The Cross-Entropy Method for Continuous Multi-Extremal Optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.      

A smoothing spline based test of model adequacy in polynomial regression

For the regression model % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa% aajeaWbaGaamyAaaWcbeaakiabeccaGiabg2da9iabeccaGiaabAga% caGGOaGaamiDamaaBaaajeaWbaGaamyAaaWcbeaakiaacMcacaqGGa% Gaey4kaSIaaeiiamaavababeqcbaCaaiaadMgaaSqab0qaaiabew7a% LbaakiaabccacaGGOaGaeqyTduMaai4jaiaadohacaqGGaGaamyAai% aadMgacaWGKbGaaeiiaiaad6eacaGGOaGaam4taiaacYcacaqGGaGa% eq4Wdm3aaWbaaSqabKqaGgaacaaIYaaaaOGaaiykaiaacMcaaaa!57B9!\[y_i = {\rm{f}}(t_i ){\rm{ }} + {\rm{ }}\mathop \varepsilon \nolimits_i {\rm{ }}(\varepsilon 's{\rm{ }}iid{\rm{ }}N(O,{\rm{ }}\sigma ^2 ))\], it is proposed to test the null hypothesis that f is a polynomial of degree less than some given value m. The alternative is that f is such a polynomial plus a scale factor b ^1/2 times an (m–1)-fold integrated Wiener process. For this problem, it is shown that no uniformly (in b) most powerful test exists, but a locally (at b=0) most powerful test does exist. Derivation and calculation of the test statistic is based on smoothing spline theory. Some approximations of the null distribution of the test statistic for the locally most powerful test are described. An example using real data is shown along with a computing algorithm.This author's research was supported by the National Science Foundation under grants numbered DMS-8202560 and DMS-8603083.     

Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities

In this paper, we present a smoothing Newton-like method for solving non-linear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.     

LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

关于Hirota-Satsuma系统初值问题的局部和整体适定性

本文利用ＫＤＶ方程所对应的线性方程解所具有的光滑效应及压缩映像原理,得到了Ｈｉｒｏｔａ－Ｓａｔｓｕｍａ系统初值问题的局部和整体适定性结果．     

二维振荡叶栅非定常粘性流动数值模拟

采用显式四步Runge-Kutta格式，结合Baldwon-Lomax紊流模型求解Navier-Stokes方程，借助运动网格技术，完成了对二维振荡叶栅非定常粘性流动的数值模拟。为了加速求解过程，引入了变系数隐式残差光顺方法，取得了较好效果。数值结果与已公布的数据有很好的一致性。     

基于鲁棒双参数指数平滑法的BDS卫星钟差预报

为提高北斗(BDS)卫星钟差预报精度与稳定性,基于BDS卫星钟工作原理与数据特征,提出了一种基于鲁棒双参数指数平滑法的BDS卫星钟差预报方法.将双参数指数平滑法引入BDS钟差预报,并通过鲁棒化建模与优化初始值选取方式提升了双参数指数平滑法的抗差与适应能力,减小了数据异常干扰对钟差预报性能的影响.与常用的多项式模型、谱分析模型、灰色预测模型及超快速钟差预报产品进行对比分析,结果表明:所提方法适用于不同BDS轨道与类型的卫星钟差预报,取得了良好的预报精度与稳定性,其对 BDS 卫星钟的 6 h 平均预报精度分别提升了 40.3%、31.7%、63.6%和36.6%,预报稳定性分别提升了 43.8%、38.9%、65.4%和 33.1%.     

基于电子病历的乳腺癌群组与治疗方案可视分析

乳腺癌是当前最常见的恶性肿瘤之一,其电子病历数据可用于挖掘隐含规律,对治疗与预后分析有重要意义。通过与乳腺科医生合作,选择合适的预测模型和可视化方法,搭建了一个基于电子病历的乳腺癌群组和治疗方案可视分析系统。首先,对具有高维属性的病人进行降维和聚类处理,形成病人群组,并采用南丁格尔图、词云和时间轴可视化方法,直观展示病人群组间特征的差异;然后,用支持向量机（support vector machine,SVM）模型预测治疗方案,用平行坐标、矩阵热力图和分类图分别展示属性相关性、训练后的特征权重和预测结果;最后,用真实案例验证了系统在群组分析、治疗方案及病人属性关联分析中的有效性,从而较好地帮助医生选择合适的治疗方案。