Toeplitz矩阵填充的四种流形逼近算法比较

 本文提出Toeplitz矩阵填充的四种流形逼近算法。在左奇异向量空间中对已知部分运用最小二乘法逼近,形成新的可行矩阵;并将对角线上的元素分别用均值,l₁范数,l_∞范数和中间数四种方法逼近使得迭代后的矩阵仍保持Toeplitz结构,节约了奇异向量空间的分解时间。最终找到合理的低秩矩阵来逼近未知的高秩矩阵,进而精确地完成Toeplitz矩阵的填充。理论上,分析了在一定条件下算法的收敛性。实验上,通过取不同的采样密度进行数值实验展示了四种算法的优劣。实验结果说明均值算法和l_∞范数算法大多用的时间较少,但是当采样密度和矩阵规模较大时,中间数算法的精度较高。     

Haar wavelet approximation for magnetohydrodynamic flow equations

This study proposes Haar wavelet (HW) approximation method for solving magnetohydrodynamic flow equations in a rectangular duct in presence of transverse external oblique magnetic field. The method is based on approximating the truncated double Haar wavelets series. Numerical solution of velocity and induced magnetic field is obtained for steady-state, fully developed, incompressible flow for a conducting fluid inside the duct. The calculations show that the accuracy of the Haar wavelet solutions is quite good even in the case of a small number of grid points. The HW approximation method may be used in a wide variety of high-order linear partial differential equations. Application of the HW approximation method showed that it is reliable, simple, fast, least computation at costs and flexible.     

Block mesh refinement for incompressible flows in curvilinear domains

A method for the solution of the Navier–Stokes equation for the prediction of flows inside domains of arbitrary shaped bounds by the use of Cartesian grids with block-refinement in space is presented. In order to avoid the complexity of the body fitted numerical grid generation procedure, we use a saw tooth method for the curvilinear geometry approximation. By using block-nested refinement, we achieved the desired geometry Cartesian approximation in order to find an accurate solution of the N–S equations. The method is applied to incompressible laminar flows and is based on a cell-centred approximation. We present the numerical simulation of the flow field for two geometries, driven cavity and stenosed tubes. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single grid algorithm. The Cartesian block refinement algorithm can be used in any complex curvilinear geometry simulation, to accomplish a reduction in memory requirements and the computational time effort.     

基于均值的Toeplitz矩阵填充的子空间算法

本文提出一种基于均值的Toeplitz矩阵填充的子空间算法.通过在左奇异向量空间中对已知元素的最小二乘逼近,形成了新的可行矩阵;并利用对角线上的均值化使得迭代后的矩阵保持Toeplitz结构,从而减少了奇异向量空间的分解时间.理论上,证明了在一定条件下该算法收敛于一个低秩的Toeplitz矩阵.通过不同已知率的矩阵填充数值实验展示了Toeplitz矩阵填充的新算法比阈值增广Lagrange乘子算法在时间上和精度上更有效.     

An Approximation Method for Improving Dynamic Network Model Fitting

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, that is, networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a nonnegligible computational burden, is much easier. This article examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail—networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.     

Empirical likelihood inference for censored median regression model via nonparametric kernel estimation

An alternative to the accelerated failure time model is to regress the median of the failure time on the covariates. In the recent years, censored median regression models have been shown to be useful for analyzing a variety of censored survival data with the robustness property. Based on missing information principle, a semiparametric inference procedure for regression parameter has been developed when censoring variable depends on continuous covariate. In order to improve the low coverage accuracy of such procedure, we apply an empirical likelihood ratio method (EL) to the model and derive the limiting distributions of the estimated and adjusted empirical likelihood ratios for the vector of regression parameter. Two kinds of EL confidence regions for the unknown vector of regression parameters are obtained accordingly. We conduct an extensive simulation study to compare the performance of the proposed methods with that normal approximation based method. The simulation results suggest that the EL methods outperform the normal approximation based method in terms of coverage probability. Finally, we make some discussions about our methods.     

Structured construction and simulation of nondeterministic stochastic activity networks

In this work we deal with nondeterministic stochastic activity networks (NDSANs). Their stochastic character results from activity durations, which are given by nonnegative continuous random variables. The nondeterministic behavior of an NDSAN is a consequence of its variable topology, based on two additional features. First, by associating choice probabilities with the immediate successors of an activity, some branches of execution are not always taken. Second, by allowing iterated executions of a group of activities according to predetermined probabilities, the number of times an activity is to be executed is not determined a priori. These properties lead to a wide variety of activity networks, capable of modelling many real situations in process engineering and project management. We describe a simple, recursively structured construction of NDSANs, which both provides a coherent syntactic mechanism to incorporate the two abovementioned nondeterminism features and allows the analytic formulation of completion time. This construction also directly gives rise to a recursive simulation algorithm for NDSANs, whose repeated execution produces an estimate of the probability distribution of the completion time of the network. We also report on real-world case studies, using the Komolgorov–Smirnov statistic for validation.     

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.     

Recursive prediction of chaotic time series

Summary Considerable progress has been made in recent years in the analysis of time series arising from chaotic systems. In particular, a variety of schemes for the short-term prediction of such time series has been developed. However, hitherto all such algorithms have used batch processing and have not been able to continuously update their estimate of the dynamics using new observations as they are made. This severely limits their usefulness in real time signal processing applications. In this paper we present a continuous update prediction scheme for chaotic time series that overcomes this difficulty. It is based on radial basis function approximation combined with a recursive least squares estimation algorithm. We test this scheme using simulated data and comment on its relationship to adaptive transversal filters, which are widely used in conventional signal processing.     

A hybrid analysis approach for finite-capacity queues with general inputs and phase type service

A new analysis method for queueing systems with general input stream and phase type service time distributions is introduced. The approach combines discrete event simulation and numerical analysis of continuous time Markov chains. Simulation is used to represent the arrival process, whereas the service process is analyzed with numerical techniques. In this way the state of the system is characterized by a probability vector rather than by a single state. The use of a distribution vector reduces the variance of result estimators such that the width of confidence intervals is often reduced compared to discrete event simulation. This, in particular, holds for measures based on rare events or states with a small probability. The analysis approach can be applied for a wide variety of result measures including stationary, transient and accumulated measures. This revised version was published online in June 2006 with corrections to the Cover Date.     

Risk minimization for atmospheric data restoration

The paper deals with filling gaps in meteorological fields aimed at weather simulation. A universal local approximation approach is described which allows us to fill gaps in meteorological fields under various conditions, and at the same time, effect time-step weather forecasts. We present results of small sample gap filling for some meteorological elements. The results are compared against those obtained with local averaging and inertia methods. Some possibilities of data restoration and prediction based on available global meteorological data are discussed.     

The arbitrary order implicit multistep schemes of exponential fitting and their applications

We develop the arbitrary order implicit multistep schemes of exponential fitting (EF) for systems of ordinary differential equations. We use an explicit EF scheme to predict an approximation, and then use an implicit EF scheme to correct this prediction. This combination is called a predictor–corrector EF method. We demonstrate the accuracy and efficiency of the new predictor–corrector methods via application to a variety of test cases and comparison with other analytical and numerical results. The numerical results show that the schemes are highly accurate and computationally efficient.     

The constrained minimum weighted sum of job completion times problem

We consider the problem of minimizing the weighted sum of job completion times on a single machine (subject to certain job weights) with an additional side constraint on the weighted sum of job completion times (with respect to different job weights). This problem is NP-hard, and we provide a polynomial time approximation scheme for this problem. Our method is based on Lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule. An earlier version of this paper appeared in the Proceedings of the 10th International IPCO Conference.     

New fuzzy models for time-cost trade-off problem

The time-cost trade-off problem is a specific type of the project scheduling problem which studies how to modify project activities so as to achieve the trade-off between the completion time and the project cost. In real projects, the trade-off between the project cost and the completion time, and the uncertainty of the environment are both considerable aspects for managers. In this paper, three new fuzzy time-cost trade-off models are proposed, in which credibility theory is applied to describe the uncertainty of activity duration times. A searching method by integrating fuzzy simulation and genetic algorithm is produced to search the quasi-optimal schedules under some decision-making criteria. The purpose of the paper is to reveal how to obtain the optimal balance of the completion time and the project cost in fuzzy environments.     

On the tail index of a heavy tailed distribution

This paper proposes some new estimators for the tail index of a heavy tailed distribution when only a few largest values are observed within blocks. These estimators are proved to be asymptotically normal under suitable conditions, and their Edgeworth expansions are obtained. Empirical likelihood method is also employed to construct confidence intervals for the tail index. The comparison for the confidence intervals based on the normal approximation and the empirical likelihood method is made in terms of coverage probability and length of the confidence intervals. The simulation study shows that the empirical likelihood method outperforms the normal approximation method.     

Optimum service capacity and demand management with price incentives

Service firms periodically face fluctuating demand levels. They incur high costs to handle peak demand and pay for under-utilized capacity during low demand periods. In this paper, we develop a mixed integer programming (MIP) model based on the real life experience of a Brazilian telecommunications firm. The model determines the optimum staffing requirements with different seniority levels for employees, as well as the distribution and balancing of workload utilizing flexibility of some customers in their service completion day. The proposed MIP uses monetary incentives to smooth the workload by redistributing some of the peak demand, thereby increasing capacity utilization. Due to the intractable nature of optimizing the proposed MIP model, we present a heuristic solution approach. The MIP model is applied to the case of the examined Brazilian Telecommunications firm. The computational work on this base case and its extensions shows that the proposed MIP model is of merit, leading to approximately seventeen percent reduction in the base case operating costs. Extensive computational work demonstrates that our heuristic provides quality solutions in very short computational times. The model can also be used to select new customers based on the workload, the revenue potential of these new customers and their flexibility in accepting alternate service completion dates. The generic structure of the proposed approach allows for its application to a wide variety of service organizations facing similar capacity and demand management challenges. Such wide applicability enhances the value of our work and its expected benefits.     

基于BP神经网络的时间序列预测问题研究

分析指出了基于标准BP神经网络的时间序列预测问题存在的不足.根据基于BP神经网络的时间序列预测问题的特点,研究给出了一种以y=x作为传递函数的时间序列预测方法,经实例验证表明,给出的以y=x作为传递函数的时间序列预测方法较基于标准BP神经网络的时间序列预测方法具有较好的结果.     

Credit contagion in a network of firms with spatial interaction

This contribution studies the effects of credit contagion on the credit risk of a portfolio of bank loans. To this aim we introduce a model that takes into account the counterparty risk in a network of interdependent firms that describes the presence of business relations among different firms. The location of the firms is simulated with probabilities computed using an entropy spatial interaction model. By means of a wide simulation analysis we investigate the behavior of the model proposed and study the effects of default contagion on the loss distribution of a portfolio of bank loans.     

Research on permutation flow shop scheduling problems with general position-dependent learning effects

Machine learning exists in many realistic scheduling situations. This study focuses on permutation flow shop scheduling problems, where the actual processing time of a job is defined by a general non-increasing function of its scheduled position, i.e., general position-dependent learning effects. The objective functions are to minimize the total completion time, the makespan, the total weighted completion time, and the total weighted discounted completion time, respectively. To solve these problems, we present approximation algorithms based on the optimal permutations for the corresponding single machine scheduling problems and analyze their worst-case error bound.     

Posterior Simulation in the Generalized Linear Mixed Model With Semiparametric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model with normal base measure, Gibbs samplingalgorithms based on the Pólya urn scheme are often used to simulate posterior draws in conjugate models (essentially, linear regression models and models for binary outcomes). In the nonconjugate case, some common problems associated with existing simulation algorithms include convergence and mixing difficulties.

This article proposes an algorithm for MDP models with exponential family likelihoods and normal base measures. The algorithm proceeds by making a Laplace approximation to the likelihood function, thereby matching the proposal with that of the Gibbs sampler. The proposal is accepted or rejected via a Metropolis-Hastings step. For conjugate MDP models, the algorithm is identical to the Gibbs sampler. The performance of the technique is investigated using a Poisson regression model with semi-parametric random effects. The algorithm performs efficiently and reliably, even in problems where large-sample results do not guarantee the success of the Laplace approximation. This is demonstrated by a simulation study where most of the count data consist of small numbers. The technique is associated with substantial benefits relative to existing methods, both in terms of convergence properties and computational cost.