A Numerical Study of Diagonally Split Runge–Kutta Methods for PDEs with Discontinuities

Diagonally split Runge–Kutta (DSRK) time discretization methods are a class of implicit time-stepping schemes which offer both high-order convergence and a form of nonlinear stability known as unconditional contractivity. This combination is not possible within the classes of Runge–Kutta or linear multistep methods and therefore appears promising for the strong stability preserving (SSP) time-stepping community which is generally concerned with computing oscillation-free numerical solutions of PDEs. Using a variety of numerical test problems, we show that although second- and third-order unconditionally contractive DSRK methods do preserve the strong stability property for all time step-sizes, they suffer from order reduction at large step-sizes. Indeed, for time-steps larger than those typically chosen for explicit methods, these DSRK methods behave like first-order implicit methods. This is unfortunate, because it is precisely to allow a large time-step that we choose to use implicit methods. These results suggest that unconditionally contractive DSRK methods are limited in usefulness as they are unable to compete with either the first-order backward Euler method for large step-sizes or with Crank–Nicolson or high-order explicit SSP Runge–Kutta methods for smaller step-sizes. We also present stage order conditions for DSRK methods and show that the observed order reduction is associated with the necessarily low stage order of the unconditionally contractive DSRK methods. The work of C.B. Macdonald was partially supported by an NSERC Canada PGS-D scholarship, a grant from NSERC Canada, and a scholarship from the Pacific Institute for the Mathematical Sciences (PIMS). The work of S. Gottlieb was supported by AFOSR grant number FA9550-06-1-0255. The work of S.J. Ruuth was partially supported by a grant from NSERC Canada.     

Lose Fat, Not Muscle: An Examination of Supervisor Reduction in Discrete-Event Systems

This paper is concerned with the elimination of unnecessary states in discrete-event system control agents. Several approaches to supervisor reduction are studied and a new relation between agents, comparability, is defined to encapsulate most of the concepts found in the aforementioned methods. This relation is also proven to be preserved under conjunction, which is commonly employed to determine the centralized representation of two decentralized DES supervisors.

Mixtures of robust probabilistic principal component analyzers

Mixtures of probabilistic principal component analyzers model high-dimensional nonlinear data by combining local linear models. Each mixture component is specifically designed to extract the local principal orientations in the data. An important issue with this generative model is its sensitivity to data lying off the low-dimensional manifold. In order to address this problem, the mixtures of robust probabilistic principal component analyzers are introduced. They take care of atypical points by means of a long tail distribution, the Student-t. It is shown that the resulting mixture model is an extension of the mixture of Gaussians, suitable for both robust clustering and dimensionality reduction. Finally, we briefly discuss how to construct a robust version of the closely related mixture of factor analyzers.     

Test frame updating in CPM testing of Prolog programs

Category Partition Method (CPM) is a general approach to specification-based program testing, where test frame reduction and refinement are two important issues. Test frame reduction is necessary since too many test frames may be produced, and test frame refinement is important since during CPM testing new information about test frame generation may be achieved and considered incrementally. Besides the information provided by testers or users, implementation related knowledge offers alternative information for reducing and refining CPM test frames. This paper explores the idea by proposing a call patterns semantics based test frame updating method for Prolog programs, in which a call patterns analysis is used to collect information about the way in which procedures are used in a program. The updated test frames will be represented as constraints. The effect of our test frame updating is two-fold. On one hand, it removes “uncared” data from the original set of test frames; on the other hand, it refines the test frames to which we should pay more attention. The first effect makes the input domain on which a procedure must be tested a subset of the procedure’s input domain, and the latter makes testers stand more chance to find out the faults that are more likely to show their presence in the use of the program under consideration. Our test frame updating method preserves the effectiveness of CPM testing with respect to the detection of faults we care. The test case generation from the updated set of test frames is also discussed. In order to show the applicability of our method an approximation call patterns semantics is proposed, and the test frame updating on the semantics is illustrated by an example.

基于关联规则的覆盖领域约简算法

前向神经网络的网络覆盖算法根据样本数据构造性地建立神经网络,其结构易于确定,执行效率高。但由于噪声数据的存在,可能造成覆盖领域多的现象,增加了网络结构的复杂度,并产生一些不必要的误识。该文借鉴数据挖掘中关联规则的支持度与可信度的概念,对覆盖领域进行约简,理论分析和实验表明,该算法可以有效地简化覆盖网络的结构,提高网络的稳定性和推广能力。     

一种改进的支持向量机降维方法

提出了一种基于支持向量机的改进的降维方法.在输入和特征空间中,特征子集的选取分别根据原始特征每一维对分类的贡献来获得.最后,通过将输入和特征空间中的特征选取联合起来,得到了一种改进的降维方法.实验表明:使用这种方法,在保持对分类准确率不受明显的影响的同时,能大大地提高训练和预测的速度.     

基于遗传算法的粗糙集属性约简算法

为了研究粗糙集理论中属性约简问题,给出了一种属性相对重要度定义,证明了其合理性,并将它应用到基于遗传算法的约简算法中,提出一种启发式遗传算法.算法采用修正策略保证群体进化收敛于最小约简,同时引入属性相对重要度作为启发信息,加快算法的收敛速度.对算法进行的时间复杂度和完备性分析以及数值实验表明,基于遗传算法的粗糙集属性约简算法具有完备、快速收敛等特点.     

Cryptanalysis of RSA for a special case with d > e

In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N ^0.258 ⩽ e ⩽ N ^0.854, d > e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee’s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems. Supported partially by the National Basic Research Program of China (Grant No. 2003CB314805), the National Natural Science Foundation of China (Grant Nos. 90304014 and 60873249), and the Project funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua     

基于RgPCA的表情特征提取与选择

将RgPCA算法应用于表情图像的特征提取。其核心思想:先用PCA处理表情图像,提取表情特征;然后,将此表情特征集作为一个粗糙集用FAI算法进行约简,从而实现表情特征选择。RgPCA算法继承了PCA在特征提取时的简洁,并充分考虑模式分类的要求,提高了特征选择的科学性。     

遗传算法与文本特征选择方法相结合的研究

对文本特征选择的传统方法进行了深入分析并对各自的优缺点进行了详细的对比;其次,通过利用遗传算法自身的寻优特点,把它与传统特征选择方法相结合,并得出了算法。最后,在对各自算法进行了分析,表明了在性能上有了明显的提高。