A note on a sufficient-decrease criterion for a non-derivative step-length procedure

A step-length algorithm is an essential part of many descent methods for unconstrained and constrained optimization. In this note we present a criterion that defines an acceptable step length when only function values are available at trial step lengths.This research was supported by the U.S. Department of Energy Contract DE-AC03-76SF00326, PA No. DE-AT03-76ER72018; National Science Foundation Grants MCS-7926009 and ECS-8012974; the Office of Naval Research Contract N00014-75-C-0267; and the U.S. Army Research Office Contract DAAG29-79-C-0110.     

Selections, extensions and collectionwise normality

We demonstrate that the classical Michael selection theorem for l.s.c. mappings with a collectionwise normal domain can be reduced only to compact-valued mappings modulo Dowker's extension theorem for such spaces. The idea used to achieve this reduction is also applied to get a simple direct proof of that selection theorem of Michael's. Some other possible applications are demonstrated as well.     

当方差未知时选取有最大均值总体的两阶段抽样方案

考虑ｋ个有连续分布Ｆｉ＝Ｆ（ｘ－μｉ／σ）的总体，ｉ＝１，．．．，ｋ。其中μｉ和σ均未知，我们通过两阶段抽取样本以得到最大均值的那个总体，第一步根据抽样删去一部分看来不可能的总体，第二步再从余下总体中抽样，取含样本均值最大的那个总体为所需总体，我们用渐过分布方法得到了在所定规则下能选到正确总体的概率下界。特别对Ｌｏｇｉｓｔｉｃ总体计算了有关数值以及关于一次抽样的相对效。     

<Emphasis Type="Italic">A priori</Emphasis> evaluation of the adequacy of reference materials

The concept of adequacy of reference materials (RMs) to samples under analysis is discussed. It is emphasized that effectiveness of RM as a measurement standard can depend dramatically on assessment of the RM adequacy. A score is proposed for quantitative adequacy evaluation that formalizes the existing analytical knowledge. The score is based on the comparison of the compositions and physico-chemical parameters of RM with those of a sample, choosing the parameters influencing the analytical results. The score allows us to find the most adequate RM before analysis, using RM catalogues and prior information about the sample and analytical method.     

Accuracy of energy extrapolation in multireference configuration interaction calculations

The accuracy of extrapolation procedures in conjunction with energy-based configuration selection in CI calculations is examined. The normally high accuracy of such extrapolation can deteriorate in multireference CI calculations when configuration functions of low weight are included in the root (reference) set. This is due to the inadequacy of second-order energy contribution estimates for the very large number of discarded low-contribution functions generated as single and double excitations from the minor members of the root set. The problem may be overcome by increasing the number of configurations included in the zero-order function used for the energy contribution estimation process. Illustrative results are presented for excited states of the H₂O molecule and the H₂O⁺ ion.     

Gene selection from microarray data for cancer classification--a machine learning approach

A DNA microarray can track the expression levels of thousands of genes simultaneously. Previous research has demonstrated that this technology can be useful in the classification of cancers. Cancer microarray data normally contains a small number of samples which have a large number of gene expression levels as features. To select relevant genes involved in different types of cancer remains a challenge. In order to extract useful gene information from cancer microarray data and reduce dimensionality, feature selection algorithms were systematically investigated in this study. Using a correlation-based feature selector combined with machine learning algorithms such as decision trees, nave Bayes and support vector machines, we show that classification performance at least as good as published results can be obtained on acute leukemia and diffuse large B-cell lymphoma microarray data sets. We also demonstrate that a combined use of different classification and feature selection approaches makes it possible to select relevant genes with high confidence. This is also the first paper which discusses both computational and biological evidence for the involvement of zyxin in leukaemogenesis.     

Global minimum potential energy conformations of small molecules

A global optimization algorithm is proposed for finding the global minimum potential energy conformations of small molecules. The minimization of the total potential energy is formulated on an independent set of internal coordinates involving only torsion (dihedral) angles. Analytical expressions for the Euclidean distances between non-bonded atoms, which are required for evaluating the individual pairwise potential terms, are obtained as functions of bond lengths, covalent bond angles, and torsion angles. A novel procedure for deriving convex lower bounding functions for the total potential energy function is also introduced. These underestimating functions satisfy a number of important theoretical properties. A global optimization algorithm is then proposed based on an efficient partitioning strategy which is guaranteed to attain -convergence to the global minimum potential energy configuration of a molecule through the solution of a series of nonlinear convex optimization problems. Moreover, lower and upper bounds on the total finite number of required iterations are also provided. Finally, this global optimization approach is illustrated with a number of example problems.     

Working principles,behavior, and performance of MOEAs on MNK-landscapes

This work studies the working principles, behavior, and performance of multiobjective evolutionary algorithms (MOEAs) on multiobjective epistatic fitness functions with discrete binary search spaces by using MNK-landscapes. First, we analyze the structure and some of the properties of MNK-landscapes under a multiobjective perspective by using enumeration on small landscapes. Then, we focus on the performance and behavior of MOEAs on large landscapes. We organize our study around selection, drift, mutation, and recombination, the four major and intertwined processes that drive adaptive evolution over fitness landscapes. This work clearly shows pros and cons of the main features of MOEAs, gives a valuable guide for the practitioner on how to set up his/her algorithm, enhance MOEAs, and presents useful insights on how to design more robust and efficient MOEAs.     

A selection limiter of DSMC for near continuum flows

A selection limiter for the direct simulation monte carlo (DSMC) method is proposed to simulate near continuum flows. The selection limiter is calculated according to a continuum breakdown parameter and is used to limit the number of potential collision pairs. A Couette flow, a supersonic flow into a pitot probe and a nozzle plume flow are studied and compared with the standard DSMC to validate present method. It is found that its computational cost is about 35% of that of the standard DSMC method with satisfactory accuracy in the near continuum regime.     

奖学金的评定与模糊优选数学模型

本文运用模糊数学思想 ,按照相对隶属度原则 ,通过制定各门课程之间的权重系数 ,建立了一种新的奖学金评定的模糊优选数学模型 .该模型解决了按总成绩排名评定法中所存在的一些问题 .使评定的结果更具科学性与合理性 ,同时模型可推广到其它评比当中