A procedure for parameterizing a constraint in linear programming

A post-optimal procedure for parameterizing a constraint in linear programming is proposed. In the derivation of the procedure, the technique of pivotal operations (Jordan eliminations) is applied. The procedure is compared to another by Orchard-Hays [2], and a numerical example of the procedure is provided.     

Analysis of cross classified data by AIC

Summary The purpose of the present paper is to propose a simple but practically useful procedure for the analysis of multidimensional contingency tables of survey data. By the procedure we can determine the predictor on which a specific variable has the strongest dependence and also the optimal combination of predictors. The procedure is very simply realized by the search for the minimum of the statistic AIC within a set of models proposed in this paper. The practical utility of the procedure is demonstrated by the results of some successful applications to the analysis of the survey data of the Japanese national character. The difference between the present procedure and the conventional test procedure is briefly discussed. The Institute of Statistical Mathematics     

A note on the separation of subtour elimination constraints in elementary shortest path problems

This note proposes an alternative procedure for identifying violated subtour elimination constraints (SECs) in branch-and-cut algorithms for elementary shortest path problems. The procedure is also applicable to other routing problems, such as variants of travelling salesman or shortest Hamiltonian path problems, on directed graphs. The proposed procedure is based on computing the strong components of the support graph. The procedure possesses a better worst-case time complexity than the standard way of separating SECs, which uses maximum flow algorithms, and is easier to implement.     

Construction of approximate periodic solutions to a modified van der Pol oscillator

A new iteration scheme is proposed and applied for the modified van der Pol oscillator. A simple and effective iteration procedure to search for the periodic solutions of the equation is given. This procedure is a powerful tool for the determination of the approximate frequencies and periodic solutions of the nonlinear differential equations. The solutions obtained using the present iteration procedure are in good agreement with the numerical integration obtained by a fourth order Runge–Kutta method, which shows the applicability of the procedure.     

Harmonic projection methods for large non-symmetric eigenvalue problems

The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh–Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to preconditioning methods, and to other methods for nonsymmetric eigenvalue problems that use the Rayleigh–Ritz procedure. The subject of estimating the boundary of the entire spectrum is briefly discussed, and the importance of preconditioning for interior eigenvalue problems is mentioned. © 1998 John Wiley & Sons, Ltd.     

A note on sequential estimation of the mean

A sequential procedure for estimating the population mean is proposed. The procedure is shown to have a risk less than that of the existing procedure for a certain class of distributions which depends on the skewness and the kurtosis, and includes several common distributions.     

Selecting mixed-effects models based on a generalized information criterion

The generalized information criterion (GIC) proposed by Rao and Wu [A strongly consistent procedure for model selection in a regression problem, Biometrika 76 (1989) 369-374] is a generalization of Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). In this paper, we extend the GIC to select linear mixed-effects models that are widely applied in analyzing longitudinal data. The procedure for selecting fixed effects and random effects based on the extended GIC is provided. The asymptotic behavior of the extended GIC method for selecting fixed effects is studied. We prove that, under mild conditions, the selection procedure is asymptotically loss efficient regardless of the existence of a true model and consistent if a true model exists. A simulation study is carried out to empirically evaluate the performance of the extended GIC procedure. The results from the simulation show that if the signal-to-noise ratio is moderate or high, the percentages of choosing the correct fixed effects by the GIC procedure are close to one for finite samples, while the procedure performs relatively poorly when it is used to select random effects.     

The complexity of the word problems for commutative semigroups and polynomial ideals

Any decision procedure for the word problems for commutative semigroups and polynomial deals inherently requires computational storage space growing exponentially with the size of the problem instance to which the procedure is applied. This bound is achieved by a simple procedure for the semigroup problem.     

Asymptotically efficient parameter estimation for ordinary differential equations

Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate for statistical inference. Ramsay et al. (2007) proposed a generalized profiling procedure. It is easily implementable and has been demonstrated to have encouraging numerical performance. However, little is known about statistical properties of this procedure. In this paper, we provide a theoretical justification of the generalized profiling procedure. Under some regularity conditions, the procedure is shown to be consistent for a broad range of tuning parameters. When the tuning parameters are sufficiently large, the procedure can be further shown to be asymptotically normal and efficient.     

FEASIBILITY OF THE REICH PROCEDURE IN THE DECOMPOSITION OF PLANE QUASICONFORMAL MAPPINGS

ＦＥＡＳＩＢＩＬＩＴＹＯＦＴＨＥＲＥＩＣＨＰＲＯＣＥＤＵＲＥＩＮＴＨＥＤＥＣＯＭＰＯＳＩＴＩＯＮＯＦＰＬＡＮＥＱＵＡＳＩＣＯＮＦＯＲＭＡＬＭＡＰＰＩＮＧＳ￥ＬＡＩＷＡＮＣＡＩ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＨｕａＱｉａ...     

Convergence of the arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus

The convergence of the arithmetic-geometric mean procedure is checked for complex variables. The procedure is shown to be useful for the evaluation of the complete elliptic integrals of the first and second kinds with complex modulus. It is suggested that the procedure will be useful also for the numerical calculation of the elliptic integrals and the Jacobian elliptic functions with complex modulus in general.     

Smart greedy procedure for solving a nOnlinear knapsack class of reliability optimization problems

A new heuristic procedure, which is called Smart Greedy, is proposed for solving a kind of general reliability optimization problems (non-DGR type knapsack problems). Smart Greedy uses Recursive Greedy with multiple greedy functions designated by balance coefficients, generates several solutions and then determines the best solution among them as the smart greedy solution. Recursive Greedy first checks the feasibility of sets of items for a given problem and removes infeasible items from the item sets. Second, the procedure checks the gain ratio of increments of objective function to constraint function and reduces the problem to DGR type problem by invoking LP dominance. Third, the procedure continues to allocate the increments for current items until the constraint is violated. With the current solution, the procedure then repeats the greedy procedure for current items that are added to the items removed by the LP dominance in the previous step.Computational results show that the Smart Greedy is more effective than the previously reported methods.     

An information‐based burn‐in procedure for minimally repaired items from mixed population

Burn‐in is a method used to eliminate the initial failures in field use. In this paper, we will consider an information‐based burn‐in procedure for repairable items, which is completely new type of burn‐in procedure. By this procedure, based on the operational (failure and repair) history of the items observed during burn‐in procedure, those with poor reliability performance are eliminated. From a probabilistic point of view, this burn‐in procedure utilizes the information contained in the ‘random paths’ of the corresponding point processes. A general formulation of the model will be suggested, and under the suggested framework, two‐stage optimization procedure for determining optimal burn‐in procedures will be studied in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

Autoregressive-output-analysis methods revisited

We revisit and update the autoregressive-output-analysis method for constructing a confidence interval for the steady-state mean of a simulated process by using Rissanen's predictive least-squares criterion to estimate the autoregressive order of the process. This order estimator is strongly consistent when the output is autoregressive. The order estimator is combined with the standard autoregressive-output-analysis method to form a confidence-interval procedure. Alternatives for estimating the degrees of freedom for the procedure are investigated. The main result is an asymptotically valid confidence-interval procedure that, empirically, has good small-sample properties.     

A procedure for the modeling of non-stationary time series

Summary A minimum AIC procedure for the fitting of a locally stationary autoregressive model is proposed. The least squares computation for the procedure is realized by using the Householder transformation which makes the procedure computationally more flexible and efficient than the one originally proposed by Ozaki and Tong. The Institute of Statistical Mathematics     

An efficient procedure for determining mixed-mode energy release rates in practical problems of delamination

A computationally efficient procedure is presented for the prediction of mixed-mode strain energy release rates in practical problems of delamination. In this procedure, an analytical crack tip element analysis is used for the determination of all singular field quantities. By comparison with two- and three-dimensional finite element results, the procedure is shown to be accurate for mixed-mode problems where mode I, mode II and/or mode III crack tip singularities are present. The procedure is applicable for those cases where a near-tip inverse-square-root singularity exists, as well as those where an oscillatory singularity exists. For these latter cases, an alternative approach to using oscillatory field quantities to characterize crack advance is suggested.     

分组测试与迫进控制标准

1引言 在第二次世界大战期间,珍珠港事件发生后,美国为了反击德国法西斯挑起的侵略战争,多次进行大规模的征兵活动．在征兵活动中,需要对大量报名入伍者进行健康检查,看其身体是否符合入伍的条件．其中一项健康检查的内容是血液抗体检测,通过血液抗体检测,查出梅毒的携带者．当时,由于被检测者数量巨大,部队又急需补充兵员,检测时间紧、任务重,这就需要找到一种科学的检测方法,用尽可能少的测试次数检测出所有病毒携带者,这一问题后来称为搜索坏硬币的最优化问题．在这个问题中,被检测者抽象为硬币,血液不带病毒者抽象为标准硬币,血液带病毒者抽象为伪硬币,检测的设备称为装置．如何用特定性能的若干台装置,以尽可能少的测试次数从由硬币组成的集合中检测出全部伪硬币,是一个有很强实际背景的最优化问题,正因为如此,近一段时间组合搜索中的伪硬币问题一直受到人们的广泛关注．     

有序处理连续比较的置信区间

为有序均值的连续比较提出了一个新的检验过程.他们的过程对满足简单序的均值有重要的应用价值,例如在研究增长剂量对药物效用的影响. 与其它检验过程相比(例:Hayter\ucite{4}中的检验), 其优点在于产生了更短的连续比较的置信限,从而能够提供更多机会发现在何药剂量处有不同的效用.但作为有序均值的齐性检验, 它的势表现远劣于其它检验.本文的目的是提出一检验过程在尽量保持Lee andSpurrier\ucite{8}检验的优点的同时大大地提高其势表现.     

Fixed and Random Effects Selection by REML and Pathwise Coordinate Optimization

We propose a two-stage model selection procedure for the linear mixed-effects models. The procedure consists of two steps: First, penalized restricted log-likelihood is used to select the random effects, and this is done by adopting a Newton-type algorithm. Next, the penalized log-likelihood is used to select the fixed effects via pathwise coordinate optimization to improve the computation efficiency. We prove that our procedure has the oracle properties. Both simulation studies and a real data example are carried out to examine finite sample performance of the proposed fixed and random effects selection procedure. Supplementary materials including R code used in this article and proofs for the theorems are available online.     

A proof-search procedure for intuitionistic propositional logic

A sequent root-first proof-search procedure for intuitionistic propositional logic is presented. The procedure is obtained from modified intuitionistic multi-succedent and classical sequent calculi, making use of Glivenko’s Theorem. We prove that a sequent is derivable in a standard intuitionistic multi-succedent calculus if and only if the corresponding prefixed-sequent is derivable in the procedure.