An improved approximation for settling time of second-order linear systems

An improved approximate expression is developed for the settling time of a second-order linear system subjected to a step input. The new expression is more accurate than several existing approximate expressions. Furthermore, although it is slightly more complicated than one of the existing approximations, it is much more convenient to use than the other, which requires iteration for design application. Finally, it is noted that explicit results in dimensionless graphical form are given for the first time for the exact settling time versus damping ratio.     

Practical methods for computing power in testing the multivariate general linear hypothesis

Four test statistics are commonly used in multivariate general linear hypothesis tests such as MANOVA: Roy's largest root, Wilks' Lambda, Hotelling-Lawley trace and Pillai-Bartlett trace. Closed form, finite series expressions do not exist for the distribution functions in either the null or non-null case (except for special cases). In practice, asymptotic approximations, based on F or chi square distributions, are used for the null case. It is not widely known that similarly accurate and general approximations have been published for the non-null case, for all except the largest root [15,38].In this paper new approximations, based on noncentral F's, are provided for power for all but the largest root. These generalize existing F approximations for the central case. Much less calculation is needed than for earlier approximations and accuracy appears not to suffer in practice. An upper bound F approximation is provided for the largest root power.Power calculation can be used to help choose a test statistic as well as for experimental design. A particularly convenient method for estimating power, using standard linear models programs [20], is generalized to the multivariate case.     

Moments and root-mean-square error of the Bayesian MMSE estimator of classification error in the Gaussian model

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the root-mean-square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.     

计算优势关系粗糙集中近似集的快速算法*

优势关系粗糙集克服经典粗糙集无法处理偏序关系数据的缺陷,而减少近似集的计算时间可以提高数据处理的效率.基于此种情况,文中提出计算优势关系粗糙集中近似集的快速算法,在对象和属性同时增加时,能快速计算优势关系粗糙集的近似集.算法改进近似集相关参数的定义,通过尽可能少的参数求出近似集,简化计算过程,提高算法运算速度,节省内存.实验表明,文中算法具有较快的运算速度,尤其当数据量增大或数据类别增多时效果更明显.     

Evolutionary computation and the vega risk of American put options

While European style options and American call options can be priced using analytical exact valuation models, closed-form solutions for the valuation of American puts have not yet been derived. The American put price as well as the corresponding greeks (e.g., delta, gamma, vega) can be calculated using numerical procedures or analytical approximations. We use a parallel implementation of the genetic programming approach and derive analytical approximations for determining the vega of an American put option because calculating vegas numerically requires even more computational effort than determining deltas or gammas. Applying our approximations to experimental data sets we can show that the genetically derived approximations outperform other approximations based on frequently used American put pricing formulas.     

Variance error quantifications that are exact for finite-model order

This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of improved accuracy, this paper provides new expressions whose accuracy depends only on data length. They are therefore "exact" for arbitrarily small true model order. Other authors have recognized the importance of such expressions and have derived them for the case of finite-impulse response-like model structures in which denominators are fixed at true values and only numerator terms are estimated. This paper progresses beyond this situation to address the more general output-error and Box-Jenkins structures in which full dynamics models (both numerator and denominator terms) and noise models may be estimated. A key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed.     

On the frequency domain accuracy of closed-loop estimates

It has been argued that the frequency domain accuracy of high model-order estimates obtained on the basis of closed-loop data is largely invariant to whether direct or indirect approaches are used. The analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order, and hence are approximations when either of these are finite. However, recent work has provided variance expressions that are exact for finite (possibly low) model order, and hence can potentially deliver more accurate quantification of estimation accuracy. This paper, and a companion one, revisits the study of identification from closed-loop data in light of these new quantifications and establishes that, under certain assumptions, there can be significant differences in the accuracy of frequency response estimates. These discrepencies are established here and in the companion paper to be dependent on what type of direct, indirect or joint input-output identification strategy is pursued.     

Stochastic modeling of the NLMS algorithm for complex Gaussian input data and nonstationary environment

This paper presents a stochastic model for the normalized least-mean-square (NLMS) algorithm operating in a nonstationary environment with complex-valued Gaussian input data. To derive this model, several approximations commonly used in the modeling of algorithms with normalized step size are avoided, thus giving rise to very accurate model expressions describing the algorithm behavior in both transient and steady-state phases. Such accuracy comes mainly from the strategy used for computing the normalized autocorrelation-like matrices arising from the model development, for which analytical solutions are also derived here. In addition, based on the proposed model expressions, the impact of the algorithm parameters on its performance is discussed, clarifying the tracking properties of the NLMS algorithm in a nonstationary environment. Through simulation results, the effectiveness of the proposed model is assessed for different operating scenarios.     

Neighborhood rough sets for dynamic data mining

Approximations of a concept in rough set theory induce rules and need to update for dynamic data mining and related tasks. Most existing incremental methods based on the classical rough set model can only be used to deal with the categorical data. This paper presents a new dynamic method for incrementally updating approximations of a concept under neighborhood rough sets to deal with numerical data. A comparison of the proposed incremental method with a nonincremental method of dynamic maintenance of rough set approximations is conducted by an extensive experimental evaluation on different data sets from UCI. Experimental results show that the proposed method effectively updates approximations of a concept in practice. © 2012 Wiley Periodicals, Inc.     

Kalman filter variants in the closed skew normal setting

The filtering problem (or the dynamic data assimilation problem) is studied for linear and nonlinear systems with continuous state space and over discrete time steps. Filtering approaches based on the conjugate closed skewed normal probability density function are presented. This distribution allows additional flexibility over the usual Gaussian approximations. With linear dynamic systems the filtering problem can be solved in analytical form using expressions for the closed skew normal distribution. With nonlinear dynamic systems an ensemble-based version is proposed for fitting a closed skew normal distribution at each updating step. Numerical examples discuss various special cases of the methods.     

对称密码算法中两类线性表达式的概率优势

分析欧洲序列密码候选算法ABC的安全性,提炼出两类与安全性密切相关的具有概率优势的线性表达式。两个概率优势反映了模加法运算之间的两种线性相关性。利用每类表达式及其概率优势都可以推导出ABC算法的大量弱密钥。在弱密钥条件下,可以计算出算法的1 257 bit初始密钥,从而导致了算法的有效破解方法。第一类表达式反映了两个模加法方程普遍存在的一种线性相关性,第二类表达式反映了三个模加法方程的比特进位之间的线性相关性。其中,第二类中一个典型的表达式最初是由Wu和Preneel发现,并由此得到2~(96)个弱密钥,但他们只是通过测试试验数据得到了该表达式的概率优势估计值,并未给出严格证明。文中给出两类表达式的概率优势的严格证明。模加运算被广泛应用于对称密码的设计中,相信这两类线性表达式的概率优势不仅可以用来分析其它对称密码算法,而且对于设计安全的对称密码算法也是非常重要的。     

On the simulation of continuous non-linear filters A comparative study of second- and third-order approximations

Among several second-order approximations to the filter of a non-linear system, it is found that the extended Kalman filter is generally the most versatile. The second-order likelihood filter, also known ns the Detchmendy—Sridhar filter is inferior to the ahove and at the same time involves more computation. In the special ease when analytical expressions For the gaussian expectation integrals of the non-linearities can be found, the extended Kalman filter can be further improved by using stochastic linear approximations as suggested by Sunahara. The third-order likelihood filter derived in this paper is more accurate than the above, but calls for considerable storage space and computing time.     

Closed-form root loci for quasi-dipoles with control design applications

A quasi-dipole is defined to be a pole-zero pair embedded in a suitable approximation to a linear phase field. When complex conjugate plant poles occur near the stability boundary, quasi-dipoles often result from controller designs having compensating zeros. Closed-form root loci expressions are developed for quasi-dipoles; these expressions are shown to provide excellent root locus approximations for practical problems.     

覆盖族动态变化时粗集计算的矩阵方法

在覆盖信息系统中覆盖个数动态变化的背景下,针对如何有效、快速地计算集合的上、下近似集的问题,通过引入特征函数的概念,定义了一个关系矩阵,提出了集合的覆盖近似算子、正域、负域、边界域的矩阵表达式.其次,在覆盖信息系统中覆盖个数变化的条件下,利用矩阵方法研究和讨论了集合近似集的增量更新方法.这些结果丰富了覆盖粗糙集的动态知识更新理论,同时也为动态覆盖信息系统中知识更新提供了一种新的方法.     

Parameterized ABD preconditioning technique for time-periodic convection–diffusion problems

In this paper, a parameterized additive block diagonal (PABD) preconditioning technique is present for solving the nine-point approximations of the time-periodic convection–diffusion problems. The explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrices are presented. The range of the optimal parameters is derived. Numerical experiments show that the generalized minimal residual method preconditioned by the PABD preconditioner with the experimental optimal parameters or some special values is effective for a wide range of problem sizes.     

Error evaluation in approximate reanalysis of structures

It was found in previous studies that the combined approximations (CA) approach developed recently provides accurate results in approximate reanalysis of structures. In this study it is first shown that nonlinear reanalysis and eigenproblem reanalysis can be formulated as a linear reanalysis problem. Then, the convergence behaviour of approximate linear and eigenproblem reanalysis is investigated, and expressions for error evaluation are developed. Some numerical examples show that small errors in the response are obtained for very large changes in the design variables by low-order approximations. The errors evaluated by the expressions developed are similar to the true errors. It was found that lower and upper bounds introduced by the CA method provide good estimation of the exact eigenvalues.     

A rough sets based characteristic relation approach for dynamic attribute generalization in data mining

Any attribute set in an information system may be evolving in time when new information arrives. Approximations of a concept by rough set theory need updating for data mining or other related tasks. For incremental updating approximations of a concept, methods using the tolerance relation and similarity relation have been previously studied in literature. The characteristic relation-based rough sets approach provides more informative results than the tolerance-and-similarity relation based approach. In this paper, an attribute generalization and its relation to feature selection and feature extraction are firstly discussed. Then, a new approach for incrementally updating approximations of a concept is presented under the characteristic relation-based rough sets. Finally, the approach of direct computation of rough set approximations and the proposed approach of dynamic maintenance of rough set approximations are employed for performance comparison. An extensive experimental evaluation on a large soybean database from MLC shows that the proposed approach effectively handles a dynamic attribute generalization in data mining.     

LaTeX数学表达式解析与索引方法

针对数学表达式复杂二维结构特性所导致的普通文本检索技术难以对其进行检索的问题,提出了一种面向数学检索的LaTeX数学表达式解析与索引方法。在充分考虑公式特点的基础上,通过对LaTeX构成特点的分析和归纳,设计了LaTeX数学表达式的解析和检索特征提取算法;以此为基础,构建了一种适应数学表达式特性的双层索引结构,利用所提取数学表达式各层次运算数和运算符信息,分别以Treap数据结构和倒排索引结构构成数学表达式索引,为实现进一步的数学表达式检索匹配打下基础。在浏览器/服务器模式下采用6234条数学教材中的公式作为数据集进行实验,在解析获得的124960个基线层数最高为11层的表达式节点上,建立索引平均耗时为33.8317 s。实验结果表明所提出的LaTeX表达式解析算法和索引结构能够适应数学表达式的特点,有助于实现具有较高效率和准确性的数学表达式检索。     

基于多尺度分层双线性池化网络的细粒度表情识别模型

人脸表情细微的类间差异和显著的类内变化增加了人脸表情识别难度。构建一个基于多尺度双线性池化神经网络的识别模型。设计3种不同尺度网络提取人脸表情全局特征,并引入分层双线性池化层,集成多个同一网络及不同网络的多尺度跨层双线性特征以捕获不同层级间的部分特征关系,从而增强模型对面部表情细微特征的表征及判别能力。同时,使用逐层反卷积融合多层特征信息,解决神经网络通过多层卷积层、池化层提取特征时丢失部分关键特征的问题。实验结果表明,该模型在FER2013和CK+公开数据集上的识别率分别为73.725%、98.28%,优于SLPM、CL、JNS等人脸表情识别模型。     

Efficient additive kernels via explicit feature maps

Large scale nonlinear support vector machines (SVMs) can be approximated by linear ones using a suitable feature map. The linear SVMs are in general much faster to learn and evaluate (test) than the original nonlinear SVMs. This work introduces explicit feature maps for the additive class of kernels, such as the intersection, Hellinger's, and χ2 kernels, commonly used in computer vision, and enables their use in large scale problems. In particular, we: 1) provide explicit feature maps for all additive homogeneous kernels along with closed form expression for all common kernels; 2) derive corresponding approximate finite-dimensional feature maps based on a spectral analysis; and 3) quantify the error of the approximation, showing that the error is independent of the data dimension and decays exponentially fast with the approximation order for selected kernels such as χ2. We demonstrate that the approximations have indistinguishable performance from the full kernels yet greatly reduce the train/test times of SVMs. We also compare with two other approximation methods: Nystrom's approximation of Perronnin et al., which is data dependent, and the explicit map of Maji and Berg for the intersection kernel, which, as in the case of our approximations, is data independent. The approximations are evaluated on a number of standard data sets, including Caltech-101, Daimler-Chrysler pedestrians, and INRIA pedestrians.