Asyptotics for linear difference equations I:basic theory

We present here a unified treatment of asymptotic theory of linear difference equations. This is based on anadapted theory of discrete dichotomy. The obtained results narrow the gap between Poincarés Theorem and (the discrete analoue of) Levinson's Theorem.     

Measure and integration: The basic extension and representation theorems in terms of new inner and outer envelopes

The work of the author in measure and integration is based on new inner and outer envelope formations, which replace the traditional Carathéodory outer measure and certain simple suprema and infima. The new formations lead to essential improvements in both the extent and the adequacy of the basic results. However, they did not find an entrance into the recent textbook literature. The present paper seeks to demonstrate their power with the examples of the basic inner and outer extension and representation theorems for set functions and functionals.     

A conformal mapping approach for investigating the free-boundary seepage from symmetric channels

We present a new method to investigate the two-dimensional free-boundary groundwater seepage from symmetric soil channels into a homogeneous isotropic porous medium. We use Levi–Civitá’s function to construct an integral representation for the conformal mapping of the complex potential domain onto the physical flow domain. A genetic algorithm (GA) is used to calculate the coefficients of the Maclaurin series expansion of Levi–Civitá’s function. The coordinates of the points from the channel contour, calculated by means of the integral representation, must satisfy the analytic equation of the contour. We use this condition to define the objective function of the genetic algorithm. Levi–Civitá’s function is afterwards used to calculate the seepage loss, the free lines, the streamlines, the equipotential lines, the isobars and the velocity field. Some examples illustrate the method.     

面向目标检测的稀疏表示方法研究进展

目标检测作为图像理解的一个基础而重要的课题深受国内外学者的重视,在军事和民用中具有广泛应用.应用背景的多样性和复杂性使得传统目标检测算法难以克服复杂背景、噪声干扰、光照变化以及非刚体形变、遮挡、弱特征、尺度、视角和姿态变化等因素的影响.近些年来发展起来的稀疏表示方法为图像处理及目标检测研究提供了新的思路,本文概述了稀疏表示基本概念和理论研究进展,综述了稀疏表示方法在目标特征学习、目标分类器和滤波器设计以及多源信息融合目标检测等目标检测领域中的国内外重要研究进展,并展望了稀疏表示方法在目标检测领域的发展方向.     

基于稀疏表达残差的自然场景运动目标检测

本文提出一种基于稀疏表达残差的非参数化运动目标检测算法,在假设前景变化相对静态背景可以视为稀疏残差的基础上,采用视频前n帧初始化稀疏表达字典;利用字典对后续视频帧进行重构,提取每帧的重构残差;结合基于光照强度的全局阈值矩阵,将残差图像二值化,提取图像前景;利用前景区域和边缘点关系剔除ghost区域;采用增量PCA(Principal Component Analysis)算法和保守更新的思想对背景模型进行更新.在changedetection.net提供的shadow数据集上实验表明,采用全局更新和残差计算的方法,可以有效的解决由于自然场景光线变化导致的阴影变化,并且对自然场景中背景的小幅度抖动和相机抖动等问题也具有一定的抵抗能力.     

非平稳确定性信号与非平稳随机信号统一分类法的探讨

根据信号通过线性系统可产生新信号的理论,对非平稳确定性信号与非平稳随机信号的统一分类方法进行了深入研究,分别给出格林函数描述的线性时变系统法、调制函数作用于边界稳定线性系统的自激振荡正弦波法、随机输入线性时不变系统与边界稳定的与不稳定的线性系统组合法。这3种分类法便于对非平稳确定性信号与非平稳随机信号进行统一分类研究,并具有比较全面与系统性好的优点。     

基于多重稀疏字典的行人检测方法

针对于稀疏编码在行人检测问题中提取的特征维数高和不能够有效描述行人的问题,提出了一种基于多重稀疏字典直方图的特征提取方法。通过稀疏表示方法,预先学习多个不同稀疏度的字典,分别利用每一个字典对行人图像进行稀疏编码,统计每个字典中对应稀疏编码单元的分布直方图作为行人图像的特征描述子。该方法提取到的特征维数低,并且能够有效地描述行人,具有良好的检测性能。     

Spectral representation of reduced protein models

We consider a spectrum-like two-dimensional graphical representation of proteins based on a reduced protein model in which 20 amino acids are grouped into five classes. This particular grouping of amino acids was suggested by Riddle and co-workers in 1997. The graphical representation is based on depicting sequentially the amino acids on five horizontal lines at equal separations. One-letter codes, B, O, U, X and Y, to which numerical values 1 to 5 have been assigned, are suggested as labels for the fictional amino acids that represent all the amino acids within each group. The approach is illustrated on ND6 proteins of eight species having from 168 to 175 amino acids. While visual inspection of the novel spectral graphical representations of proteins may reveal local similarities and dissimilarities of protein sequences, arithmetic manipulations of spectra offer an elegant route to graphic visualization of the degree of similarity for selected pairs of proteins.