基于U-正交变换的图像编码算法

为了更有效地进行图像编码,先用U-正交函数系构造出一类新型的U-正交变换, 并以三次U-正交变换为例,研究了基于U-正交变换的图像编码算法。该编码算法首先通过离散U-正交函数系的基函数构造U-正交变换的变换矩阵,并根据U-正交矩阵的对称性给出了U-正交变换的快速算法; 然后应用三次U-正交变换对图像实施2维变换, 再用JPEG标准中的量化矩阵、Huffman码表与熵编码方法对图像的三次U-变换系数进行量化与编码, 实现了基于三次U-正交变换的图像编码算法。实验结果表明, 三次U-正交变换的编码增益、去相关效率与DCT基本相同,而编码效果却与JPEG编码效果非常接近, 且计算复杂度与基于FFT的快速DCT算法基本一致。由此可见, 应用U-正交变换对图像进行编码压缩是一类行之有效的方法,并有望在视频编码中得到应用。     

Performance bounds in linear control of unstable MIMO systems with pole location constraint

This paper proposes a methodology to compute quadratic performance bounds when the closed loop poles of a discrete-time multivariable control loop are confined to a disk, centred at the origin, and with radius less than one. The underlying philosophy in this constraint is to avoid certain undesirable dynamic features which arise in quadratic optimal designs. An expression for the performance loss due to the pole location constraint is also provided. Using numerical examples, we show that the performance loss is compensated by an improved transient performance, specially visible in the control signals.     

Automatic Construction and Verification of Isotopy Invariants

We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by considering the isotopy equivalence relation. Isotopism is an important generalisation of isomorphism, and is studied by mathematicians in domains such as loop theory. This extension was not straightforward, and we had to solve two major technical problems, namely, generating and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on subblocks. In addition, given the complexity of the theorems that verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an interplay of computer algebra, model generation, theorem proving, and satisfiability-solving methods. To demonstrate the power of the approach, we generate isotopic classification theorems for loops of size 6 and 7, which extend the previously known enumeration results. This work was previously beyond the capabilities of automated reasoning techniques. The author’s work was supported by EPSRC MathFIT grant GR/S31099.     

基于DNA计算自组装模型的Diffie-Hellman算法破译(英文)

DNA自组装计算模型是近年来引人关注的计算模型,已有基于自组装模型的二进制加法、乘法以及有限域中的加法和乘法的讨论．文中利用DNA自组装模型设计的模乘系统,实现了素数P的本原根g连续乘方后模p的数的排列,从而可以在线性时间内求解离散对数,为破译Diffie—Hellman密钥交换算法提供了新的生物方法．该模乘系统使用了Θ（p）种自组装类型,组装的时间复杂度为Θ（p-1）．系统最后组装结果提取出报告链后,经过PCR和凝胶电泳读取离散对数结果．该模型扩展了DNA自组装计算模型的应用,为求取离散对数提供了新思路．     

A new approach based on a discrete hidden Markov model using the Rocchio algorithm for the diagnosis of heart valve diseases

Abstract: Application of the Doppler ultrasound technique in the diagnosis of heart diseases has been increasing in the last decade since it is non‐invasive, practicable and reliable. In this study, a new approach based on the discrete hidden Markov model (DHMM) is proposed for the diagnosis of heart valve disorders. For the calculation of hidden Markov model (HMM) parameters according to the maximum likelihood approach, HMM parameters belonging to each class are calculated by using training samples that only belong to their own classes. In order to calculate the parameters of DHMMs, not only training samples of the related class but also training samples of other classes are included in the calculation. Therefore HMM parameters that reflect a class's characteristics are more represented than other class parameters. For this aim, the approach was to use a hybrid method by adapting the Rocchio algorithm. The proposed system was used in the classification of the Doppler signals obtained from aortic and mitral heart valves of 215 subjects. The performance of this classification approach was compared with the classification performances in previous studies which used the same data set and the efficiency of the new approach was tested. The total classification accuracy of the proposed approach (95.12%) is higher than the total accuracy rate of standard DHMM (94.31%), continuous HMM (93.5%) and support vector machine (92.67%) classifiers employed in our previous studies and comparable with the performance levels of classifications using artificial neural networks (95.12%) and fuzzy‐C‐means/CHMM (95.12%).     

A neural networks learning algorithm for minor component analysis and its convergence analysis

The eigenvector associated with the smallest eigenvalue of the autocorrelation matrix of input signals is called minor component. Minor component analysis (MCA) is a statistical approach for extracting minor component from input signals and has been applied in many fields of signal processing and data analysis. In this letter, we propose a neural networks learning algorithm for estimating adaptively minor component from input signals. Dynamics of the proposed algorithm are analyzed via a deterministic discrete time (DDT) method. Some sufficient conditions are obtained to guarantee convergence of the proposed algorithm.     

一个模拟网格上并行作业调度的离散事件系统

为评估计算网格上并行作业的无中心式调度,设计了基于离散事件的模拟系统J3S.离散事件包括作业提交、开始和终止,作业状态可以是等待、运行或完成.事件引起作业状态的变化 ,并触发网格层次或本地层次调度.作业由网格工作负荷模型产生,该模型基于并行计算机工作负荷模型构建.网格层次调度通过网格调度器之间的协作完成.本地层次调度模拟改进的装填法,使作业可有不同的调度优先级.网格资源性能可有差异,作业执行性能依赖作业指派.模块化实现使J3S可模拟网格上并行作业的无中心式调度的各种场景.     

高等师范院校计算机专业离散数学的教学改革与实践

根据当前高等师范院校计算机专业人才培养的特点和离散数学的教学现状,从离散数学的教学内容、教学手段和实验教学等方面探讨了计算机专业离散数学的教学改革。通过这几年的改革实践,离散数学的教学效果得到了明显提高。     

高职多媒体教学在《高等数学》中的应用探讨

探讨了在高职院校中《高等数学》课程使用多媒体进行教学的特点,并结合近年来多媒体教学的实践体会提出其中存在的问题,及就进一步推进多媒体教学改革提出了一些思路。     

几何画板在中学数学教学中的应用

多媒体技术的应用为数学教学的更新创造了条件,也给学校教育带来了一场深刻的变革。数学作为一门独立的自然科学,有它自身的特点、体系和规律,而几何画板作为电子尺规,是研究几何图形的关系、动态地观察几何图形运动状态、探索数学信息的有力工具。从几何画板辅助中学数学教学的现状、目标及其意义入手,结合几何画板辅助中学数学教学的实例,就几何画板在中学数学教学中的应用及其在教学活动中的重要作用做了系统地阐述和说明。