基于相似块线性旋转变换的分形图象编码方法

针对Jacquin分形编码算法中选取的相似块数目较少,从而与图象块匹配的效率不高的缺点,提出了通过线性旋转变换来扩充相似块数目,以进行最佳匹配的分形编码方法,与通常方法不同,为了充分发掘图象自身的相似性,该方法首先在图象中的多个方向上选取相似块,然后通过对称变换和线性旋转变换生成新的相似块集来进行编码,当旋转方向数取4时,就可以将Jacquin提出的Isometries变换归结为该方法的一种特例,通过调整旋转方向的数目,能有效地改善Isometries变换相似块数目不足的缺点,并得到了较优的压缩结果。另外,针对线性旋转变换还提出了基于查找表的加速算法,从而显著减少了编码时间。     

基于特征参数空间的交互约束自动求解方法*

提出了一种新的约束求解方法求解特征交互过程中两个特征形状在空间上发生重叠的约束。这个约束求解器在特征模型的参数空间进行取样的基础之上,利用蒙特卡罗技术来减少样本数据量。该方法不但可以产生一组正确的几何约束,而且提高了效率约束转换的效率。     

Global approximation for some functions

Approximate closed form representations of functions are useful for mathematical manipulations. Nonlinear sequence transforms can be used to evaluate the function using a few terms of the series representation of the function and these transforms can be used for functions with complex argument as well. Moreover, if an asymptotic expansion of the function is available, an approximant for the function, valid for the entire range of the variable, can be obtained with Padé approximants as well as Levin and Weniger transforms. In addition, one can obtain an approximation for a function using quadratic Padé approximation which is also valid for the entire range of the variable. We demonstrate this for some functions frequently encountered in scientific problems. These include the error function, the Fresnel integral, the Dawson integral, the Euler integral and the elliptic integral. A comparison is made between the approximants obtained with Padé approximants and those generated by Levin and Weniger transforms.     

A distance-based fuzzy time series model for exchange rates forecasting

Fuzzy time series model has been successfully employed in predicting stock prices and foreign exchange rates. In this paper, we propose a new fuzzy time series model termed as distance-based fuzzy time series (DBFTS) to predict the exchange rate. Unlike the existing fuzzy time series models which require exact match of the fuzzy logic relationships (FLRs), the distance-based fuzzy time series model uses the distance between two FLRs in selecting prediction rules. To predict the exchange rate, a two factors distance-based fuzzy time series model is constructed. The first factor of the model is the exchange rate itself and the second factor comprises many candidate variables affecting the fluctuation of exchange rates. Using the exchange rate data released by the Central Bank of Taiwan, we conducted several experiments on exchange rate forecasting. The experiment results showed that the distance-based fuzzy time series outperformed the random walk model and the artificial neural network model in terms of mean square error.     

Sampling Archimedean copulas

The challenge of efficiently sampling exchangeable and nested Archimedean copulas is addressed. Specific focus is put on large dimensions, where methods involving generator derivatives are not applicable. Additionally, new conditions under which Archimedean copulas can be mixed to construct nested Archimedean copulas are presented. Moreover, for some Archimedean families, direct sampling algorithms are given. For other families, sampling algorithms based on numerical inversion of Laplace transforms are suggested. For this purpose, the Fixed Talbot, Gaver Stehfest, Gaver Wynn rho, and Laguerre series algorithm are compared in terms of precision and runtime. Examples are given, including both exchangeable and nested Archimedean copulas.     

A microchannel heat exchanger design for microelectronics cooling correlating the heat transfer rate in terms of Brinkman number

Microchannel heat exchangers are a well known device in the application of microelectronics cooling. In this paper, liquid microchannel heat exchangers were designed and investigated with varying channel width in order to find the maximum cooling efficiency when combined with pumping performance. A recently developed correlation of heat transfer rate in terms of Nusselt number and Brinkman number was adopted to predict cooling efficiency of the microchannel heat exchanger and was compared with the experimental results. Conventional heat transfer theories and numerical commercial code were also used to predict the cooling efficiency. The measured minimum thermal resistance of the microchannel heat exchanger showed a good agreement with the prediction from the new correlation, whereas calculation results from conventional theories and numerical code showed large divergence. It can be seen that the microchannel heat exchanger can be optimized when combined with pumping performance. In addition, the new correlation of heat transfer rate in terms of Brinkman number can be quite a useful tool in design of microchannel heat exchanger.     

Number-Theoretical Methods of Factoring Composite Numbers and Calculating the Discrete Logarithm

Cybernetics and Systems Analysis - The article is devoted to the new application of number-theoretic transforms. Representing number systems by these transforms allows us to create fundamentally...     

An efficient coupling of FORM and Karhunen–Loève series expansion

The topic of this paper is the solution of reliability problems where failure is influenced by the spatial random fluctuations of loads and material properties. Homogeneous random fields are used to model this kind of uncertainty. The first step of the investigation is the random field discretization, which transforms a random field into a finite set of random variables. The second step is the reliability analysis, which is performed using the FORM in this paper. A parametric analysis of the reliability index is usually performed with respect to the random field discretization accuracy. This approach requires several independent reliability analyses. A new and efficient approach is proposed in this paper. The Karhunen–Loève series expansion is combined with the FEM for the discretization of the random fields. An efficient solution of the reliability problem is proposed to predict the reliability index as the discretization accuracy increases.     

Methods for fast morphological image transforms using bitmapped binary images

In this paper we present new implementations for morphological binary image processing on a general-purpose computer, using a bitmap representation of binary images instead of representing binary images as bitplanes inserted in gray value images. The bitmap data representation is a very efficient one, both in terms of memory requirements and in terms of algorithmic efficiency because of the CPU operates on 32 pixels in parallel. The algorithms described in this paper are capable of performing the basic morphological image transforms using structuring elements of arbitrary size and shape. In order to speed up morphological operations with respect to commonly used, large, convex structuring elements, the logarithmic decomposition of structuring elements is used. Experiments indicate that the new algorithms are more than 30 times faster for pixelwise operations and about an order of magnitude faster for the basic morphological transforms than the fastest known software implementations.     

基于单尺度脊波变换的阈值滤波方法

分析了高斯白噪声在单尺度脊波域中的统计性质，提出了一种新的基于单尺度脊波变换的阈值滤波算法。仿真结果表明，这种算法不仅比传统基于小波变换的各种滤波算法有更高的PSNR值，而且能更好地保持图像细节。     

基于多尺度的时间序列固定分段数线性表示

针对目前的时间序列线性表示方法多采用启发式方法提取局部特征点作为分段点,容易陷入局部最优化,不能很好地表示时间序列全局特征,而且多采用单一的拟合误差作为阈值,不能准确预计分段数量,不利于后期进行的时间序列分析应用的问题。提出了一种新的固定分段数的表示方法--PLR_BTBU,首先根据二叉树层次遍历的思想,提取时间序列全局特征点将时间序列初始分段,再通过斜率变化特征将整个时间序列符号化,以各初始分段内的符号特征来确定各初始分段中的分段点分布,最后采用一种改进的固定分段数的自底向上融合算法,将各个子序列逐步融合到要求的分段数。实验结果表明,与已有的方法相比,该方法不仅较好地保留时间序列的全局特征,而且拟合后的时间序列和原时间序列之间的拟合误差更小。     

基于Huang变换和BP神经网络的时间序列预测方法

Huang变换是近几年发展起来处理非平稳信号的新方法。时间序列同信号一样具有非平稳的特性,研究了Huang变换在时间序列预测中的应用。首先将时间序列通过Huang变换分解为有限个固有模态函数和一个残余函数之和,每一个的固有模态函数反映了时间序列在各个尺度的特征,而残余函数则很好地反映了时间序列的总体趋势,然后应用BP神经网络对各个固有模态函数和残余函数进行预测,最后将所有的预测值重构叠加,就得到原始时间序列的预测值。实例证明,基于Huang变换和BP神经网络的时间序列的预测方法,优于小波变换和神经网络相结合的预测方法,提高了预测精度。     

Walvelet Analysis of Commodity Price Behavior

We propose a form of semi-nonparametric regression based on wavelet analysis. Traditional time series methods usually involve either the time or the frequency domain, but wavelets can combine the information from both of these. While wavelet transforms are typically restricted to equally spaced observations an integer power of 2 in number, we show how to go beyond these constraints. We use our methods to construct 'patios' for 21 important international commodity price series. These graph the magnitude of the variations in the series at different time scales for various subperiods of the full sample.     

基于多尺度分析和神经网络的时间序列预报

本文提出一种由小波变换和神经网络相结合,进行时间序列预报的新方法。其中,小波作为滤波部分对原始序列进行多尺度分解,产生更容易建模和预测的子序列,再把上述子序列作为神经网络的输入进行时域预报。该方法考虑原时间序列的频率特性,采用不同的神经网络进行预报。     

Functional approximation for inversion of Laplace transforms via polynomial series

A method for finding the inverse of Laplace transforms using polynomial series is discussed. It is known that any polynomial series basis vector can be transformed into Taylor polynomials by use of a suitable transformation. In this paper, the cross product of a polynomial series basis vector is derived in terms of Taylor polynomials, and as a result the inverse of the Laplace transform is obtained, using the most commonly used polynomial series such as Legendre, Chebyshev, and Laguerre. Properties of Taylor series are first briefly presented and the required function is given as a Taylor series with unknown coefficients. Each Laplace transform is converted into a set of simultaneous linear algebraic equations that can be solved to evaluate Taylor series coefficients. The inverse Laplace transform using other polynomial series is then obtained by transforming the properties of the Taylor series to other polynomial series. The method is simple and convenient for digital computation. Illustrative examples are also given,     

Minimization of Haar wavelet series and Haar spectral decision diagrams for discrete functions

In this paper, a minimization of Haar wavelet series for simplification of circuits and Haar based decision diagrams representing discrete multiple-valued functions is proposed. The minimization is performed by permutation of indices of generalized Haar functions. Experimental results show that this method provides reasonable reduction in the number of non-zero coefficients. The Haar series reduced this way can be useful in the circuit synthesis for realization of multiple-valued functions. The same algorithm can be also used to reduce the number of paths in decision diagrams related to the Haar wavelet transforms. In many cases, this reduction provides smaller size of such decision diagrams.     

Assessment of vegetation indexes useful for browse (forage) prediction in semi-arid rangelands

Considerable significance is placed on the mapping and monitoring of degraded areas in semi-arid regions of the world, including Botswana. Degraded areas include those suffering from bush encroachment, believed to result from heavy cattle grazing over a number of years. However, certain bush encroachment species have been found to be relatively nutrient-rich. The present work considers the extent to which a series of quantified layers through mainly bush encroachment canopies can be identified using conventional and newly derived vegetation indexes and transforms based on Thematic Mapper (TM) imagery. Field work involved the stratification of green biomass into firstly the herbaceous cover layer; secondly the 0.3-1.5 m browse layer; then the 1.5-2.5 m browse layer; and finally the >2.5 m browse layer. Biomass measurements from these layers were statistically associated with conventional vegetation indexes and transforms such as the Normalized Difference Vegetation Index (NDVI), brightness and greenness values, and relatively newly derived darkening indexes involving the mid-infrared bands. When green biomass and transformed pixel data were averaged per classified vegetation unit, weak negative correlations emerged between grass biomass and the transformed pixel data and no significant correlations developed with the woody biomass (browse) layers. However, when point data were used in the analyses, results showed that most indexes and the brightness transform were significantly correlated with the lower browse layer. Only the darkening indexes and brightness function were sensitive to the browse layers individually and the browse plus grass layers. This work shows the limitations of conventional indexes such as the NDVI in terms of browse and herbaceous layer assessment. New indexes for forage assessment based on relationships between the mid-infrared bands, such as those found in the new MODIS TERRA platform, are urgently required for semi-arid areas.     

Nonlinear Discrete Wavelet Transforms over Finite Sets and an Application to Binary Image Compression

The discrete wavelet transform was originally a linear operator that works on signals that are modeled as functions from the integers into the real or complex numbers. However, many signals have discrete function values. This paper builds on two recent developments: the extension of the discrete wavelet transform to finite-valued signals and the research of nonlinear wavelet transforms triggered by the introduction of the lifting scheme by Sweldens. It defines discrete wavelet transforms as bijective, translation-invariant decompositions of signals that are functions from the integers into any finite set. Such transforms are essentially nonlinear, but they can be calculated very time efficiently since only discrete arithmetic is needed. Properties of these generalized discrete wavelet transforms are given along with an elaborate example of such a transform. In addition, the paper presents some ideas to find explicit examples of discrete wavelet transforms over finite sets. These ideas are used to show that, in case the finite set is a ring, there are much more nonlinear transforms than linear transforms. Finally, the paper exploits this increased number of transforms to do lossless compression of binary images.The research is sponsored (grant no. 613.006.570) by the Dutch Science Foundation (NWO).     

Parallel architecture for fast transforms with trigonometric kernel

We present an unified parallel architecture for four of the most important fast orthogonal transforms with trigonometric kernel: Complex Valued Fourier (CFFT), Real Valued Fourier (RFFT), Hartley (FHT), and Cosine (FCT). Out of these, only the CFFT has a data flow coinciding with the one generated by the successive doubling method, which can be transformed on a constant geometry flow using perfect unshuffle or shuffle permutations. The other three require some type of hardware modification to guarantee the constant geometry of the successive doubling method. We have defined a generalized processing section (PS), based on a circular CORDIC rotator, for the four transforms. This PS section permits the evaluation of the CFFT and FCT transforms in n data recirculations and the RFFT and FHT transforms in n-1 data recirculations, with n being the number of stages of a transform of length N=rⁿ. Also, the efficiency of the partitioned parallel architecture is optimum because there is no cycle loss in the systolic computation of all the butterflies for each of the four transforms     

Mellin transforms and asymptotics

Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divide-and-conquer algorithms. This note illustrates the techniques by providing a precise analysis of the standard topdown recursive mergesort algorithm, in the average case, as well as in the worst and best cases. It also derives the variance and shows that the cost of mergesort has a Gaussian limiting distribution. The approach is applicable to a number of divide-and-conquer recurrences.