Parallel computation of multidimensional discrete orthogonal transforms reducible to a discrete Fourier transform

Algorithms of parallel computation of multidimensional discrete orthogonal transforms that rely on a previously developed approach to paralleling discrete Fourier transforms and methods of reducing different discrete orthogonal transforms (discrete Hartley transform, discrete cosine transform, etc.) to discrete Fourier transforms of a special form are considered.     

Dualization, decision lists and identification of monotone discrete functions

Many data-analysis algorithms in machine learning, datamining and a variety of other disciplines essentially operate on discrete multi-attribute data sets. By means of discretisation or binarization also numerical data sets can be successfully analysed. Therefore, in this paper we view/introduce the theory of (partially defined) discrete functions as an important theoretical tool for the analysis of multi-attribute data sets. In particular we study monotone (partially defined) discrete functions. Compared with the theory of Boolean functions relatively little is known about (partially defined) monotone discrete functions. It appears that decision lists are useful for the representation of monotone discrete functions. Since dualization is an important tool in the theory of (monotone) Boolean functions, we study the interpretation and properties of the dual of a (monotone) binary or discrete function. We also introduce the dual of a pseudo-Boolean function. The results are used to investigate extensions of partially defined monotone discrete functions and the identification of monotone discrete functions. In particular, we present a polynomial time algorithm for the identification of so-called stable discrete functions. This revised version was published online in June 2006 with corrections to the Cover Date.     

Energy Levels of “Hydrogen Atom” in Discrete Time Dynamics

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (but discrete time!) dynamics is compatible with discrete energy levels.     

线性混合系统的可观性分析

线性混合系统的控制输入(包括离散控制和连续控制)会影响混合系统的状态可观性．混合系统的可观性包括初始的离散状态和连续状态，以及离散状态的切换时间．对此．分析了系统的控制输入对线性混合系统状态(主要是离散状态)的影响，并论述这将有助于改善某些线性混合系统状态的可观性．通过分析给出了在这种情形下比较宽松的线性混合系统状态可观性条件及其秩检验条件，并给出说明性示例．     

Migration Processes II: The Discrete Case

Following the study of migration processes in the continuous domain in Part I of this paper, we reformulate the concept of migration in the discrete domain (Z^m) and define Discrete Migration Processes (DMP). We demonstrate that this model is a natural discrete representation of the continuous model and maintains the model's features in a qualitative sense. We show that under discrete migration any discrete set shrinks to a limit in finitely many iterations. The discrete representation provides an advantageous basis for digitally implementing the MP model. Using this implementation we illustrate the discrete migration of various types of sets under various types of constraints.     

Generalized Discrete Software Reliability Modeling With Effect of Program Size

Generalized methods for software reliability growth modeling have been proposed so far. But, most of them are on continuous-time software reliability growth modeling. Many discrete software reliability growth models (SRGM) have been proposed to describe a software reliability growth process depending on discrete testing time such as the number of days (or weeks); the number of executed test cases. In this paper, we discuss generalized discrete software reliability growth modeling in which the software failure-occurrence times follow a discrete probability distribution. Our generalized discrete SRGMs enable us to assess software reliability in consideration of the effect of the program size, which is one of the influential factors related to the software reliability growth process. Specifically, we develop discrete SRGMs in which the software failure-occurrence times follow geometric and discrete Rayleigh distributions, respectively. Moreover, we derive software reliability assessment measures based on a unified framework for discrete software reliability growth modeling. Additionally, we also discuss optimal software release problems based on our generalized discrete software reliability growth modeling. Finally, we show numerical examples of software reliability assessment by using actual fault-counting data     

基于级联离散小波变换的信号去噪方法研究

提出了基于级联离散小波变换的信号去噪方法。该方法通过对带噪信号作一层离散小波变换(DWT)后提取的低频部分和高频部分分别作一层DWT和四层DWT,然后,对低频部分提取的低频成分和高频成分均作三层DWT,接着,对所有分解的小波系数进行阈值处理,最后,完成信号重构。实验结果表明:在同样的小波分解层次下,本方法去噪效果好于DWT法和WPD法。     

On properties of discretized convex curves

The connection between a continuous convex curve and its discrete image is investigated using an appropriate definition of discrete convexity. It is shown that the discrete image of continuous convex curve may not be convex; however, its deviation from convexity (in the discrete definition) is bounded by a small constant. The actual pixel patterns that are obtained by discretizing convex curves are studied. Certain constraints on the context of discrete images of continuous convex curves were discovered     

离散微粒群优化算法的研究进展

首先,介绍了近年来出现的５种较为典型的离散ＰＳＯ,并分析了它们与基本ＰＳＯ 之间的联系和区别;然后,归纳了提高离散ＰＳＯ 优化性能的若干途径,并总结了离散ＰＳＯ 的应用现状;最后,探讨了离散ＰＳＯ 有待进一步研究的若干方向和内容．     

基于向量变换的离散GM(1,1)模型病态性

离散GM(1,1)模型建模时的病态性会导致模型的不稳定.运用向量的数乘和旋转变换研究离散GM(1,1)模型的 病态性问题, 发现离散GM(1,1)模型的病态性产生的原因与累加向量和全1向量的长度比值和夹角有关.运用数乘 和旋转变换将矩阵转化为良态矩阵, 用以解决离散GM(1,1)模型的病态性问题.算例结果表明, 向量变换是解决离散GM(1,1)模型 病态性的一种有效的方法.     

Imperceptible digital watermarking scheme in multiple transform domains

A novel imperceptible digital watermarking scheme in multiple transform domains is presented, where the cover image is dealt with by discrete wavelet transform (DWT), discrete cosine transform (DCT) and discrete fractional random transform (DFRNT), while the watermark image is scrambled by Arnold transform and logistic map. First the watermark is scrambled by the Arnold transform, then the row and the column of the resulting watermark are scrambled by the Logistic map, respectively. In addition, four sub-band images are generated from the host image by the two-dimensional discrete wavelet transform. The low-frequency sub-band images are divided into 8?×?8 small matrices, and a coefficient matrix is produced by performing the discrete cosine transform on each matrix. An intermediate matrix with the same size as the watermark image is constructed by the intermediate frequency coefficients. Then the discrete fractional random transformation is performed on the intermediate frequency coefficient matrix and the scrambled watermark is embedded into the discrete fractional random transformation domain. Compared with the previous schemes, the proposed digital watermarking scheme has stronger imperceptibility and robustness.     

Fault tolerant control design via hybrid petri nets

This paper proposes a novel fault tolerant control (FTC) scheme for hybrid systems modeled by hybrid Petri nets (HPNs). The HPNs model consists of discrete and continuous PNs. The faults are represented by unobservable discrete transitions or the normal observable discrete transitions with abnormal firing time in discrete PNs. First, an observer‐based fault diagnosis method is proposed to estimate the marking in discrete places with unknown initial marking and diagnose the faulty behavior simultaneously. Then, an adaptive fault tolerant controller is designed to maintain the general mutual exclusion constraints (GMEC) of discrete PNs, and a scheme that adjusts firing speeds of continuous transitions is provided to maintain the optimality of continuous PNs. Finally, an example of an intelligent transportation system consisting of automated vehicles on a bridge is included to demonstrate the effectiveness of our developed techniques. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Critical stability and stabilization of discrete-time stochastic systems and its applications

In this paper, critical stability and critical stabilization for discrete stochastic systems with both state and control dependent noise are discussed via the spectrum technique. The Popov-Belevitch-Hautus (PBH) criterion for exact observability in a discrete version is presented. As applications, some interesting results on a class of generalized Lyapunov equations (GLE), unremovable spectra and discrete generalized algebraic Riccati equation (GARE) are obtained. Finally, the problem of assigning the spectra of discrete stochastic systems in a specified disk is considered and some numerical examples are given to demonstrate our results.     

A discrete post-processing method for structural optimization

This paper introduces a discrete variable post-processing method for structural design optimization. The motivation behind the method is to find a good discrete solution at manageable cost while the traditional discrete optimization algorithms are regarded as impractical for large-scale structural design problems. In this paper, the Design of Experiments (DOE) and Conservative Discrete Design (CDD) approaches have been proposed to deal with discrete variables with limited computational cost. Both methods work on the explicit approximate discreteproblem to explore the discrete design. These two approaches, together with engineering rounded-off methods, can be used to process discrete variables at any specified continuous design optimization cycle for structural design problems. Brief background and a theoretical discussion about these approaches are given in this paper. Finally, the methods that have been implemented in MSC.Nastran are demonstrated by academic and real engineering examples.     

The generalized unified computation of multidimensional discrete orthogonal transforms

By introducing a form of reorder for multidimensional data, we propose a unified fast algo-rithm that jointly employs one-dimensional W transform and multidimensional discrete polynomial trans-form to compute eleven types of multidimensional discrete orthogonal transforms, which contain three types of m-dimensional discrete cosine transforms ( m-D DCTs) ,four types of m-dimensional discrete W transforms ( m-D DWTs) ( m-dimensional Hartley transform as a special case), and four types of generalized discrete Fourier transforms ( m-D GDFTs). For real input, the number of multiplications for all eleven types of the m-D discrete orthogonal transforms needed by the proposed algorithm are only 1/m times that of the commonly used corresponding row-column methods, and for complex input, it is further reduced to 1/(2m) times. The number of additions required is also reduced considerably. Furthermore, the proposed algorithm has a simple computational structure and is also easy to be im-plemented on computer, and th     

Scale-space for discrete signals

A basic and extensive treatment of discrete aspects of the scale-space theory is presented. A genuinely discrete scale-space theory is developed and its connection to the continuous scale-space theory is explained. Special attention is given to discretization effects, which occur when results from the continuous scale-space theory are to be implemented computationally. The 1D problem is solved completely in an axiomatic manner. For the 2D problem, the author discusses how the 2D discrete scale space should be constructed. The main results are as follows: the proper way to apply the scale-space theory to discrete signals and discrete images is by discretization of the diffusion equation, not the convolution integral; the discrete scale space obtained in this way can be described by convolution with the kernel, which is the discrete analog of the Gaussian kernel, a scale-space implementation based on the sampled Gaussian kernel might lead to undesirable effects and computational problems, especially at fine levels of scale; the 1D discrete smoothing transformations can be characterized exactly and a complete catalogue is given; all finite support 1D discrete smoothing transformations arise from repeated averaging over two adjacent elements (the limit case of such an averaging process is described); and the symmetric 1D discrete smoothing kernels are nonnegative and unimodal, in both the spatial and the frequency domain     

基于DWT-DCT-SVM的人脸表情识别

提出了一种基于二维离散小波一离散余弦变换-支持向量机（DWT-DCT-SVM）面部表情识别算法。该算法先利用DWT在不明显损失图像信息的基础上对表情图像进行变换，变换后的图像数据量大大减少。再利用DCT提取代表原图像绝大部分能量的数据作为表情特征矢量，最后利用SVM来识别。实验表明：本算法提取的500个数据长度的表情矢量在一定条件下能较准确地识别出通用的6种表情，但是泛化性能较差。     

Schemas,logics, and neural assemblies

To implement schemas and logics in connectionist models, some form of basic-level organization is needed. This paper proposes such an organization, which is termed a discrete neural assembly. Each discrete neural assembly is in turn made up of discrete neurons (nodes), that is, a node that processes inputs based on a discrete mapping instead of a continuous function. A group of discrete neurons (nodes) closely interconnected form an assembly and carry out a basic functionality. Some substructures and superstructures of such assemblies are developed to enable complex symbolic schemas to be represented and processed in connectionist networks. The paper shows that logical inference can be performed precisely, when necessary, in these networks and with certain genaralization, more flexible inference (fuzzy inference) can also be performed. The development of various connectionist constructs demonstrates the possibility of implementing symbolic schemas, in their full complexity, in connectionist networks.     

Synthesis of digital control systems using discrete Walsh polynomials

The use of discrete Walsh polynomials to synthesize a digital control system and determine suitable internal system structure from its prescribed external (input/output) behaviour is studied in this paper. Algorithms for the synthesis of discrete system transfer functions and state equations are presented. The discrete Walsh approach method transforms the original model difference equations into computationally convenient algebraic forms. Two examples in which a transfer function and a state equation are synthesized illustrate the discrete Walsh technique.     

BACKLASH COMPENSATION WITH FILTERED PREDICTION IN DISCRETE TIME NONLINEAR SYSTEMS BY DYNAMIC INVERSION USING NEURAL NETWORKS

A dynamics inversion compensation scheme is designed for control of nonlinear discrete‐time systems with input backlash. This paper extends the dynamic inversion technique to discrete‐time systems by using a filtered prediction, and shows how to use a neural network (NN) for inverting the backlash nonlinearity in the feedforward path. The technique provides a general procedure for using NN to determine the dynamics preinverse of an invertible discrete time dynamical system. A discrete‐time tuning algorithm is given for the NN weights so that the backlash compensation scheme guarantees bounded tracking and backlash errors, and also bounded parameter estimates. A rigorous proof of stability and performance is given and a simulation example verifies performance. Unlike standard discrete‐time adaptive control techniques, no certainty equivalence (CE) or linear‐in‐the‐parameters (LIP) assumptions are needed.