无线传感器网络三维定位算法

基于在传感器网络中基站能够测量未知节点(M)S发出的辐射到达不同基站的时间差和它们之间的相对角度,提出了一种基于TDOA/AOA混合三维定位算法,根据基站测得的到达时间差(TDOA)和到达角度(AOA),将两种信息进行融合,建立节点位置估计值的混合算法,得到三维空间内的无线传感器节点坐标.仿真结果表明:在AOA测量值精度比较高时,此种混合算法能够实现比其他算法更好的定位性能     

Sink移动的无线传感网中高连通性密钥预分配方案研究

在Sink移动的无线传感器网络中,安全性和连通性是密钥预分配方案研究中的两个难点.根据节点间安全通信的设计原理,移动Sink节点与传感器节点按一定概率进行安全通信,当网络规模较大时存在大量节点无法与移动Sink节点进行通信,从而降低整个网络的数据收集率.针对这一问题,基于算法N-PGPS为网络提供安全通信的前提下,提出了一种基于树的密钥预分配方案IN-PGPS.该方案以移动Sink节点为根节点,与其通信范围内的传感器节点构成一颗局部树,以此提高传感器节点与移动Sink节点连通的概率、提高网络连通性.分析结果表明,与已有的密钥预分配方案相比,IN-PGPS方案有效提高了网络的连通性.     

基于多元线性回归分析和Chan算法的三维精确定位研究

基于无线通信基站的室内三维定位问题主要是在已知TOA和基站三维信息的情况计算出终端的位置信息,实际上就是求解方程组中的未知数.首先建立通用模型和算法求解出终端的定位,接着通过优化得到使用尽量少的基站数目实现近似最优精度的定位,然后利用提出的算法实现终端移动轨迹的二维定位,最后结合实际情况,考虑了基站的有效测量距离并设计了有效基站识别算法对问题进行了分析.     

基于单目视觉的SLAM算法研究

利用一种新型的人工路标系统-MR二维码,提出了基于单目视觉和里程计的SLAM方法.首先介绍了MR二维码系统,然后在对机器人运动模型和视觉传感器观测模型进行分析和验证的基础上,给出了一种实用的里程计位置估计误差模型.机器人移动过程中,利用扩展卡尔曼滤波器对视觉信息与里程计信息进行融合.在室内环境下进行了实际实验,实验结果表明该算法可提高机器人定位和构建地图的精度,验证了算法的有效性.     

基于迭代加权回归的推荐算法

评分预测问题是推荐系统研究的核心.本文利用用户评分数据集发掘商品之间的自相关性:将商品看作数据网络中的节点,用商品间的差异度定义节点间的距离,进而将评分预测问题转化为网络回归问题.然后使用迭代加权回归算法进行评分预测.通过对电影评分数据集Movie Lens的分析,验证了算法的有效性,结果表明迭代加权回归算法优于基于项目邻域的协同过滤算法.     

一种非视距环境下基于TOA三维定位的新方法研究

为消除非视距环境对TOA三维定位带来的误差,引入演化博弈模型,以各个测量基站作为博弈局中人,为非视距环境下的TOA三维定位问题建立了一般形式的复制动态模型.研究提出了基于演化博弈的TOA定位算法,通过迭代计算消除非视距误差,获得移动端的位置估计.进一步地,针对基站位置分布明显不均的情况,在演化博弈TOA定位算法的基础上,通过构造虚拟基站和虚拟测量值,提出了基于虚拟基站的三维定位算法.实验对比显示基于演化博弈的TOA定位算法略优于经典定位算法,在基站位置分布明显不均的情况下,基于虚拟基站的三维定位算法效果较明显.     

基于多尺度中心性算法的复杂网络节点影响力研究

复杂网络中重要节点的影响力度量是网络信息挖掘中的关键问题,传统的重要节点识别方法仅考虑单一因素影响,具有一定的局限性.提出了一种基于位置信息,拓扑结构和边重要性的多尺度中心性(Multi-Scale Centrality (MSC))的度量新方法.方法融合了多样性因子影响,在K-shell分解的基础上根据节点与其位于不同k核层的邻居间的关系构建外连边尺度衡量节点的位置信息,克服了同层节点重要性无法被区分的缺陷.又结合具有结构洞特性的节点相对其邻居节点的信息传播和控制优势,对节点的重要性更进一步地作区分.最后根据边的可替代性衡量边重要性,并依据边对其相连节点的重要性贡献构造多尺度MSC中心性算法模型.经与SIR疾病传播模型在真实网络模拟的结果进行对比,验证了本算法可行性和有效性.     

节点密度的度量方法及其应用

应用随机分布的节点集进行函数逼近时,点的支撑域的大小对逼近的有效性及精度有很大影响.为研究移动最小二乘法中最优的支撑域半径,首先给出了一种全新的节点密度的概念,它不仅能刻画节点分布的疏密程度,而且其计算算法简单,也便于点的支撑域半径的选取;其次,基于节点密度的概念给出了搜索支撑域内节点的领域搜索算法,与通常使用的全域搜索算法相比,领域搜索算法提高了计算效率,节省了搜索节点需要的时间;最后给出算例,验证文中提出的计算点的支撑域半径算法的有效性.     

社会网络二元不对称关系预测中的非独立性检验问题

社会网络中普遍存在着二元不对称关系,在网络动态演化过程中对二元不对称关系预测是基于现有的大量网络结构信息,判定信息的有效性是提高预测效率和预测结果正确率的重要保证.文章针对二元不对称关系预测提出了变量非独立性假设以及检验算法,并通过建立正态性检验算法进一步提高非独立性检验的效率.实例验证表明本文所提出的方法是合理的.     

多基站下基于信号到达时间的室内三维定位

对基于无线电信号的到达时间(TOA)的定位技术进行了研究.首先,建立了TOA测量值与真实值间的函数关系,通过求解含惩罚项的非线性最小二乘问题实现终端定位和噪声估计,并在已有研究的基础上提出了Alternating Iterative Reweighting(AIR)算法;其次,利用基站之间的几何位置进行筛选,根据每个终端信息完成自适应的最少基站的选择及定位;并结合物理特性实现终端运动轨迹预测;最后,根据基站通信半径筛选出可被定位终端,完成定位精度与终端平均连接度数之间关系的建模.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].