Matlab在线性代数实践教学中的应用

文中论述了在线性代数教学中培养学生科学计算能力的必要性和重要性,通过把Matlab引入到定理验证、含符号变量行列式和线性方程组的教学实践,说明将线性代数理论、应用及Matlab有机结合,可以帮助学生直观地理解掌握理论知识,通过Matlab的应用掌握科学计算方法,提高学生的科学计算能力。     

曲线分形维数的数值分析方法及应用

对于一条分形曲线复杂性的分析，首先归结对其分子形维数的度量，一般文献上介绍基于典型曲线（如，Ｃａｎｔｏｒ集，Ｋｏｃｈｓｎｏｗｆｌａｃｋｅ集等）的分维计算方法，由于典型曲线可迭代生成，介绍的方法大都基于解析方法，（如计算相似比）这类方法在实际应用中有很大的局限性，文中提出一个适用于计算机的数值计算方法，对于任一具有分形特征的曲线，先进行数字化，然后采用从曲线端点开始的弦步行算法，较好地解决了实用中的     

Parallel Iterative Schemes of Linear Algebra with Application to the Stability Analysis of Solutions of Systems of Linear Differential Equations

Parallel modifications of linear iteration schemes are proposed that are used to solve systems of liner algebraic equations and to achieve the time complexity equal to T = log₂ k · O(log₂ n), where k is the number of iterations of an original scheme and n is the dimension of a system. Such schemes are extended to the case of approximate solution of systems of linear differential equations with constant coefficients. Based on them and using a program, the stability of solutions in the Lyapunov sense is analyzed.     

Application of Runge–Kutta–Rosenbrock Methods to the Analysis of Flexible Multibody Systems

Numerical integration methods are discussed for general equations of motion for multibody systems with flexible parts, which are fairly stiff, time-dependent and non-linear. A family of semi-implicit methods, which belong to the class of Runge–Kutta–Rosenbrock methods, with rather weak non-linear stability properties, are developed. These comprise methods of first, second and third order of accuracy that are A-stable and L-stable and hence introduce numerical damping and the filtering of high frequency components. It is shown, both from theory and examples, that it is generally preferable to use deformation mode coordinates to global nodal coordinates as independent variables in the formulation of the equations of motion. The methods are applied to a series of examples consisting of an elastic pendulum, a beam supported by springs, a four-bar mechanism, and a robotic manipulator with collocated control.     

Dynamic Partitioning in Linear Relation Analysis: Application to the Verification of Reactive Systems

We apply linear relation analysis (P. Cousot and N. Halbwachs, in 5th ACM Symposium on Principles of Programming Languages, POPL'78, Tucson (Arizona), January 1978; N. Halbwachs, Y.E. Proy, and P. Roumanoff, Formal Methods in System Design, Vol. 11, No. 2, pp. 157–185, 1997) to the verification of declarative synchronous programs (N. Halbwachs, Science of Computer Programming, Special Issue on SAS'94, Vol. 31, No. 1, 1998). In this approach, state partitioning plays an important role: on one hand the precision of the results highly depends on the fineness of the partitioning; on the other hand, a too much detailed partitioning may result in an exponential explosion of the analysis. In this paper, we propose to dynamically select a suitable partitioning according to the property to be proved. The presented approach is quite general and can be applied to other abstract interpretations.     

An Auto-Adaptive Multidomain Spectral Technique for Linear Stability Analysis: Application to Viscous Compressible Flows

An auto-adaptive multidomain pseudo-spectral technique is considered in order to solve the linear stability problem of viscous compressible flows. Both the locations of the interfaces and the parameters of the mappings in each subdomain are adapted by minimizing the H ² -norm of the calculated solution. Such method provides automatically—this is the key point—the best polynomial interpolation of the basic state the stability of which is studied. It turns out that the whole procedure is needed to obtain reliable results. The method is first validated against results available in the literature (both viscous incompressible and inviscid compressible Rayleigh–Taylor configurations). The efficiency of the numerical method is illustrated with results on the linear stability of the compressible viscous diffusive Rayleigh–Taylor flow where no analytical or numerical results are available. New results showing the influence of stratification, viscosity, diffusity between species and thermal diffusivity are presented.     

企业云应用演进策略多时段分析

随着云计算技术的发展,企业急需一种有效方法将原本孤立的应用系统向云平台迁移。将网络层次分析法(ANP)及其超级矩阵收敛过程应用于企业云应用演进计划制定,提出一个演进策略的多时段分析方法。通过对企业云应用体系结构的建模与仿真分析,构建ANP多属性决策模型,解析超级矩阵从初始状态到极限状态的收敛过程,挖掘各云应用系统的分时段关键性影响因素,为企业的整体演进策略提供支持。最后,通过一个案例展示多时段分析方法的具体过程,提取出相关关键因素,为企业策略的动态规划提供理论依据。     

基于谐波分析和线性光谱模型的耕地信息提取

耕地是重要的农业资源,如何利用遥感技术快速准确地提取耕地信息是目前研究的热点。利用2000年MODIS/EVI时间序列数据提取关中地区耕地资源信息。以不同地类的EVI时间序列数据年内变化差异为分类依据,采用时间序列谐波分析法对全年时间谱EVI数据进行重构分析,减少噪音对信息提取的影响。经最小噪声分离变换(MNF变换)、纯净像元指数(PPI)计算以及N维可视化工具进行人机交互选取植被、耕地、城镇和水体4种端元,基于线性光谱混合模型,获取该地区耕地资源分布信息。通过与同年1∶10万土地利用数据对比验证,本研究提取的耕地总体精度为83%。研究表明：基于时间序列谐波分析法对EVI数据进行重构,利用不同地类的特征差异,采用混合像元分解的方法,可以精确获取耕地资源定量信息。该方法可为长期、大范围、动态的耕地分布和变化遥感监测提供技术参考,同时为国土资源管理部门提供决策支持。     

结合领域知识的因子分析: 在金融风险模型上的应用

因子分析是一种在工业领域广泛使用的统计学方法. 在金融资产管理中, 因子分析通过对历史价格波动的极大似然估计推导自适应的统计学因子来生成风险模型. 与通过使用预先设定具有经济学含义的因子来生成风险模型的基本面因子模型相比, 通过因子分析生成的模型不仅更灵活, 还能发现在基本面模型中缺失的因子. 然而, 由于因子分析所生成模型中的统计学因子缺少可解释性, 因此当金融数据中存在显著噪音时容易过拟合. 针对中国股市数据的风险模型生成问题, 本文提出快速因子分析算法以及将基本面因子结合到因子分析中的挑选基本面因子的混合因子分析方法, 使风险模型同时在因子探索及模型可解释性上达到最优. 实验结果显示快速因子分析方法能够达到31倍以上的加速比, 且新混合因子分析方法能够增大人造数据集以及真实数据集上预测的对数似然估计值. 在真实数据集上, 新方法能最好够达到平均对数似然估计值12.00, 比因子分析构建模型的7.56大4.44, 并且两个算法均值差值的标准差为1.58, 表现出新方法能构建更准确的风险模型.     

Weakly Constrained Minimization: Application to the Estimation of Images and Signals Involving Constant Regions

We focus on the question of how the shape of a cost-function determines the features manifested by its local (and hence global) minimizers. Our goal is to check the possibility that the local minimizers of an unconstrained cost-function satisfy different subsets of affine constraints dependent on the data, hence the word weak. A typical example is the estimation of images and signals which are constant on some regions. We provide general conditions on cost-functions which ensure that their minimizers can satisfy weak constraints when noisy data range over an open subset. These cost-functions are non-smooth at all points satisfying the weak constraints. In contrast, the local minimizers of smooth cost-functions can almost never satisfy weak constraints. These results, obtained in a general setting, are applied to analyze the minimizers of cost-functions, composed of a data-fidelity term and a regularization term. We thus consider the effect produced by non-smooth regularization, in comparison with smooth regularization. In particular, these results explain the stair-casing effect, well known in total-variation methods. Theoretical results are illustrated using analytical examples and numerical experiments.     

异种语料融合方法基于统计的中文词法分析应用

基于统计的中文词法分析往往依赖大规模标注语料,语料的规模和质量直接影响词法分析系统的性能。高覆盖率、高质量的语料资源非常有限,而且适用于不同领域的语料往往具有不同的分词和词性标注标准,难以直接混合使用,从而导致既有资源未能充分利用,分词精度下降等问题。针对该问题,该文提出了简单有效的异种语料的自动融合方法,并通过实验验证了提案方法的有效性、较强的实用性以及对多种语料融合的可扩展性。     

Satisfaction Benchmarking and Customer Classification: An Application to the Branches of a Banking Organization

Banking services constitute a highly competitive market and indicate a representative example of customer–oriented organizations. For this reason, customer satisfaction is of vital importance, offering a quantitative measure for current and future performance of these organizations. On the other hand, classifying customers according to their satisfaction behavior may indicate different client clusters with distinctive preferences and expectations. This approach serves the development of a truly customer–focussed culture by determining a set of improvement strategies that best fit the different customer segments. In this paper, the multi–criteria method MUSA is implemented in order to measure and analyze customer satisfaction in different branches of a banking organization. These results are also used to benchmark these branches according to the provided services. Moreover, segmentation analysis is performed in order to identify the different groups of customers and estimate the homogeneity of preferences in distinct customer segments. Data are based on a pilot customer–satisfaction survey, while the most important results are focussed on the determination of the critical service dimensions.     

Application of Relational Interval Arithmetic to Computer Performance Analysis: a Survey

This paper presents a survey of the existing work in the area of interval-based performance analysis of computing systems. Intervals in performance analysis is required when uncertainties or variabilities exist in the workload parameters for the performance model of the system. Intervals are also useful for computing upper and lower bounds on system performance. Most conventional analytic models accept a set of single valued parameters and produce a single valued model output. Adaptation of these existing models to handle interval parameters require new techniques that use interval arithmetic. Experiences with relational interval arithmetic provided by a constraint logic programming language in solving a number of performance analysis problems in conventional multiprogrammed computers as well as distributed processing systems are described.     

Inclusion of Textual Documentation in the Analysis of Multidimensional Data Sets: Application to Gene Expression Data

Recently, biology has been confronted with large multidimensional gene expression data sets where the expression of thousands of genes is measured over dozens of conditions. The patterns in gene expression are frequently explained retrospectively by underlying biological principles. Here we present a method that uses text analysis to help find meaningful gene expression patterns that correlate with the underlying biology described in scientific literature. The main challenge is that the literature about an individual gene is not homogenous and may addresses many unrelated aspects of the gene. In the first part of the paper we present and evaluate the neighbor divergence per gene (NDPG) method that assigns a score to a given subgroup of genes indicating the likelihood that the genes share a biological property or function. To do this, it uses only a reference index that connects genes to documents, and a corpus including those documents. In the second part of the paper we present an approach, optimizing separating projections (OSP), to search for linear projections in gene expression data that separate functionally related groups of genes from the rest of the genes; the objective function in our search is the NDPG score of the positively projected genes. A successful search, therefore, should identify patterns in gene expression data that correlate with meaningful biology. We apply OSP to a published gene expression data set; it discovers many biologically relevant projections. Since the method requires only numerical measurements (in this case expression) about entities (genes) with textual documentation (literature), we conjecture that this method could be transferred easily to other domains. The method should be able to identify relevant patterns even if the documentation for each entity pertains to many disparate subjects that are unrelated to each other.     

The Geometer’s Angle: An Introduction to the Art and Science of Geometric Analysis

Last summer, at the Nexus 2000 conference in Ferrara, Italy, a round table discussion was initiated by Kim Williams and chaired by Carol Watts where the issues of working out the inherent problems and possible procedures required to perform geometric analysis were initially opened and addressed [Watts 2001]. I would like to carry the theme forward in this column.     

Multidisciplinary Medical Team Meetings: An Analysis of Collaborative Working with Special Attention to Timing and Teleconferencing

In this paper we describe the process of a multi-disciplinary medical team meeting (MDTM), its functions and operation in colocated and teleconference discussions. Our goal is to identify the elements and mechanics of operation that enhance or threaten the dependability of the MDTM as a “system” and propose technologies and measures to make this system more reliable. In particular, we assess the effect of adding teleconferencing to the MDTM, and identify strengths and vulnerabilities introduced into the system by the addition of teleconferencing technology. We show that, with respect to the system’s external task environment, rhythms of execution of pre-meeting and post-meeting activities are critical for MDTM success and that the extension of the MDTM to wider geographic locations with teleconferencing might disrupt such rhythms thereby posing potential threats to dependability. On the other hand, an analysis of vocalisation patterns demonstrates that despite difficulties related to coordination and awareness in video-mediated communication (evidenced by increased time spent in case discussion, longer turns, decreased turn frequency and near lack of informal exchanges) the overall case discussion structure is unaffected by the addition of teleconferencing technology into proceedings.     

An Empirical Analysis of Using Text-to-Speech Software to Revise First-Year College Students’ Essays

Traditionally, composition experts have suggested reading drafts aloud as a means of revising essays; however, the method of reading drafts aloud is severely limited by a single factor: student writers do not always read what is on the page (Hartwell, 1985). Text-to-speech (TTS) software allows students to have their essays read to them so that the limiting factor of reading their own drafts aloud becomes minimized. TTS programs read what is written on the computer screen, and the result is that the students can “hear” the problems of their essays as opposed to simply “seeing” them. Nevertheless, composition researchers have not conducted any empirical studies to determine whether or not TTS is beneficial for “local” and “global” revision, nor have any studies been conducted to determine if TTS is beneficial for students above the fifth grade. This article documents an experimental study conducted at a southwestern university in the United States with fifty-one students to determine whether or not TTS software is useful in the revision process. The results show that users of TTS were as likely as users in the control group to make proofreading changes but less inclined to make local or global changes in the revision process, indicating that TTS possibly works well for proofreading but not necessarily as well for higher-order revision. Further research is recommended to determine TTS's effectiveness during a longitudinal study as well as for auditory learners and ESL students.     

Corrigendum to the paper ‘Linear Time Varying Model Predictive Control and its Application to Active Steering Systems: Stability Analysis and Experimental Validation’ (International Journal of Robust and Nonlinear Control 2008; 18(8):862–875)

This note is a corrigendum of the paper ‘Linear Time Varying Model Predictive Control and its Application to Active Steering Systems: Stability Analysis and Experimental Validation’, published on the volume 18, issue 8, pages 862–875 of the International Journal of Robust and Nonlinear Control in 2008. Next we point out a technical error in the proof of Lemma 2 of the paper, and provide the corrected version of the lemma. Copyright © 2011 John Wiley & Sons, Ltd.     

PLATA: An Application of LEGAL, a Machine Learning Based System, to a Typology of Archaeological Ceramics

The authors here show that machine learning techniques can be used for designing an archaeological typology, at an early stage when the classes are not yet well defined. The program (LEGAL, LEarning with GAlois Lattice) is a machine learning system which uses a set of examples and counter-examples in order to discriminate between classes. Results show a good compatibility between the classes such as the yare defined by the system and the archaeological hypotheses. This revised version was published online in July 2006 with corrections to the Cover Date.     

Development of PCA-based cluster quantile regression (PCA-CQR) framework for streamflow prediction: Application to the Xiangxi river watershed,China

In this study, a PCA-based cluster quantile regression (PCA-CQR) method was proposed through integrating principal component analysis and quantile regression approaches into a stepwise cluster analysis framework. In detail, the principal component analysis was adopted to overcome the multicollinearity among the explanatory variables, while the quantile regression approach was used to provide probabilistic information in prediction. The proposed PCA-CQR method can effectively capture discrete and nonlinear relationships between explanatory and response variables. The applicability of PCA-CQR was demonstrated by a case study of monthly streamflow prediction in the Xiangxi River, China. The nonlinearity between the hydro-meteorological variables and the streamflow measurements was characterized through the measure of maximal information coefficient (MIC), which demonstrated the need of the proposed PCA-CQR method. The results showed that the previous monthly streamflow and precipitation, as well as potential evapotranspiration in current month posed significant nonlinear impacts on the streamflow in current month. Three components could well reflect the total variance of the input variables. Comparison between traditional SCA and PCA-CQR showed that the proposed approach could provide more accurate predictions than traditional SCA methods. Moreover, probabilistic forecasts could be provided by PCA-CQR, and the 90% predictive intervals could well bracket the observations in both calibration and validation periods. Also, sensitivity analysis was performed to identify the impacts of the control parameters in PCA-CQR on the performance of the proposed model. The results showed the proposed PCA-CQR improved the robustness of traditional SCA. Finally, comparison among PCA-CQR, GRNN and MLR also showed the effectiveness of the proposed method.