An alternative approach to Privault's discrete-time chaotic calculus

In this paper, we present an alternative approach to Privault's discrete-time chaotic calculus. Let Z be an appropriate stochastic process indexed by N (the set of nonnegative integers) and l²(Γ) the space of square summable functions defined on Γ (the finite power set of N). First we introduce a stochastic integral operator J with respect to Z, which, unlike discrete multiple Wiener integral operators, acts on l²(Γ). And then we show how to define the gradient and divergence by means of the operator J and the combinatorial properties of l²(Γ). We also prove in our setting the main results of the discrete-time chaotic calculus like the Clark formula, the integration by parts formula, etc. Finally we show an application of the gradient and divergence operators to quantum probability.     

A note on the Sarmanov bivariate distributions

We investigate the maximum correlation for Sarmanov bivariate distributions with fixed marginals and strengthen the existing results in the literature. The improvement in the maximum correlation is significant. A characterization of the Sarmanov distribution via chi-square divergence is also given. This extends Nelsen [13] result about the Farlie-Gumbel-Morgenstern (FGM) distribution.     

Sequential optimizing strategy in multi-dimensional bounded forecasting games

We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001) [10]. By studying the asymptotic behavior of its capital process, we prove a generalization of the strong law of large numbers, where the convergence rate of the sample mean vector depends on the growth rate of the quadratic variation process. The growth rate of the quadratic variation process may be slower than the number of rounds or may even be zero. We also introduce an information criterion for selecting efficient betting items. These results are then applied to multiple asset trading strategies in discrete-time and continuous-time games. In the case of a continuous-time game we present a measure of the jaggedness of a vector-valued continuous process. Our results are examined by several numerical examples.     

根值判别法的两个推广

讨论正项级数的根值判别法．若将判别极限lim↓n→∞ n√an更改为lim↓n→∞或lim↓n→∞^n√am^n＋i,则相应结果在一定条件下将比原判别方法更为精细,且应用范围也有所推广．     

交错级数敛散性判别法

给出交错级数的几个判别法,它们可直接用以判别交错级数是绝对收敛,条件收敛还是发散.     

随机Bregman ADMM及其在训练具有离散结构的支持向量机中的应用

针对具有多块可分结构的非凸优化问题提出了一类新的随机Bregman交替方向乘子法,在周期更新规则下, 证明了该算法的渐进收敛性; 在随机更新的规则下, 几乎确定的渐进收敛性得以证明。数值实验结果表明, 该算法可有效训练具有离散结构的支持向量机。     

Mapping of powdery mildew using multi-spectral HJ-CCD image in Beijing suburban area

Powdery mildew is one of the most serious diseases, which has a significant impact on the production of winter wheat. As an effective alternative to traditional sampling methods, remote sensing can be a useful tool in disease detection. This study examines the potential of a moderate resolution multispectral satellite image in disease monitoring at regional scale. At the suburban area around Beijing, a large size ground survey sample (n = 90) and the corresponding HJ-CCD image were acquired at the grain filling stage of winter wheat. A number of spectral features were found to be sensitive to powdery mildew through an independent t-test. Based on these spectral features, classification models were established using both spectral information divergence (SID) and spectral angle mapper (SAM), respectively. The results showed that the overall accuracies of disease identification and severity estimation were moderate. The estimation of normal and seriously infected samples yielded higher accuracies than slightly infected samples. The single phase HJ-CCD can only be used for locating the infected areas of powdery mildew, whereas is unable to discriminate the severity levels of disease. The presence of several stressors and disturbances other than disease is a possible reason of the unsatisfactory performance of disease monitoring models. Therefore, the integration of multi-phase onboard data and some relevant ancillary data is necessary to improve the accuracy and reliability of disease monitoring at regional scale.     

GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE

In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.     

相空间路径积分中的Feynman规则和广义Ward恒等式

基于Green函数的相空间生成泛函,导出了广义正则Ward恒等式.指出无须作出相空间生成泛函中对正则动量的路径积分,即可求得树图近似下的Feynman规则.对场的拉氏量添加一个四维散度项后,场的传播子发生了改变.     

Fuzzy measures for color image retrieval

In this paper we present a scheme for fuzzy similarity based strategy to retrieve an image from a library of color images. Color features are among the most important features used in image database retrieval. Due to its compact representation and low complexity, direct histogram comparison is the most commonly used technique in measuring color similarity of images. A gamma membership function, derived from the Gamma distribution, has been proposed to find the membership values of the gray levels of the histogram. We present here an image retrieval scheme with some popular vector fuzzy distance measures using a gamma membership function for finding the membership values of the gray levels and evaluate the matching function to select the appropriate retrieval mechanism.