多元$t$分布数据的局部影响分析

对于多元$t$分布数据, 直接应用其概率密度进行影响分析是困难的\bd 本文通过引入服从Gamma分布的权重, 将其表示为特定多元正态分布的混合\bd 在此基础上, 进而将权重视为缺失数据, 引入EM算法; 从而利用基于完全数据似然函数的条件期望进行局部影响分析\bd 本文进一步系统研究了加权扰动模型下的局部影响分析, 得到了相应的诊断统计量; 并通过两个实例说明了这种方法的有效性.     

单纯形分布非线性模型的局部影响分析及其应用

讨论了单纯形分布非线性模型的局部影响分析问题.应用Cook(1986)的影响曲率方法研究了该模型关于微小扰动的局部影响,得到了局部影响分析的曲率度量.同时也应用PoonW Y和Poon Y S(1997)的保形法曲率方法研究了该模型的局部影响.对常见的扰动模型,分别进行了局部影响分析,得到了计算影响矩阵的简洁公式.最后还研究了两个实例,说明文中方法的应用价值.     

Assessing Local Influence in Canonical Correlation Analysis

The first order local influence approach is adopted in this paper to assess the local influence of observations to canonical correlation coefficients, canonical vectors and several relevant test statistics in canonical correlation analysis. This approach can detect different aspects of influence due to different perturbation schemes. In this paper, we consider two different kinds, namely, the additive perturbation scheme and the case-weights perturbation scheme. It is found that, under the additive perturbation scheme, the influence analysis of any canonical correlation coefficient can be simplified to just observing two predicted residuals. To do the influence analysis for canonical vectors, a scale invariant norm is proposed. Furthermore, by choosing proper perturbation scales on different variables, we can compare the different influential effects of perturbations on different variables under the additive perturbation scheme. An example is presented to illustrate the effectiveness of the first order local influence approach.     

ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE ANALYSIS

ＡＳＳＥＳＳＭＥＮＴＯＦＬＯＣＡＬＩＮＦＬＵＥＮＣＥＩＮＭＵＬＴＩＶＡＲＩＡＴＥＡＮＡＬＹＳＩＳ￥（石磊，王学仁）ＳｈｉＬｅｉ；ＷａｎｇＸｕｅｒｅｎ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓｏｆＹｕｎｎａｎＰｒｏｖｉｎｃｅＤｅｐａｒ...     

Perturbation Sensitivity and Limit Loads of Shells

The perturbation sensitivity and its influence on the limit loads of shells are widely discussed phenomena. Both phenomena may be classified with respect to the type of perturbation. As perturbations influence the stability of shells, the identification of unfavourable perturbations is essential. The perturbation energy concept enables to identify unfavourable non–initial perturbation loads and to evaluate the perturbation sensitivity of fundamental states by the perturbation energy. This measure is also the basis for a load–level–specific optimisation of the perturbation sensitivity. Hence, the present paper discusses primarily the perturbation sensitivity of axially loaded cylindrical shells with different boundary conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of variable viscosity and viscous dissipation on the Hagen‐Poiseuille flow and entropy generation

In this article, the steady‐state flow of a Hagen‐Poiseuille modelin a circular pipe is considered and entropy generation due tofluid friction and heat transfer is examined. Because of variationin fluid viscosity, the entropy generation in the flow varies. Inhis model, Arrhenius law is applied for temperature equation‐dependent viscosity, and the influence of viscosity parameters on the entropy generation number and distribution of temperature and velocity is investigated. The governing momentum and energy equations, which are coupled due to the dissipative term in the energy equation, were solved by analytical techniques. The solutions of equations via perturbation method and homotopy perturbation method are obtained and then compared with those of numerical solutions. It is found that the fluid viscosity influences considerably the temperature distribution in the fluid close to the pipe wall, and increasing pipe wall temperature enhances the rate of entropy generation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 529–540, 2011     

On computation of the steady-state probability distribution of probabilistic Boolean networks with gene perturbation

Given a Probabilistic Boolean Network (PBN), an important problem is to study its steady-state probability distribution for network analysis. In this paper, we present a new perturbation bound of the steady-state probability distribution of PBNs with gene perturbation. The main contribution of our results is that this new bound is established without additional condition required by the existing method. The other contribution of this paper is to propose a fast algorithm based on the special structure of a transition probability matrix of PBNs with gene perturbation to compute its steady-state probability distribution. Experimental results are given to demonstrate the effectiveness of the new bound, and the efficiency of the proposed method.     

The new Neyman type A beta Weibull model with long-term survivors

For the first time, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the Neyman type A distribution and the time to this event has the beta Weibull distribution. This new model can be used to analyze survival data when the hazard rate function is increasing, decreasing, bathtub or unimodal-shaped. It includes some commonly used lifetime distributions and some well-known cure rate models as special cases. Maximum likelihood and non-parametric bootstrap are used to estimate the regression parameters. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. The usefulness of the new model is illustrated by means of an application in the medical area.     

圆截面螺旋管道内非定常流动研究

以血液流动为背景,利用双参数摄动法研究了圆截面螺旋管内低频振荡流动,得到问题的二阶摄动解,分析了轴向速度、二次流、壁面剪应力在不同时刻的特点及随时间和Womersley数的变化情况。研究表明:挠率对圆截面曲线管道内低频振荡流动的影响不可忽略,尤其是轴向压力梯度绝对值很小时,挠率将对二次流动结构起主要影响作用。流函数的剧烈变化只发生在正、负数值发生转变的很小的时间段内,大部分时间段内变化平缓。壁面剪应力随θ的变化也很大。     

Analysis of stresses in an infinite elastic body with a locally curved covered nanofiber

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for determining the stress distribution in nanocomposites with unidirectional locally curved covered nanofibers is used to investigate the normal stresses acting along nanofibers. The investigation is carried out for an infinite elastic body containing a single locally curved covered nanofiber in the case where there exists a bond covering cylinder of constant thickness between the nanofiber and the matrix material. It is assumed that the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. Upon formulation and mathematical solution of the boundary value problem, the boundary form perturbation method is used. Numerical results for the stress distribution in the body and the influence of geometrical nonlinearity on this distribution are presented and interpreted.     

On non-Newtonian lubrication with the upper convected Maxwell model

A long-standing theoretical and practical problem, whether the viscoelasticity can have a measurable and beneficial effect on lubrication performance characteristics, is readdressed in this paper. The upper convected Maxwell model is chosen to study the influence of viscoelasticity on lubricant thin film flows. By employing characteristic lubricant relaxation times in an order of magnitude analysis, a perturbation method is developed for analysing the flow of a Maxwell lubricant between two narrow surfaces. The effect of viscoelasticity on the lubricant velocity and pressure is examined, and the influence of minimum film thickness on lubrication characteristics is investigated. An order of magnitude analysis reveals that the pressure distribution is significantly affected by the presence of fluid viscoelasticity when the minimum film thickness is sufficiently small. This mechanism suggests that viscoelasticity does indeed enhance the lubricant pressure field and produce a beneficial effect on lubrication performance, which is consistent with some experimental observations.     

Perturbation models

A Markov chain (with a discrete state space and a continuous parameter) is perturbed by forcing a chain to return to “permissible” states whenever it happens to enter “forbidden” states, with returns governed by a replacement distribution.The compensation method is employed to obtain the distribution for the modified chain, in terms of the original chain and the perturbation mechanism.Emphasis is placed on ergodic chains, and interpretation of results in terms of perturbation theory of semi-groups and the ergodic potential theory (based on the fundamental matrix of a chain) is mentioned.     

一般形式下的协方差分析模型的局部影响分析

利用局部影响的方法对一般形式下的协方差分析模型进行了讨论.把数据点或数据子集的扰动拓展到更广泛的扰动模式并进行了局部影响评价,导出了一般形式下的协方差分析模型在方差扰动下局部影响的曲率度量.     

A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations

Modeling genetic regulatory interactions is an important issue in systems biology. Probabilistic Boolean networks (PBNs) have been proved to be a useful tool for the task. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution involves the construction of the transition probability matrix of the PBN. The size of the transition probability matrix is 2ⁿ×2ⁿ where n is the number of genes. Although given the number of genes and the perturbation probability in a perturbed PBN, the perturbation matrix is the same for different PBNs, the storage requirement for this matrix is huge if the number of genes is large. Thus an important issue is developing computational methods from the perturbation point of view. In this paper, we analyze and estimate the steady-state probability distribution of a PBN with gene perturbations. We first analyze the perturbation matrix. We then give a perturbation matrix analysis for the captured PBN problem and propose a method for computing the steady-state probability distribution. An approximation method with error analysis is then given for further reducing the computational complexity. Numerical experiments are given to demonstrate the efficiency of the proposed methods.     

LOCAL INFLUENCE ASSESSMENT BASED ON LOCAL DIVERGENCE IN STOCHASTIC REGRESSION MODEL

Abstract. This paper describes the local influence assessment for parameter inferenceof a statistlcual model by using curvatures assoclated with Iota| divergence under ageneric perturbatlon scheme. The results are applied to examine the local influence instochastlc regresslon model under two perturbation schemes. An economic examp|e isanalyzed to ~llustrate results here.     

Quantitative stability analysis of optimal solutions in PDE-constrained optimization

PDE-constrained optimization problems under the influence of perturbation parameters are considered. A quantitative stability analysis for local optimal solutions is performed. The perturbation directions of greatest impact on an observed quantity are characterized using the singular value decomposition of a certain linear operator. An efficient numerical method is proposed to compute a partial singular value decomposition for discretized problems, with an emphasis on infinite-dimensional parameter and observation spaces. Numerical examples are provided.     

The reverse effects of random perturbation on discrete systems for single and multiple population models

The natural species are likely to present several interesting and complex phenomena under random perturbations, which have been confirmed by simple mathematical models. The important questions are: how the random perturbations influence the dynamics of the discrete population models with multiple steady states or multiple species interactions? and is there any different effects for single species and multiple species models with random perturbation? To address those interesting questions, we have proposed the discrete single species model with two stable equilibria and the host-parasitoid model with Holling type functional response functions to address how the random perturbation affects the dynamics. The main results indicate that the random perturbation does not change the number of blurred orbits of the single species model with two stable steady states compared with results for the classical Ricker model with same random perturbation, but it can strength the stability. However, extensive numerical investigations depict that the random perturbation does not influence the complexities of the host-parasitoid models compared with the results for the models without perturbation, while it does increase the period of periodic orbits doubly. All those confirm that the random perturbation has a reverse effect on the dynamics of the discrete single and multiple population models, which could be applied in reality including pest control and resources management.     

Hybrid stress finite element formulation based on additional internal displacements – application of microscopic geometric perturbation and extension to linear dynamics

Based on the variational principle for hybrid stress finite element method, the assumed stress distribution can be determined through a variational process which includes a microscopic geometric perturbation. An interpretation of such geometric perturbation is discussed. For the creation of, what is called, hyper-bioelement and for the purpose of maintaining invariance, tensor notations of the physical quantities are represented by the use of covariant and contravariant basis vectors of the natural coordinate system. This process is illustrated by a simple 4-node plane element. Furthermore, based on the legitimate variational principle for linear dynamics and the presently proposed method to choose the assumed stress distribution, the finite element formulation different from the ordinary formula is advocated.     

复合载荷下圆薄板的大挠度问题

本文引入载荷分布函数使复合载荷依单参数变化,并选取平均挠角作为单一的位移摄动参数,给出了在均布载荷和中心集中力联合作用下边缘固定夹紧的圆薄板大挠度问题的摄动解,并讨论了中心点挠度为零的特殊情况.     

具有均匀结构的多元$t$\,-模型的局部影响分析

本文研究具有均匀结构的多元$t$\,-模型的局部影响分析问题\bd 依据Cook的曲率度量, 我们考虑了微小扰动对统计推断的影响, 由此导出了局部影响分析中最为关心的统计量---最大曲率方向\bd作为一种应用, 本文还祥细讨论了常见的协方差加权扰动形式.