounds. A bit-rate constraint model is established and an encoding–decoding mechanism is proposed, under which an upper bound of the decoding error is acquired. The primary purpose of the issue considered in this paper is to design a gain-scheduled state estimator to obtain an estimate of the network state with an acceptable accuracy according to available output measurements. By means of the stochastic analysis and Lyapunov stability theory, a sufficient condition is provided such that the estimation error dynamics achieve the exponentially mean-square ultimate boundedness. The required estimator gain matrix is parameterized by solving a series of matrix inequalities. A numerical simulation is exploited to show the usefulness of the obtained gain-scheduled state estimator. [ABSTRACT FROM AUTHOR]

• Novel methodology for variable flow CO 2 pipeline design optimisation. • Utilises logit-normal distribution to describe variable flow scenarios. • Methodology is validated for different flow rates and transport lengths. • Oversized pipeline diameter minimises unitised transport cost. • Oversized design yields lower cost compared to buffer tanks. Pipeline transport has emerged as the most cost-effective method for transporting CO 2 onshore. The CO 2 flow rate is a key factor driving transport costs, underscoring the need to understand the impact of flow rate variability in CO 2 pipeline networks on their design and economics. This paper presents an optimal pipeline design methodology for CO 2 pipelines operating under variable flow that considers the probability distribution of CO 2 flow rate and the pipeline length. The results imply that pipelines designed for optimal performance under variable flow rates often demand a higher level of overdesign compared to pipelines intended for steady-state conditions. Decision-makers must balance the trade-offs between pipeline oversizing and installing multiple pressure boosting stations, especially applicable to large transportation distances and projects of extended duration. The examination of different approaches to pipeline design reveals that a variable flow pipeline design based on mean flow rate is not recommended, because it is incapable of handling the maximum flow rate. This drawback is overcome by adopting the variable flow stochastic pipeline design presented in this paper. [ABSTRACT FROM AUTHOR]

We consider the model Y = X + ξ where Y is observable, ξ is a noise random variable with density f ξ , X has an unknown mixed density such that P (X = X c) = 1 − p , P (X = a) = p with X c being continuous and p ∈ (0 , 1) , a ∈ R. Typically, in the last decade, the model has been widely considered in a number of papers for the case of fully known quantities a , f ξ . In this paper, we relax the assumptions and consider the parametric error ξ ∼ σ N (0 , 1) with an unknown σ > 0. From i.i.d. copies Y 1 , ... , Y m of Y we will estimate (σ , p , a , f X c ) where f X c is the density of X c. We also find the lower bound of convergence rate and verify the minimax property of established estimators. [ABSTRACT FROM AUTHOR]

This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is critical for high-dimensional analysis and stands in contrast to classical metrics (e.g. , the Wasserstein metric). The proposed metrics fall into the category of integral probability metrics, for which we specify criteria of test function spaces to guarantee the property of being free of CoD. Examples of the selected test function spaces include the reproducing kernel Hilbert spaces, Barron space, and flow-induced function spaces. Three applications of the proposed metrics are presented: 1. The convergence of empirical measure in the case of random variables; 2. The convergence of n -particle system to the solution to McKean–Vlasov stochastic differential equation; 3. The construction of an ɛ -Nash equilibrium for a homogeneous n -player game by its mean-field limit. As a byproduct, we prove that, given a distribution close to the target distribution measured by our metric and a certain representation of the target distribution, we can generate a distribution close to the target one in terms of the Wasserstein metric and relative entropy. Overall, we show that the proposed class of metrics is a powerful tool to analyze the convergence of empirical measures in high dimensions without CoD. [ABSTRACT FROM AUTHOR]

In the first part of this paper we develop some theorems in linear algebra applicable to information theory when all random variables involved are linear functions of the individual bits of a source of independent bits. We say that a collection of subspaces of a vector space are coordinated if the vector space has a basis such that each subspace is spanned by its intersection with the basis. We measure the failure of a collection of subspaces to be coordinated by an invariant that we call the discoordination of the family. We develop some foundational results regarding discoordination. In particular, these results give a number of new formulas involving three subspaces of a vector space. We then apply a number of our results, along with a method of Tian to obtain some new lower bounds in a special case of the basic coded caching problem. In terms of the usual notation for these problems, we show that for N = 3 documents and K = 3 caches, we have 6 M + 5 R ≥ 11 for a scheme that achieves the memory-rate pair (M , R) , assuming the scheme is linear. [ABSTRACT FROM AUTHOR]

• The proposed method (P-SuS) generalises subset simulation from, to the capability of handling distributional responses. • P-SuS can be used in reliability analyses with partially-converged simulations, probabilistic and surrogate models. • The algorithm can be used in lieu of subset simulation in reliability analysis, optimisation, and pre-calibration. Reliability analysis can be performed efficiently through subset simulation. Through Markov chain Monte Carlo, subset simulation progressively samples from the input domain of a performance function (typically a computer model) to find the failure domain, that is, the set of input configurations that result in an output higher than a prescribed threshold. Recently, a probabilistic framework for numerical analysis was proposed, whereby computation is treated as a statistical inference problem. The framework, called probabilistic numerics, treats the output of a computer code as a random variable. This paper presents a generalisation of subset simulation, which enables reliability analysis for probabilistic numerical models. The advantages and challenges of the method are discussed, and an example with industrial application is presented. [ABSTRACT FROM AUTHOR]

We study the approximation of integrals of the form ∫ D f (x ⊤ A) d μ (x) , where the measure μ is of product form and A is a matrix, by quasi-Monte Carlo (QMC) rules N − 1 ∑ k = 0 N − 1 f (x k ⊤ A). We are interested in cases where the main computational cost in the approximation arises from calculating the products x k ⊤ A. We design QMC rules for which the computation of x k ⊤ A , k = 0 , 1 , ... , N − 1 , can be done in a fast way, and for which the approximation error of the QMC rule is similar to the standard QMC error. We do not require that the matrix A has any particular structure. Problems of this form arise in some important applications in statistics and uncertainty quantification. For instance, this approach can be used when approximating the expected value of some function with a multivariate normal random variable with some given covariance matrix, or when approximating the expected value of the solution of a PDE with random coefficients. The speed-up of the computation time of our approach is sometimes better and sometimes worse than the fast QMC matrix–vector product from [Josef Dick, Frances Y. Kuo, Quoc T. Le Gia, and Christoph Schwab, Fast QMC Matrix-Vector Multiplication, SIAM J. Sci. Comput. 37 (2015), no. 3, A1436–A1450]. As in that paper, our approach applies to lattice point sets and polynomial lattice point sets, but also applies to digital nets (we are currently not aware of any approach which allows one to apply the fast QMC matrix–vector paper from the aforementioned paper of Dick, Kuo, Le Gia, and Schwab to digital nets). The method in this paper does not make use of the fast Fourier transform, instead we use repeated values in the quadrature points to derive a significant reduction in the computation time. Such a situation naturally arises from the reduced CBC construction of lattice rules and polynomial lattice rules. The reduced CBC construction has been shown to reduce the computation time for the CBC construction. Here we show that it can additionally be used to also reduce the computation time of the underlying QMC rule. One advantage of the present approach is that it can be combined with random (digital) shifts, whereas this does not apply to the fast QMC matrix–vector product from the earlier paper of Dick, Kuo, Le Gia, and Schwab. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete f -moment convergence for maximal randomly weighted sums of arrays of rowwise widely orthant dependent random variables under some general conditions. The results obtained in the paper extend and improve some previous known ones. As applications of our main results, we not only present convergence for the state observers of linear-time-invariant systems but also obtain complete consistency for the estimators of errors-in-variables regression models based on widely orthant dependent errors. We further perform a numerical simulation to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents an uncertain random multi-state k -out-of- n system (urm- k -out-of- n system, for short), where both random components and uncertain components coexist. States of the system and components display multiplicity and are defined as uncertain random variables. Since reliability is a crucial index to reflect system performance, this paper proves some formulas to calculate the reliability of urm- k -out-of- n systems in accordance with chance theory, which have two special cases, random systems and uncertain systems. Later, a mixed algorithm for multi-valued decision diagram (MDD) and binary search is designed to assess the reliability index. Compared to the general algorithm, it operates in significantly less time when the system becomes complex. [ABSTRACT FROM AUTHOR]

In this paper, complete convergence and complete moment convergence for maximal weighted sums of arrays of rowwise extended negatively dependent random variables are investigated, and some sufficient conditions for convergence are provided. Three ways of optimising the conditions for convergence, namely reducing the moment condition, narrowing the boundary function, and raising the weight function respectively, are considered under light weights. Besides, rather than assuming stochastic domination, we turn to a weaker assumption of uniformly bounded expectations to describe the moment conditions. The results obtained in the paper extend the corresponding ones for independent random variables and some dependent random variables. In addition, the results are applied to establish strong consistency for estimators in some statistical models. [ABSTRACT FROM AUTHOR]

In this paper, we consider feature selection in ultrahigh-dimensional additive models with heterogeneous frequency component functions. Firstly, we introduce a new concept, weighted sum of squared conditional correlations (WSSCC), which measures the correlation between a random variable and its function. Afterwards, we propose a sure independence screening procedure based on WSSCC (WSSCCSIS), whose sure screening property is established. Furthermore, a sequential feature selection procedure based on WSSCC (WSSCCFR) is proposed. Numerical studies including comprehensive simulation and a real data analysis are carried out to demonstrate the advantage of our method over other existing approaches. • We proposed a new concept WSSCC measuring the correlation between a random variable and its function. • We proposed a novel feature screening procedure WSSCCSIS and a novel feature selection procedure WSSCCFR. • Our proposed procedures are capable of handling heterogeneous component functions for ultrahigh-dimensional additive models. • We provided sufficient numerical evidences to demonstrate the advantages of our methods. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of stochastic trajectory planning for 6-DOF spacecraft close proximity in the presence of external disturbances and initial state uncertainties. Nonlinear chance constraints on collision avoidance, docking corridor, sensor field-of-view, and control magnitude are considered in the corresponding optimal control problem. Nominal trajectory along with affine feedback controller that restricts the dispersion caused by disturbances are optimized simultaneously. The nonlinear stochastic dynamics are transformed into equality constraints on the first two statistical moments of the random states by linearization and discretization, and further, the non-convex covariance update equation is relaxed to a semidefinite cone constraint. The nonlinear path chance constraints are first approximated by affine chance formations, and then are convexified by introducing auxiliary variables instead of direct linearization of the covariance matrix. Combined with the tail bound of sub-exponential random variables, the constraints on control input are replaced with conservative deterministic inequalities. The sub-optimal solution to the original problem is obtained by iteratively solving a series of semidefinite cone programs. The effectiveness of the proposed framework is verified using numerical simulations. • The state-triggered chance constraint is used to describe multi-stage maneuver. • The update equation for covariance is relaxed to semidefinite cone constraint. • A strategy is given to convert nonlinear chance constraint into convex form. • A theorem is given to convert chance control constraint into deterministic form. [ABSTRACT FROM AUTHOR]

This paper studies the issue of developing the optimal deception attacks on the multiple channels in cyber–physical systems, where the attackers are limited by energy constraints. To fully utilize the eavesdropped data, by linearly combining the innovations from the different channels, a fusion attack model is proposed under the stealthiness condition. According to the statistical characteristics of the correlated stochastic variables and the orthogonality principle, the state estimation error is quantified and analyzed by deriving the iteration of the error covariance matrices of the remote estimators under the proposed attack framework. Moreover, by analyzing the correlations of the decision variables in the objective function, it is shown that the attack parameters and energy allocation strategy can be derived by two steps without loss of optimality, such that the optimal attack scheme is acquired by solving a multivariate semi-definite programming (SDP) problem and a linear 0–1 programming problem respectively. Finally, simulation examples are provided to illustrate the effectiveness of the proposed method. • A novel energy constrained fusion attack model is proposed as the linear combination of transmitted innovations. • Under the proposed attack framework, the remote state estimation errors are analyzed. • By analyzing the structure of the objective function, the optimal attack scheme is found by solving a multivariate SDP problem and a linear 0–1 programming problem. [ABSTRACT FROM AUTHOR]

• An (r, Q) inventory policy with deterministic demand and defective items is proposed. • Two formulations for the percentage of defective items are considered. • Full inspection of lot size is conducted • The non-planned shortages during inspection period are modeled. • Properties are established for the optimal problem solution. In this paper an (r , Q) stock policy is used to control an inventory system with deterministic demand and defective items. The fraction of defective items in a batch is a random variable whose variance maybe dependent and independent of the order quantity. Considering the numerous benefits of selling high quality items (noting the vital importance for firms like medical device companies), a full inspection of the order quantity is conducted. Although full inspection reduces returns, ensures high quality products and improves customer satisfaction, it requires a substantial inspection time. Consequently, during this time a non-zero probability of undesirable (unplanned) shortages exists. The dominant suggestion in the literature, is to set the reorder level equal to the total demand during inpection period. This paper suggests an alternative reorder level to prevent shortages during this period and to formulate the backlogging cost in the case that unplanned shortages are permitted. Then, theoretical results ensure the determination of the reorder level and the order quantity that minimize the average total cost of the inventory system. Comparisons, through numerical examples and simulation, demonstrate that the proposed model leads to significant reduction both in cost and probability of shortages (if allowed), in relation to other existing models. [ABSTRACT FROM AUTHOR]

• Pedestrian-injury severities at pedestrian-vehicle crash hotspots with an annual upward trend are modeled. • Spatiotemporal trend analysis is used to identify spatial aggregated pedestrian-vehicle crash hotspots with annual uptrends. • Average nearest neighbor and spatial autocorrelation tests are used to give a reference for grid and neighborhood distances. • Latent class random parameter logit models are utilized to explore the heterogeneity within and between the subgroups. • Contributing factors to the pedestrian-injury severity are identified and analyzed with specific countermeasures. Introduction: With the increasing trend of pedestrian deaths among all traffic fatalities in the past decade, there is an urgent need for identifying and investigating hotspots of pedestrian-vehicle crashes with an upward trend. Method: To identify pedestrian-vehicle crash locations with aggregated spatial pattern and upward temporal pattern (i.e., hotspots with an upward trend), this paper first uses the average nearest neighbor and the spatial autocorrelation tests to determine the grid distance and the neighborhood distance for hotspots, respectively. Then, the spatiotemporal analyses with the Getis-Ord Gi* index and the Mann-Kendall trend test are utilized to identify the pedestrian-vehicle crash hotspots with an annual upward trend in North Carolina from 2007 to 2018. Considering the unobserved heterogeneity of the crash data, a latent class model with random parameters within class is proposed to identify specific contributing factors for each class and explore the heterogeneity within classes. Significant factors of the pedestrian, vehicle, crash type, locality, roadway, environment, time, and traffic control characteristics are detected and analyzed based on the marginal effects. Results: The heterogeneous results between classes and the random parameter variables detected within classes further indicate the superiority of latent class random parameter model. Practical Applications: This paper provides a framework for researchers and engineers to identify crash hotspots considering spatiotemporal patterns and contribution factors to crashes considering unobserved heterogeneity. Also, the result provides specific guidance to developing countermeasures for mitigating pedestrian-injury at pedestrian-vehicle crash hotspots with an upward trend. [ABSTRACT FROM AUTHOR]

The accuracy of wind speed scenario generation is critical to the energy dispatching and planning of the wind-integrated power system. The accuracy of the modeling of wind speed can be improved with a comprehensive consideration of the dependency structure between wind speeds, and then the accuracy of wind speed scenario generation can be improved. Therefore, spatial and temporal dependence have been widely studied. However, linear correlation does not fully reflect the nonlinear nature of wind speed. Tail dependence, as a kind of non-linear dependency structure of wind speed in space and time, is studied in this paper. This paper proposes a wind speed scenario generation method based on the C-vine copula that considers spatiotemporal tail dependency structure. With the consideration of spatiotemporal dependency structure, the number of modeled random variables increase significantly. Therefore, a two-step wind speed scenario generation method is proposed to avoid the dimensional disaster. The wind speed data of two wind farms provided by the National Renewable Energy Laboratory are used in simulation analysis, the results demonstrate that reasonable consideration of the spatial and temporal tail dependence of wind speed can improve the accuracy of the spatial and temporal models, and further improve the accuracy of scenarios. • A new two-step wind speed scenario generation method is proposed. • Wind speed scenarios with spatiotemporal tail dependence are generated effectively. • Scenarios generated by the proposed method are closer to the original data. [ABSTRACT FROM AUTHOR]

This paper concentrates on the exponential synchronization problem of the delayed neural networks (DNNs) with stochastic impulses. First, the impulsive Halanay differential inequality is further extended to the case that the impulsive strengths are random variables. Then, based on the generalized inequalities, synchronization criteria are respectively proposed for DNNs with two kinds of stochastic impulses, i.e., impulses with independent property/Markovian property. It should be pointed out that only some basic statistical characteristics are needed to verify the proposed criteria. Numerical examples are provided to show the validation of the obtained theoretical results at the end of this paper. [ABSTRACT FROM AUTHOR]

Sklar's theorem represents a single multivariate distribution function through its univariate marginal distributions and a copula. However, it fails in general when it comes to the representation of the envelopes of a family F of multivariate distribution functions (i.e. its point-wise infimum and supremum), even if we allow more general representing functions than copulas. In this paper we develop an alternative representation which describes the envelopes of a family F in terms of the copulas that correspond to the members of F. Our representation is reminiscent of Sklar's representation but is based on the idea of corner patches of copulas. We prove a series of four representation theorems; (1) a general one, which holds even if the envelopes of the family do not possess a Sklar type representation, (2) a version tailored for the case when the envelopes do possess a Sklar type representation, (3) a theorem for families of continuous distribution functions, and (4) a variant appropriate for modeling dependencies of absolutely continuous random variables. In addition, we demonstrate how our results can be applied to give a Sklar type theorem in the imprecise probability setting, which offers a new approach to multivariate probability boxes. [ABSTRACT FROM AUTHOR]

Sample efficiency, which refers to the number of samples required for a learning agent to attain a specific level of performance, is central to developing practical reinforcement learning (RL) for complex and large-scale decision-making problems. The ability to transfer and generalize knowledge gained from previous experiences to downstream tasks can significantly improve sample efficiency. Recent research indicates that successor feature (SF) RL algorithms enable knowledge generalization between tasks with different rewards but identical transition dynamics. It has recently been hypothesized that combining model-based (MB) methods with SF algorithms can alleviate the limitation of fixed transition dynamics. Furthermore, uncertainty-aware exploration is widely recognized as another appealing approach for improving sample efficiency. An agent can efficiently explore to better understand an environment by tracking uncertainty about the value of each available action. Putting together two ideas of hybrid model-based successor feature (MB-SF) and uncertainty leads to an approach to the problem of sample efficient uncertainty-aware knowledge transfer across tasks with different transition dynamics or/and reward functions. In this paper, the uncertainty of the value of each action is approximated by a Kalman filter (KF)-based multiple-model adaptive estimation. This KF-based framework treats the parameters of a model as random variables. To the best of our knowledge, this is the first attempt at formulating a hybrid MB-SF algorithm capable of generalizing knowledge across large or continuous state space tasks with various transition dynamics while requiring less computation at decision time than MB methods. We highlight why previous SF-based methods are constrained to knowledge generalization across same transition dynamics, present our novel approach on a firm theoretical foundation, and design a set of demonstration tasks to empirically validate the effectiveness of our proposed approach. The number of samples required to learn the tasks was compared to recent SF and MB baselines. The results show that our algorithm generalizes its knowledge across different transition dynamics, learns downstream tasks with significantly fewer samples than starting from scratch, and outperforms existing approaches. We believe that our proposed framework can account for the computationally efficient behavioural flexibilities observed in the empirical literature and can also serve as a solid theoretical foundation for future experimental work. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical modeling of new numerical techniques which are used to approximate the probability distribution of the univariate random variable transformations, to overcome the restrictions that prevent applying common analytical methods in the most cases. The proposed study is implemented by deducing mathematical formulas that make it easy to determine the cumulative distribution function numerically for any transformation of a random variable at a point from its range. The effectiveness of employing this procedure depends on finding numerically the values of inverse transformation images of that point and since it is difficult to deal analytically with the transformation function, this research presents an alternative method that depends on using Taylor's expansion to find a best polynomial function that converges strongly to the transformation function on its domain which facilitates generating the inverse images. Mathematical algorithms are designed to illustrate the computational implementation process of all former procedures. A stochastic model related to the heat equation is considered to obtain the distribution of its probabilistic solution which has a complicated nature impedes applying the usual analytical methods, therefore applying this current study has become effective in such cases. The results have been validated using Mathematica software. [ABSTRACT FROM AUTHOR]

This paper aims to address the material and spatial uncertainties in the stochastic electric field problem by proposing two efficient algorithms based on the stable nodal integration method (SNIM). The random variables/fields are used to describe the material and spatial uncertainties and a generalized stochastic perturbation-SNIM (GS-SNIM) method is developed to address the random-variable scenario while a random field-SNIM (RF-SNIM) method is developed to address the random-field scenario. Numerical examples are studied to fully verify the accuracy and efficiency of the proposed GS/RF-SNIM. The analysis results demonstrate that (1) the GS-SNIM is able to solve the random-variable based uncertainties through different orders expansion; (2) the RF-SNIM can calculate the expected values and variances of the stochastic electric field problem; and (3) the present methods produce accurate stochastic analysis results and significantly reduce the computational cost. • GS/RF-SNIM is proposed for stochastic electric field problems. • Both material uncertainty and spatial uncertainly are considered. • The GS/RF-SNIM can achieve high level of accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Recently, few studies have been made on the stereophonic acoustic echo cancellation (SAEC) with nonlinear systems. To identify such nonlinear model, the functional link artificial neural network (FLANN) and the widely linear model can provide an approach to explore the SAEC with complex random variable. In this paper, a class of augmented complex-value functional link network (ACFLN) adaptive algorithms is developed. Based on the augmented complex-value functional least-mean-square (ACFLMS) algorithm, we have proposed the recursive augmented complex-value functional least-mean-square (RACFLMS) algorithm designed by a recursive structure. To further reduce its computational complexity and enhance its performance, a novel inverse square root function is employed in its structure of the RACFLMS algorithm. The results of several experiments demonstrate that our approach can effectively model the nonlinear systems and verify the improvement of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust H ∞ sliding mode control (SMC) for discrete delayed Markovian jumping systems subject to randomly occurring uncertainties (ROUs) and repeated scalar nonlinearities (RSNs). Here, a set of mutually independent Bernoulli distributed random variables is introduced to model the phenomenon of the ROUs, where the occurrence probabilities could be uncertain. The purpose of paper is to present an H ∞ SMC strategy via the delay-fractioning approach such that, for the Markovian jumping parameters, time-varying delays, ROUs and RSNs, the mean-square stability of the resulted sliding motion with a prescribed H ∞ performance can be guaranteed. Subsequently, the robust sliding mode controller is synthesized to guarantee that the reachability condition in the discrete-time setting is ensured. Finally, the validity of proposed robust SMC strategy is verified by providing a simulation example. • The mathematical characterization of uncertain occurrence probabilities is given. • The H ∞ SMC problem is studied via the delay-fractioning approach. • The effects from MJPs, delays, RSNs and ROUs under uncertain occurrence probabilities are examined. [ABSTRACT FROM AUTHOR]

In this paper, the non-fragile dissipative filtering problem is investigated for the two-dimensional (2-D) systems subjected to randomly occurring uncertainties and redundant channel protocol. For the redundant channel transmission, if a signal fails to be transmitted through a certain channel, the next channel is immediately activated to transmit the signal once again. The norm-bounded uncertainties are introduced in the considered system, which are governed by two stochastic variables obeying the Bernoulli distribution law. The aim of this paper is to design a dissipative filter in a non-fragile manner such that the augmented filtering error system is not only asymptotically stable in the mean-square sense but also satisfies a strict 2-D (Q , S , R) − α -dissipativity performance index. Based on the Lyapunov theory and stochastic analysis, sufficient conditions are first given to guarantee the asymptotic stability of the 2-D system in the mean-square sense. Then, the non-fragile filter is designed to ensure that the 2-D system satisfies the strict 2-D (Q , S , R) − α -dissipativity performance index, under which the expressions of the non-fragile filter gains are given by solving certain matrix inequalities. Finally, a simulation example is provided to show the effectiveness of the proposed dissipative filtering method. [ABSTRACT FROM AUTHOR]

• Launch a new avenue to capture the effects of covariance between OD flows. • Propose a more generalized model for optimizing traffic count location problem. • Examine and discuss the mathematical properties of the proposed model. • Update stochastic link choice proportions using an adapted traffic flow simulator. Vehicular traffic between different Origin-Destination (OD) pairs for a typical hourly period may statistically correlate with each other. The covariance mainly generated from the daily variation of travel patterns, network topology, and trip chaining activities of household members can be particularly high during the morning peak hour. With the increasing attention on the OD demand variance and covariance in stochastic road networks, a new criterion is proposed in this paper for measuring the estimation accuracy of OD demand covariance. The mathematical properties of this proposed criterion are analyzed to better understand the relationship between the estimation errors of mean and covariance of OD demands. This paper aims to investigate how to optimize the traffic count locations for minimizing the weighted maximum deviation of estimated mean and covariance of OD demands from the "true" values. To consider the effects of stochastic OD demands on the traffic count location problem in the proposed model, link choice proportions are regarded as stochastic variables and updated by an adapted traffic flow simulator in this study. Both the weighted-sum approach and bi-objective approach are examined with the adaption of the firefly algorithm (FA) to solve the single-objective and bi-objective problems. Numerical examples are presented to demonstrate the effects, with and without considering the covariance of the OD demands for the optimization of traffic count locations. [ABSTRACT FROM AUTHOR]