基于信息熵的粗糙集连续属性离散化算法

该文提出了一种新的粗糙集连续属性离散化算法．首先对每一个候选断点定义了信息熵，以此作为对断点重要性的量度，在此基础上给出了断点选择的粗糙集连续属性离散化算法．最后采用多组数据对此算法的性能进行了检验，并与其它算法做了对比实验．实验结果表明此算法是有效的，而且当候选断点个数增多时仍有很高的计算效率．     

Estimation of generalized entropies with sample spacing

In addition to the well-known Shannon entropy, generalized entropies, such as the Renyi and Tsallis entropies, are increasingly used in many applications. Entropies are computed by means of nonparametric kernel methods that are commonly used to estimate the density function of empirical data. Generalized entropy estimation techniques for one-dimensional data using sample spacings are proposed. By means of computational experiments, it is shown that these techniques are robust and accurate, compare favorably to the popular Parzen window method for estimating entropies, and, in many cases, require fewer computations than Parzen methods.     

Analysis of stability of stochastic dynamic systems under Poisson perturbations. II. Stability of solutions in quadratic mean of systems of linear stochastic differential equations under Poisson perturbations

Necessary and sufficient conditions of asymptotic stability in quadratic mean are obtained for trivial solutions of systems of linear stochastic differential equations under Poisson perturbations. Model problems are analyzed. Part I of this article is published in No. 4 (2005). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 50–66, November–December 2005.     

用于网络新闻热点识别的热点新词发现

通过分析网络新闻热点词的特点，提出了一种用于网络新闻热点识别的热点新词发现方法。首先，用改进FP-tree算法提取频繁出现的词串作为热点新词候选，删除新闻数据中非频繁1-词串，并利用1、2-非频繁词串切割新闻数据，从而删除新闻数据中的大量无用信息，大幅降低FP-tree复杂度；其次，根据二元逐点互信息（PMI）扩展成多元PMI，并引入热点词的时间特征形成时间逐点互信息（TPMI），用TPMI判定热点新词候选的内部结合度和时间性，剔除不合格的候选词；最后，采用邻接熵确定候选新词边界，从而筛选出热点新词。采集百度网络新闻的7 222条新闻标题作为数据集进行实验验证。在将半月内报道次数不低于8次的事件作为热点新闻且时间特征的调节系数为2时，采用TPMI可以正确识别51个热点词，丢失识别2个长时间热点词和2个低热度词，而采用不加入时间特征的多元PMI可正确识别全部热点词55个，但错误识别97个非热点词。分析可知所提的算法降低了FP-tree复杂度，从而减少了时间空间代价，实验结果表明判定热点新词时加入时间特征提高了热点新词识别率。     

基于最优基小波的基桩弱损伤应力波检测

从提高小波分析与基桩弱损伤检测的匹配性入手，提出了基于最优基小波连续小波变换的基桩应力反射波无损检测方法。该方法首先引入膨胀参数把标准Marr基小波扩展为Marr基小波空间，增强了基小波选取的自由度；进而依赖工程目的和分析对象建立香农熵测度以确定Marr最优基小波；最后采用最优基小波对基桩检测应力波进行连续小波变换，模谱的局部能量集中指示了桩底反射。基桩动力测试数值实验验证了方法是可行、有效的，且最优基小波能够有效地提高弱损伤检测精度。     

曲面积分中值定理的一个新证明

对曲面积分中值定理,给出了一个新的证明,并举出相关例子加以应用.     

The thermal capacity and enthalpy of gadolinium sesquiselenide over a wide temperature range

Measurements have been made on the thermal capacity of γ-Gd₂Se₃ at 58.88–298.34 K. Values have been obtained for the thermal capacity, entropy, reduced Gibbs energy, and enthalpy under standard conditions: C°_p = 125.87 ± 0.5 J· mole⁻¹ · K⁻¹; S°(298.15 K) = 196.5 · 1.6 J · mole⁻¹ · K⁻¹; Φ°(298.15 K) = 103.6 ± 1.6 J · mole⁻¹ · K⁻¹; H°(298.15 K)-H°(0) = 27681 ± 138 J · mole⁻¹. The enthalpy of Gd₂Se₃ has been measured and the major thermodynamic functions have been calculated for the solid and liquid states over the temperature range 450–2300 K. The temperature dependence of the enthalpy in the ranges 300–1800 K and 2000–2300 K are represented: H°(T)-H°(298.15 K) = = 1.1949 · 10⁻² · T² + 122.38 · T + 347402 · T⁻¹ − 38716 and H°(T)-H°(298.15 K) = 262.81 · T-− 196047, respectively. The calculated temperature, enthalpy, and entropy of melting for Gd₂Se₃ are: T_m = 1925 ± 40 K, Δ_mH° (Gd₂Se₃) = 68.5 kJ · mole^-1, Δ_mS°(Gd₂Se₃) = 35.6 J · mole⁻¹ · K⁻¹. __________ Translated from Poroshkovaya Metallurgiya, Nos. 3–4(448), pp. 56–61, March–April, 2006.     

Curvature-Driven PDE Methods for Matrix-Valued Images

Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo’s concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.     

用于图像预测编码的预测器的设计及应用

设计并实现了一个用于图像预测编码的预测器。在图像压缩中,预测器是影响整个图像压缩比以及图像质量的关键环节。为了提高预测器的性能,本文结合了线性与非线性预测器的设计方法,首先对图像像素及其邻域像素之间的相关性估计值进行统计计算,确定该预测器的最佳阶数为四阶,接下来以预测差值的最小均方差标准和差值图像的期望值恒为零的约束为前提,同时对邻域模板的平坦程度加以分类,统计分析各类图像得出大量实验数据,最终设计出性能较好的四阶预测器。由于该预测器应用于星载图像的压缩,其预测系数在设计时兼备了便于硬件实现的特点。     

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

In medical image analysis and high level computer vision, there is an intensive use of geometric features like orientations, lines, and geometric transformations ranging from simple ones (orientations, lines, rigid body or affine transformations, etc.) to very complex ones like curves, surfaces, or general diffeomorphic transformations. The measurement of such geometric primitives is generally noisy in real applications and we need to use statistics either to reduce the uncertainty (estimation), to compare observations, or to test hypotheses. Unfortunately, even simple geometric primitives often belong to manifolds that are not vector spaces. In previous works [1, 2], we investigated invariance requirements to build some statistical tools on transformation groups and homogeneous manifolds that avoids paradoxes. In this paper, we consider finite dimensional manifolds with a Riemannian metric as the basic structure. Based on this metric, we develop the notions of mean value and covariance matrix of a random element, normal law, Mahalanobis distance and χ² law. We provide a new proof of the characterization of Riemannian centers of mass and an original gradient descent algorithm to efficiently compute them. The notion of Normal law we propose is based on the maximization of the entropy knowing the mean and covariance of the distribution. The resulting family of pdfs spans the whole range from uniform (on compact manifolds) to the point mass distribution. Moreover, we were able to provide tractable approximations (with their limits) for small variances which show that we can effectively implement and work with these definitions.