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In modern manufacturing and service industries, urgent orders and service tasks are common, and the speed of handling such urgent tasks is an important indicator of production and service efficiency. In this study, we consider scheduling jobs on two parallel machines with the random arrival of an emergency job. The objective is to minimise the makespan, subject to a given maximum waiting time of the emergency job. We first show that the worst-case ratio of the existing algorithm LPT $ _l $ l -SPT $ _{m-l} $ m − l is at least 3/2 when m = 2. We then analyse some properties of the optimal schedule and derive lower bounds on the optimal makespan. Finally, we present an improved approximation algorithm with a tight worst-case ratio of 4/3. We also provide numerical results showing that our proposed algorithm outperforms algorithm LPT $ _l $ l -SPT $ _{m-l} $ m − l . [ABSTRACT FROM AUTHOR]

Drones are increasingly used for last-mile delivery due to their speed and cost-effectiveness. This study focuses on a novel locker-drone delivery system, where trucks transport parcels from the warehouse to lockers, and drones complete the final delivery. This system is ideal for community and intra-facility logistics. The research optimises the network design by determining the location of lockers, the number of drones at each locker, and the assignment of demands to lockers, minimising operating costs. Both single-parcel and multi-parcel capacity drones are examined. We build an optimisation model for each system, considering drone service capacity as a critical constraint. We design an algorithm combining average sample approximation and a genetic algorithm to address demand uncertainty. The algorithm's efficiency is validated through comparative analysis with Gurobi. Numerical experiments, using real and generated data, optimise the network design. Results show that the multi-capacity drone system requires fewer lockers and drones than the singlecapacity system. Although the single-capacity system yields lower drone delivery costs, it incurs higher truck delivery costs. Additionally, a comprehensive cost analysis compares the cost-efficiency of the locker-drone system with a conventional drone delivery system, revealing the cost-saving advantage of the locker-drone system. [ABSTRACT FROM AUTHOR]

Confidence bands are used to estimate the likely range of the true parameter, whereas prediction bands provide an idea of the possible values of the parameter after applying a regression model. This study proposes an equation to construct confidence and prediction bands applicable to any linear or nonlinear chemometric regression model; that is, statistical methods used in analytical chemistry to establish relationships between two or more variables. The proposed equation is developed and presented as a useful tool to represent the uncertainty in estimates based on a set of data in chemical measurements. Once the set of data is adjusted as a regression model (linear, polynomial, or multivariable), the proposed equation can be used to construct confidence and prediction bands based on the adjustment equation. The proposed equation operates if the adjustment equation is continuous and derivable. The plot bands on any regression model provide a solid understanding of uncertainty assessment and have the advantage of total control and independence of algorithms and numeral approximations. [ABSTRACT FROM AUTHOR]

This paper studies a two-agent scheduling problem on mixed batch machines in parallel. A mixed batch machine can process several jobs simultaneously as a batch, as long as the number of jobs in the batch does not exceed the machine capacity. The processing time of a mixed batch is the weighted sum of the maximum processing time and the total processing time of jobs in the batch. The objective is to minimise the weighted sum of two agents' makespans. We present four approximation algorithms based on two strategies: the machine-centric strategy and the agent-centric strategy. For each strategy, a full batch longest processing time (FBLPT) rule and a longest processing time greedy (LPTG) rule are used. We conduct theoretical analyses based on the worst-case performance ratio to provide the provable guarantees on the performances of the algorithms, and simulation analyses based on randomly generated instances to evaluate the average performances of the algorithms. Furthermore, we verify the consistency between the theoretical and simulation results. The algorithms using agent-centric strategy perform better than ones using machine-centric strategy. Finally, we provide managerial insights for the problem by analysing the technological parameters of batches, importance of agents, and demand seasonality. [ABSTRACT FROM AUTHOR]

In this paper we give a quantitative analysis of an explicit iteration method due to C.E. Chidume for the approximation of a zero of an m-accretive operator A : X → 2 X in Banach spaces which does not involve the computation of the resolvent of A. [ABSTRACT FROM AUTHOR]

We consider a single machine rescheduling problem where a set of original jobs have been scheduled to minimize the total weighted completion time. However, before formal processing begins, a new set of jobs arrives and creates a disruption. The decision maker can reject a subset of the new jobs by paying certain rejection penalties, and reschedule the original and the remaining new jobs without excessively disrupting the original schedule, which is measured by the maximum completion time deviation for any original jobs between the original and adjusted schedules. The objective is to minimize the sum of total weighted completion time of the original jobs and the accepted new jobs in the adjusted schedule, the weighted maximum completion time deviation and the total rejection cost. We first provide a dynamic programming-based exact algorithm running in pseudo-polynomial time, and then propose a fully polynomial time approximation scheme. Given the NP-hardness for the studied problem, our result is the best possible from the approximation algorithm perspective. In addition, we conduct extensive computational experiments to evaluate the performance of our proposed methods, and provide some managerial insights on their applicability under different situations. [ABSTRACT FROM AUTHOR]

This article proposes Bayesian nonparametric inference for panel Markov-switching GARCH models. The model incorporates series-specific hidden Markov chain processes that drive the GARCH parameters. To cope with the high-dimensionality of the parameter space, the article assumes soft parameter pooling through a hierarchical prior distribution and introduces cross sectional clustering through a Bayesian nonparametric prior distribution. An MCMC posterior approximation algorithm is developed and its efficiency is studied in simulations under alternative settings. An empirical application to financial returns data in the United States is offered with a portfolio performance exercise based on forecasts. A comparison shows that the Bayesian nonparametric panel Markov-switching GARCH model provides good forecasting performances and economic gains in optimal asset allocation. [ABSTRACT FROM AUTHOR]

We consider parallel-machine scheduling with identical machine resource capacity limits and DeJong's learning effect. Each job has a resource consumption requirement and a normal processing time. The actual processing time of a job is a function of its normal processing time, subject to DeJong's learning effect, while the resource consumption of a job is a function of its actual processing time. Each machine has the same resource capacity limit. The objective is to maximise the minimum machine load. Considering three resource consumption functions, namely, linear, concave, and convex, we show that all three scheduling models are NP-hard and propose two approximation algorithms for the models and analyse their worst-case ratios. [ABSTRACT FROM AUTHOR]

The meta-analysis of P-values is a widely used method in integrating information from multiple studies, and much research has focused on combining P-values. Among the established approaches, Fisher's test may be the most popular one. Many studies have been devoted to extending or modifying Fisher's statistic. For example, Lancaster's variation of Fisher's method may outperform the weighted Z-test and recently has drawn noteworthy attention. In this study, we first extend Lancaster's statistic by incorporating a weighting scheme. An approximation and an algorithm that are suitable for use under both independence and dependence assumptions are proposed for calculating the distribution of the weighted Lancaster statistic. The relationships between this method and existing ones are discussed. An application of the main results to a linkage test method in human gene mapping is then provided to show its use. [ABSTRACT FROM AUTHOR]

Cluster failure time data are commonly encountered in survival analysis due to unobservable factors such as shared environmental conditions and genetic similarity. In such cases, careful attention needs to be paid to the correlation among the subjects within the same cluster. In addition, some diseases are curable due to the advancement of modern medical techniques. In this paper, we extend the frailty model based on Birnbaum–Saunders frailty distribution to incorporate the cure proportion. In addition, the marginal likelihood approach using Monte Carlo approximation and Expectation-Maximization algorithm are also developed for the determination of the maximum likelihood estimates of the parameters of the proposed model. An extensive simulation study is carried out to evaluate the performance of the proposed model and the methods of inference. Finally, the proposed model is applied to a real data set to analyse the effect of allogeneic and autologous bone marrow transplant treatment on acute lymphoblastic leukemia patients. [ABSTRACT FROM AUTHOR]

This paper studies the integrated scheduling of consultation and treatment appointments for chemotherapy patients, while taking into account the stochastic duration of injection. Patients may require one or both types of consultation and treatment appointments. The objective is to minimize the clinic's overtime and the waiting time of patients in the clinic. To formulate the problem, we develop two two-stage stochastic programming models. We also propose a sample average approximation algorithm as the solution method. To improve the efficiency of our solution approach, we devise a specialized algorithm that quickly evaluates a given first-stage solution for a large set of scenarios, without solving the second-stage models. Several computational experiments are carried out to evaluate the performance of proposed models and algorithms. [ABSTRACT FROM AUTHOR]

We consider the robust (min-max regret) version of identical parallel machine scheduling problem, in which jobs may be outsourced to balance total cost against production efficiency. The total cost is measured in terms of the total completion time of jobs processed in-house and the cost of outsourcing the rest. Processing times of in-house jobs are uncertain and they are described as two types of scenarios: discrete and interval. The objective is to obtain a robust (min-max regret) decision that minimises the absolute deviation of total cost from the optimal solution under the worst-case scenario. We first prove the worst-case scenario for any feasible solution. For the interval scenario, we further prove that the maximum regret value can be obtained in polynomial time for any feasible schedule. We also prove that for any discrete scenario, the minimum total cost can be obtained in polynomial time. Since the problem with the interval scenario is strongly NP-hard, we then transform the problem into an equivalent robust single machine scheduling problem. Finally, we develop 2-approximation algorithms for the problem with discrete and interval scenarios, respectively. These results are helpful for bridging the scheduling theory and practice in identical parallel machining environments with outsourcing and uncertain processing times. [ABSTRACT FROM AUTHOR]

Patient unpunctuality significantly disrupts the operations of healthcare facilities, reduces provider productivity, and increases healthcare costs. To alleviate the negative impact of unpunctual patients, this study addresses the appointment scheduling (AS) in the simultaneous presence of unpunctual patients, multiple servers, and no-shows. To determine the appointment schedule, we propose a two-stage stochastic mixed-integer programming model to minimise the total cost incurred by patient waiting and clinic overtime. It becomes challenging for a standard solver to solve this model due to the dynamic patient-to-server assignment decisions that are proactively anticipated in the determination of appointment times. To deal with this problem, a stochastic approximation algorithm is proposed under unbiased gradient estimators. The effectiveness and efficiency of this algorithm are validated in extensive numerical experiments that compare it with Benders decomposition and a heuristic algorithm. Further, the features of the optimal appointment schedule are analysed: (i) the shape of the appointment intervals relies on the number of servers; (ii) the length of intervals is sensitive to no-shows; (iii) the initial block size is greatly affected by patient unpunctuality. Managerial insights are also provided for hospital managers to schedule unpunctual patients in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a new kernel regression estimators based on the two-time-scale stochastic approximation algorithm in the case of independent functional data. We study the properties of the proposed recursive estimators and compare them with the recursive estimators based on single-time-scale stochastic algorithm proposed by Slaoui and to the non-recursive estimator proposed by Slaoui. It turns out that, with an adequate choice of the parameters, the proposed two-time-scale estimators perform better than the recursive estimators constructed using single-time-scale stochastic algorithm. We corroborate these theoretical results through some simulations and two real datasets. [ABSTRACT FROM AUTHOR]

In this paper we establish some approximation versions of the classical Dinkelbach algorithm for nonlinear fractional optimization problems in Banach spaces. We start by examining what occurs if at any step of the algorithm, the generated point desired to be a minimizer can only be determined with a given error. Next we assume that the step error tends to zero as the algorithm advances. The last version of the algorithm we present is making use of Ekeland's variational principle for generating the sequence of minimizer-like points. In the final part of the article we deliver some results in order to achieve a Palais-Smale type compactness condition that guarantees the convergence of our Dinkelbach-Ekeland algorithm. [ABSTRACT FROM AUTHOR]

In this study, we present a general framework of outer approximation algorithms to solve convex vector optimization problems, in which the Pascoletti-Serafini (PS) scalarization is solved iteratively. This scalarization finds the minimum 'distance' from a reference point, which is usually taken as a vertex of the current outer approximation, to the upper image through a given direction. We propose efficient methods to select the parameters (the reference point and direction vector) of the PS scalarization and analyse the effects of these on the overall performance of the algorithm. Different from the existing vertex selection rules from the literature, the proposed methods do not require solving additional single-objective optimization problems. Using some test problems, we conduct an extensive computational study where three different measures are set as the stopping criteria: the approximation error, the runtime, and the cardinality of the solution set. We observe that the proposed variants have satisfactory results, especially in terms of runtime compared to the existing variants from the literature. [ABSTRACT FROM AUTHOR]

Bayesian structure learning in Gaussian graphical models is often done by search algorithms over the graph space.The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart.With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart.In moderate to high-dimensions, this ratio is often approximated by using sampling-based methods as computationally expensive updates in the search algorithm.Calculating this ratio so far has been a major computational bottleneck.We overcome this issue by representing a search algorithm in which the ratio of normalizing constants is carried out by an explicit closed-form approximation.Using this approximation within our search algorithm yields significant improvement in the scalability of structure learning without sacrificing structure learning accuracy.We study the conditions under which the approximation is valid.We also evaluate the efficacy of our method with simulation studies.We show that the new search algorithm with our approximation outperforms state-of-the-art methods in both computational efficiency and accuracy.The implementation of our work is available in the R package BDgraph. [ABSTRACT FROM AUTHOR]

The makespan of operations at container terminals is crucial for the lead time of cargo and consequently the reduction of transportation costs. Therefore, an efficient transhipment and short storage of containers are demanded. Our paper refers to the consolidation process of trains in a container transhipment terminal as well as to the intermediate storage of containers in seaports in order to accelerate the loading and unloading of the vessels. It can also be encountered in automated storage/retrieval systems. Each of these (container) storage and retrieval moves corresponds to a crane operation, carrying a load from its pickup to its drop-off position. The problem is to find a permutation of the loaded crane moves that minimises the total empty crane travel time, which is the sum of times the crane needs to get from the last drop-off point of a load to the next pickup point of a load. We address the problem as an extension of an asymmetric travelling salesman problem (ATSP), assuming that n ordered pairs of points in the two-dimensional Euclidean space need to be traversed. Each point corresponds to a crane operation carrying a load from its pickup to its drop-off position. Despite that the problem seems to be easier than the ATSP, because a simple constant factor approximation exists, which was for a long time an open question for the ATSP, we are the first to prove that there is no polynomial-time approximation algorithm with an approximation guarantee less than 1 + 0.23 / n unless P = N P . [ABSTRACT FROM AUTHOR]

We consider replenishment decisions on when and how many goods to purchase for a seller under a purchase-to-order mode where there is no inventory and the seller purchases goods to fulfil orders already placed. For each purchase, there is a constant ordering cost. For each order, delay cost will be incurred if it is not fulfilled timely. Generally, the more frequent the replenishment, the higher the ordering cost but the lower the delay cost. Consequently, there is a tradeoff between the ordering cost and the delay cost for the seller to make replenishment decisions minimising the total cost. In this paper, we study three cases of the problem and investigate both offline versions and online versions according to the seller's knowledge about information of future orders. For offline versions with perfect information, we either develop an optimal policy, or prove it is NP-hard and develop an approximation policy. For online versions without any information about future orders, from the perspective of competitive analysis we prove the lower bound of competitive ratio for any possible online policy and present a 10-competitive online policy for the general case and a 2-competitive online policy for each of two special cases. [ABSTRACT FROM AUTHOR]

In this article, the Kriging surrogate model is proposed to accelerate the model-assisted probability of detection (MAPoD) analysis for eddy current nondestructive testing (NDT). The Kriging surrogate model is the key for enabling the efficient MAPoD analysis, considering huge number of uncertainties propagate in the eddy current NDT system, by replacing the time-consuming physical model. To generate the model responses of NDT system, a precise physical model based on the adaptive cross approximation algorithm accelerated boundary element method (BEM) is applied. In the numerical case, the MAPoD study of eddy current for detecting surface flaws in the conducting plate is analyzed. By comparing the PoD metrics achieved by the pure physical model and by the Kriging surrogate model, the accuracy and efficiency of the proposed surrogate model are demonstrated. [ABSTRACT FROM AUTHOR]

Selecting appropriate inputs for systems described by complex networks is an important but difficult problem that largely remains open in the field of control of networks. Recent work has proposed two methods for energy efficient input selection; a gradient-based heuristic and a greedy approximation algorithm. We propose here an alternative method for input selection based on the analytic solution of the controllability Gramian of the 'balloon graph', a special model graph that captures the role of both distance and redundant paths between a driver node and a target node. The method presented is especially applicable for large networks where one is interested in controlling only a small number of outputs, or target nodes, for which current methods may not be practical because they require computing a typically very ill-conditioned matrix, called the controllability Gramian. Our method produces comparable results to the previous methods while being more computational efficient. [ABSTRACT FROM AUTHOR]

Set-valued optimization using the set approach is a research topic of high interest due to its practical relevance and numerous interdependencies to other fields of optimization. However, it is a very difficult task to solve these optimization problems even for specific cases. In this paper, we study set-valued optimization problems and develop a multiobjective optimization problem that is strongly related to it. We prove that the set of weakly minimal solutions of this subproblem is closely related to the set of weakly minimal elements of the set-valued optimization problem and that these sets can get arbitrarily close in a certain sense. Subsequently, we introduce a concept of approximations of the solution set of the set-valued optimization problem. We define a quality measure in the image space that can be used to compare finite approximations of this kind and outline a procedure to enhance a given approximation. We conclude the paper with some numerical examples. [ABSTRACT FROM AUTHOR]

Sliced inverse regression (SIR) is a recommended method to identify and estimate the central dimension reduction (CDR) subspace. CDR subspace is at the base to describe the conditional distribution of the response Y given a d-dimensional predictor vector X. To estimate this space, two versions are very popular: the slice version and the kernel version. A recursive method of the slice version has already been the subject of a systematic study. In this paper, we propose to study the kernel version. It's a recursive method based on a stochastic approximation algorithm of the kernel version. The asymptotic normality of the proposed estimator is also proved. A simulation study that not only shows the good numerical performance of the proposed estimate and which also allows to evaluate its performance with respect to existing methods is presented. A real dataset is also used to illustrate the approach. [ABSTRACT FROM AUTHOR]

This study addresses the scheduling problem of two identical parallel machines with the objective of minimizing the total completion time under the machine availability constraints. To the best of our knowledge, this study is the first to develop a fully polynomial-time approximation scheme (FPTAS), a solution method which has been neglected in past studies, to solve the studied problem. The FPTAS, which is based on a dynamic programming algorithm is developed by applying a trimming-the-state-space approach. Theoretical proofs of the error bound and the time complexity for the proposed FPTAS are also provided. The computational results indicate that the proposed FPTAS performs more efficiently than a dynamic programming algorithm in terms of both run time and problem size. The error bound of the FPTAS is demonstrated to be within the pre-specified error bound. [ABSTRACT FROM AUTHOR]

Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex constraints. Such Pareto frontiers are composed of patches of solutions with shared assignments for the discrete variables. By adaptively creating such a patchwork, our algorithm is able to create approximations that converge quickly to the true Pareto frontier. As a quality measure, we use the difference in hypervolume between the approximation and the true Pareto frontier. At least a certain number of patches is required to obtain an approximation with a given quality. This patch complexity gives a lower bound on the number of required computations. We show that our algorithm performs a number of optimization steps that are of a similar order as this lower bound. We provide an efficient MIP-based implementation of this algorithm. The efficiency of our algorithm is illustrated with numerical results showing that our algorithm has a strong theoretical performance guarantee while being competitive with other state-of-the-art approaches in practice. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extension of the generalized class of recursive regression estimators to the case of strong mixing data. Then, we study the properties of these estimators and compare them with the well known Nadaraya-Watson estimator. The Bias, variance and Mean Integrated Square Error are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that the proposed recursive estimators allowed us to obtain quite better results compared to the non-recursive regression estimator under α-mixing condition in terms of estimation error and much better in terms of computational costs. [ABSTRACT FROM AUTHOR]

This paper introduces a general area-level model-based formulation to small area estimation based on generalized linear mixed models. By applying an optimization algorithm to the Laplace approximation of the likelihood, the maximum likelihood estimators of the model parameters are calculated. Empirical best predictors of small area quantities are derived and the corresponding mean squared errors are estimated by parametric bootstrap. Some simulation experiments are carried out to study the behavior of the fitting algorithm, the small area predictors and the estimators of the mean squared errors. By using data of the Spanish living condition survey of 2008, an application to the estimation of average annual net incomes in Spanish provinces by sex is given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel dual active-set algorithm that is based on proximal gradient and semi-smooth Newton iterations for the sparse approximation of correlation matrices in the Frobenius norm. A new dual formulation with upper and lower bounds is derived. To solve the dual, the proximal gradient method is developed to guarantee global convergence. Also, it provides information to estimate active/inactive constraints. Then, the semi-smooth Newton method is applied to accelerate the convergence of the proximal gradient method, which is the key ingredient of our algorithm. It is shown that the proposed algorithm for the dual is globally convergent under certain conditions. Some preliminary numerical results are given to illustrate the effectiveness of our algorithm on synthetic and real data sets. [ABSTRACT FROM AUTHOR]

We study a single-machine scheduling problem in a flexible framework, where both job processing times and due dates are decision variables to be determined by the scheduler. We consider the case where each of the job processing times is a convex decreasing function of the amount of non-renewable resource that is allocated to the corresponding processing operation. Moreover, we consider two of the more common due-date assignment methods. For each of the methods, our objective is to find a solution minimising the total resource consumption cost, given an upper bound on the value of the weighted number of tardy jobs plus due date assignment costs. Since the problem is known to be -hard, we focus on designing approximation algorithms. [ABSTRACT FROM AUTHOR]

In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness is illustrated by solving a collection of multiobjective test problems. [ABSTRACT FROM AUTHOR]

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, where we typically assume the network data are generated from a stochastic block model that is not necessarily of full rank. To do this, we first use the recently developed sketching algorithms to obtain two randomized spectral clustering algorithms, namely, the random projection-based and the random sampling-based spectral clustering. Then we study the theoretical bounds of the resulting algorithms in terms of the approximation error for the population adjacency matrix, the misclassification error, and the estimation error for the link probability matrix. It turns out that, under mild conditions, the randomized spectral clustering algorithms lead to the same theoretical bounds as those of the original spectral clustering algorithm. We also extend the results to degree-corrected stochastic block models. Numerical experiments support our theoretical findings and show the efficiency of randomized methods. A new R package called Rclust is developed and made available to the public. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set. [ABSTRACT FROM AUTHOR]

The correlational structure of a set of variables is often conveniently described by the pairwise partial correlations as they contain the same information as the Pearson correlations with the advantage of straightforward identifications of conditional linear independence. For mathematical convenience, multiple matrix representations of the pairwise partial correlations exist in the literature but their properties have not been investigated thoroughly. In this paper, we derive necessary and sufficient conditions for the eigenvalues of differently defined partial correlation matrices so that the correlation structure is a valid one. Equipped with these conditions, we will then emphasize the intricacies of algorithmic generations of correlation structures via partial correlation matrices. Furthermore, we examine the space of valid partial correlation structures and juxtapose it with the space of valid Pearson correlation structures. As these spaces turn out to be equal in volume for every dimension and equivalent with respect to rotation, a simple formula allows the creation of valid partial correlation matrices by the use of current algorithms for the generation and approximation of correlation matrices. Lastly, we derive simple conditions on the partial correlations for frequently assumed sparse structures. [ABSTRACT FROM AUTHOR]

We develop a real-time anomaly detection method for directed activity on large, sparse networks. We model the propensity for future activity using a dynamic logistic model with interaction terms for sender- and receiver-specific latent factors in addition to sender- and receiver-specific popularity scores; deviations from this underlying model constitute potential anomalies. Latent nodal attributes are estimated via a variational Bayesian approach and may change over time, representing natural shifts in network activity. Estimation is augmented with a case-control approximation to take advantage of the sparsity of the network and reduces computational complexity from O (N 2) to O(E), where N is the number of nodes and E is the number of observed edges. We run our algorithm on network event records collected from an enterprise network of over 25,000 computers and are able to identify a red team attack with half the detection rate required of the model without latent interaction terms. [ABSTRACT FROM AUTHOR]

In order to enhance the calculation efficiency of steady-state incompressible fluid flow, based on the existing IDEAL (i.e. the inner doubly iterative efficient algorithm for linked equations) algorithm, a novel segregated pressure-based algorithm (named as IDEALC) has been developed in this paper. The novel algorithm inherits the superiorities of the original IDEAL algorithm and at the same time improves its potential shortcomings. The specific promotions of the IDEALC algorithm consist of three aspects, including the first approximation of the SIMPLE algorithm, the approach to solving the momentum equation and the second approximation of the SIMPLE algorithm. Detailed comparisons between the IDEAL and the IDEALC algorithms are carried out by three numerical experiments on structured collocated grids. The numerical results demonstrate that the IDEALC algorithm can accurately predict the information of the flow field and has substantial advantages over the IDEAL algorithm in terms of the efficiency because of the consistent property of the former. The superiority of the IDEALC algorithm over the IDEAL algorithm is especially remarkable when the time step multiplier gets a moderate value. [ABSTRACT FROM AUTHOR]

A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding Lévy areas driven by a multidimensional Brownian motion is proposed. The algorithm is based on a truncated Fourier series approach. However, the approximation of the remainder terms differs from the approach considered by Wiktorsson (2001). As the main advantage, the presented algorithm makes use of a diagonal covariance matrix for the approximation of one part of the remainder term and has a higher accuracy due to an exact approximation of the other part of the remainder. This results in a significant reduction of the computational cost compared to, e.g., the algorithm introduced by Wiktorsson. Convergence in L p (Ω) -norm with p ≥ 2 for the approximations calculated with the new algorithm as well as for approximations calculated by the basic truncated Fourier series algorithm is proved and the efficiency of the new algorithm is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the classical and Bayesian estimation procedures for stress–strength reliability parameter (SSRP) have been considered based on two independent adaptive Type II progressive hybrid censored samples from inverted exponentiated Rayleigh distributions with different shape parameters. The maximum likelihood estimate of SSRP and its asymptotic confidence interval are attained. The Bayes estimate of SSRP is obtained under two loss functions using the Lindley's approximation and Metropolis–Hastings algorithm. The highest posterior density credible interval is successively constructed. The behavior of suggested estimators is assessed using a simulation study. Finally, the droplet splashing data under two surface wettabilities are considered to illustrate the application of the stress–strength reliability model to the engineering data. [ABSTRACT FROM AUTHOR]

Nonlinear equations are usually solved numerically. However, approximated analytical solutions of nonlinear equations are useful as an initial iteration point for numerical methods. Furthermore, these analytical approximations are sometimes quite close to the actual root. In order to teach at undergraduate level how to perform this kind of approximation, we propose problem-based learning with some nonlinear equations extracted from Applied Sciences. We also present a simple method to analytically solve nonlinear equations which are not solvable by standard computer algebra solvers. [ABSTRACT FROM AUTHOR]

In this paper, the application of randomized projection functional algorithms for numerical approximation of solutions of Fredholm equations of the second kind is discussed. Special attention is paid to the problems of numerical stability of the used orthonormal functional bases. The numerical instability of the randomized projection functional algorithm is noticed for the simple test one-dimensional equation and for the Hermite orthonormal basis. [ABSTRACT FROM AUTHOR]

The garment industry, which is traditionally labour-intensive, is facing significant challenges to reduce production costs in the face of material, labour, and infrastructure maintenance cost increases. To address this challenge, various aspects of smart factory-related technologies are being adopted by the garment industry. In this study, we introduce a production line simulation approach based on real-time power monitoring data in the form of garment production workers' individual task times. Power consumption data for workers' sewing machines are collected using ICT-based power monitoring devices, and the data are transmitted to a cloud server through a wireless network and processed by an approximation algorithm to extract accurate task time. Power monitoring data are then used as inputs to a discrete-event simulation model to measure the overall productivity, individual productivity, and other key performance indices critical to the garment production line. The simulation results were 18.8% more accurate than the results obtained by the garment production line using a conventional approach. This study demonstrates the potential of smart factory-related technologies and how they can be implemented in different types of industries, such as the garment production industry. [ABSTRACT FROM AUTHOR]

A rough volatility model contains a stochastic Volterra integral with a weakly singular kernel. The classical Euler-Maruyama algorithm is not very efficient for simulating this kind of model because one needs to keep records of all the past path-values and thus the computational complexity is too large. This paper develops a fast two-step iteration algorithm using an approximation of the weakly singular kernel with a sum of exponential functions. Compared to the Euler-Maruyama algorithm, the complexity of the fast algorithm is reduced from O (N 2) to O (N log ⁡ N) or O (N log 2 ⁡ N) for simulating one path, where N is the number of time steps. Further, the fast algorithm is developed to simulate rough Heston models with (or without) regime switching, and multi-factor approximation algorithms are also studied and compared. The convergence rates of the Euler-Maruyama algorithm and the fast algorithm are proved. A number of numerical examples are carried out to confirm the high efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The objective is to study the existence and uniqueness questions for a nonlinear Volterra-Fredholm integro-differential equation, then, develop a numerical approach using the Nyström method coupled with successive approximations algorithm. A numerical example is presented to examine the efficiency of the proposed method according to the existence and uniqueness conditions. [ABSTRACT FROM AUTHOR]

For a graph G = (V , E) , a double Roman dominating function (DRDF) is a function f : V → { 0 , 1 , 2 , 3 } having the property that if f (v) = 0 , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with f (u) = 3 , and if f (v) = 1 , then vertex v must have at least one neighbour u with f (u) ≥ 2. In this paper, we consider the double Roman domination problem, which is an optimization problem of finding the DRDF f such that ∑ v ∈ V f (v) is minimum. We propose five integer linear programming (ILP) formulations and one mixed integer linear programming formulation with polynomial number of constraints for this problem. Some additional valid inequalities and bounds are also proposed for some of these formulations. Further, we prove that the first four models indeed solve the double Roman domination problem, and the last two models are equivalent to the others regardless of the variable relaxation or usage of a smaller number of constraints and variables. Additionally, we use one ILP formulation to give an H (2 (Δ + 1)) -approximation algorithm. All proposed formulations and approximation algorithm are evaluated on randomly generated graphs to compare the performance. [ABSTRACT FROM AUTHOR]

The covariance matrix reconstruction based robust adaptive beamforming (RAB) methods overcome the performance degradation due to the imprecise knowledge of the steering vector and the covariance matrix. However, high complexity limits the application of them. In this paper, we proposed a new RAB method based on interference plus noise covariance (INC) matrix reconstruction and desired signal steering vector estimation. In this method, nominal interference steering vectors are estimated by the Capon spatial spectrum, as well as noise power. Subsequently, the iterative mismatch approximation algorithm based on maximizing the beamformer output power is proposed to estimate all the incident signal steering vectors and powers, and the INC matrix is reconstructed. Finally, the beamformer is determined by the estimated INC matrix and desired signal steering vector. Simulation results indicate that the proposed method obtains better performance than other existed methods at both the high signal to noise ratio (SNR) and the complexity. [ABSTRACT FROM AUTHOR]

In this article, we aim to solve Bayesian Risk Optimization (BRO), which is a recently proposed framework that formulates simulation optimization under input uncertainty. In order to efficiently solve the BRO problem, we derive nested stochastic gradient estimators and propose corresponding stochastic approximation algorithms. We show that our gradient estimators are asymptotically unbiased and consistent, and that the algorithms converge asymptotically. We demonstrate the empirical performance of the algorithms on a two-sided market model. Our estimators are of independent interest in extending the literature of stochastic gradient estimation to the case of nested risk measures. [ABSTRACT FROM AUTHOR]

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set. [ABSTRACT FROM AUTHOR]

The problem of minimizing the makespan on parallel identical machines is considered in the presence of additional resources, provided that some jobs at any time of their processing require one unit of a particular resource. We establish a lower bound on the worst-case performance of any group technology algorithm, which schedules the composite jobs formed of the original jobs that require the same resource. A simple group technology algorithm is given such that in the worst case no group technology algorithm performs better. An algorithm for the two-machine case is presented which guarantees a tight worst-case performance ratio of 6/5. [ABSTRACT FROM AUTHOR]

Integration of production and distribution operations at the scheduling level is one of the most important issues concerned in recent years in supply chain management. We investigate the scheduling problem with job delivery coordination. Concretely, we are given a set of jobs with non-identical processing times and non-identical sizes to be first processed by two parallel-identical machines and then delivered to a common customer by a single vehicle, which has a limited capacity that can carry up to a fixed total size of jobs in one batch. The objective is to minimize the makespan, ie, the time when all the jobs have reached the customer and the delivery vehicle has returned to the machine. The problem does not admit a polynomial time approximation algorithm with worst-case ratio smaller than 3 2 unless P = NP. By introducing some novel ideas and new methods, including algorithms solving multiple knapsack problem as subprocedures and the rediscovery of the profound nature of the bin-packing algorithm, we propose a polynomial time approximation algorithm with worst-case ratio arbitrary close to 3 2 . The algorithm, acquired after long-term research containing many earlier related works, is the first algorithm for this kind of problems and its theoretical performance is nearly best. [ABSTRACT FROM AUTHOR]

We develop several deep learning algorithms for approximating families of parametric PDE solutions. The proposed algorithms approximate solutions together with their gradients, which in the context of mathematical finance means that the derivative prices and hedging strategies are computed simultaneously. Having approximated the gradient of the solution, one can combine it with a Monte Carlo simulation to remove the bias in the deep network approximation of the PDE solution (derivative price). This is achieved by leveraging the Martingale Representation Theorem and combining the Monte Carlo simulation with the neural network. The resulting algorithm is robust with respect to the quality of the neural network approximation and consequently can be used as a black box in case only limited a-priori information about the underlying problem is available. We believe this is important as neural network-based algorithms often require fair amount of tuning to produce satisfactory results. The methods are empirically shown to work for high-dimensional problems (e.g., 100 dimensions). We provide diagnostics that shed light on appropriate network architectures. [ABSTRACT FROM AUTHOR]

We consider the following optimisation problem that we encountered during the consolidation process of trains in a container transhipment terminal as well as in the intermediate storage of containers in sea ports in order to accelerate the loading and unloading of the vessels. There arenordered pairs of points in them-dimensional metric space:. The problem is to find a permutationof numbersminimising the functionwhereis the metric of the space. The problem can be considered as a special case of the asymmetric travelling salesman problem. As for Euclidean, Manhattan and Chebyshev metric the problem is NP-hard (as a generalisation of the well-known TSP problem) we propose the simple approximation algorithm with the approximation guarantee equal to 3. The approximation guarantee is tight as will be shown by a sequence of instances for which the approximation ratio converges to 3. [ABSTRACT FROM AUTHOR]