Integrating algebraic multigrid method in spatial aggregation of massive trajectory data

The advanced technologies in location-based services and telecom have yield large volumes of trajectory data. Understanding these data effectively requires intuitive yet accurate visual analysis. The visual analysis of massive trajectory data is challenged by the numerous interactions among different locations, which cause massive clutter. This paper presents a new methodology for visual analysis by integrating algebraic multigrid (AMG) method in data aggregation. The non-parametric method helps to build a multi-layer node representation from a graph which is extracted from trajectory data. The comparison with AMG and other methods shows that AMG method is more advanced in both the spatial representation and the importance of nodes. The new method is tested with real-world dataset of cell-phone signalling records in Beijing. The results show that our method is suitable for processing and creating abstraction of massive trajectory dataset, revealing inherent patterns and creating intuitive and vivid flow maps.     

寿山石的品种简介

福建省福州市产出的寿山石由田坑石、水坑石、掘性石(坡积石)和山坑石组成。经初步统计,有田坑石16种,水坑石12种,掘性石(坡积石)18种,山坑石118种,合计164种。它们分别主要由迪开石或珍珠石或高岭石或绢云母或叶蜡石组成。     

3个代数曲面的高光滑拼接

利用计算机代数方法，讨论3个代数曲面的高光滑拼接，并将其转化为求解齐次线性方程组的问题，从而给出3个代数曲面GC^2拼接的条件．在数学软件的辅助下，给出具体实例．     

Scenario Analysis on the Adaptation of Different Maize Varieties to Future Climate Change in Northeast China

Based on gridded meteorological data for the period 1981–2100 from the RegCM3 regional model, the changing trends of climatic resources in Northeast China are analyzed, and the distributions of maize varieties are accordingly adjusted. In order to explore the effects of different adaptation countermeasures on climatic productivity and meteorological suitability in the future, maize cultivars with resistance to high temperatures and/or drought are selected. The results show that, in the future, there is likely to be a significant increase in thermal resources, and potential atmospheric evaporation will increase correspondingly.Meanwhile, radiation is predicted to increase significantly during 2041–2070 in the growing season. However, changes in precipitation are unlikely to be sufficient enough to offset the intensification in atmospheric evaporation caused by the temperature increase. Water resources and high temperatures are found to be the two major factors constraining grain yield. The results also show that the warming climate will be favorable for maize production where thermal resources are already limited, such as in central and northern Heilongjiang Province and eastern Jilin Province; while in areas that are already relatively warm, such as Liaoning Province, climatic productivity will be reduced. The climatic productivity and the meteorological suitability of maize are found to improve when the planting of resistant varieties is modeled. The utilization of agricultural climatic resources through the adaptation countermeasures of maize varieties is to increase obviously with time. Specifically, maize with drought-resistant properties will have a marked influence on meteorological suitability during 2011–2070, with suitable areas expanding. During 2071–2100, those maize varieties with their upper limit of optimum temperature and maximum temperature increased by 2℃, or water requirement reduced to 94%, or upper limit of optimum temperature and maximum temperature increased by 1℃ and water requirement reduced to 98%, all exhibit significant differences in climatic potential productivity, compared to the present-day varieties. The meteorological suitability of maize is predicted to increase in some parts of Heilongjiang Provine, with the eastern boundary of the "unavailable" area shifting westward.     

KLEIN密码代数旁路攻击

将代数分析和旁路攻击结合,基于汉明重量泄露模型,对轻量级分组密码KLEIN抗代数旁路攻击安全性进行了评估。首先应用代数方法构建KLEIN算法等价布尔方程组,然后经功耗分析获取KLEIN加密操作的汉明重量并表示为布尔方程,最后使用CryptMinisat解析器进行密钥求解。基于均值、排名和门限3种容错策略,对8位微控制器上的KLEIN开展了攻击物理实验,并对攻击复杂度进行评估,结果表明:未经防护的KLEIN软件实现易遭受代数旁路攻击,已知明文场景下,1轮泄露分析即可恢复完整KLEIN密钥;未知明密文场景下,2轮泄露分析仍可成功实施攻击。该方法对其他分组密码抗代数旁路攻击研究具有一定的借鉴意义。     

不同生育期四合木抗氧化系统的变化及生境间差异

对不同生境四合木种群特征、根际土壤理化性质进行了比较分析,对不同生育期四合木抗氧化系统的变化和生境间差异性进行了探讨。结果表明:①不同生境四合木种群密度、盖度、年龄结构存在显著差异,且低山、台地、丘陵种群所处生境有利于幼苗更新,其密度和盖度均显著大于高平原和倾斜平原种群\.②不同生境四合木根际土壤理化性质存在显著差异。对其进行聚类分析分为两类:低山、台地、丘陵为一类（A类）;高平原、倾斜平原为一类（B类）\.方差分析表明,A类样地土壤营养元素（N、P、K）和微量元素（全Fe、Mn、Zn、B、Mo与有效量）、土壤有机质含量及土壤含水量都显著高于B类。③不同生境四合木体内MDA含量、抗氧化酶类SOD、POD、CAT、AsA-POD、GR活性和非酶抗氧化剂GSH、AsA含量均随5月（营养期）、6月（花期）、8月（果期）而不断升高,二者协同作用共同抵抗干旱胁迫诱导的氧化伤害。④不同生境四合木抗氧化系统存在差异性:A类样地受到的膜脂过氧化程度相对较低,其体内的抗氧化酶活性和抗氧化剂含量较低;而B类样地四合木根际土壤干旱程度较高,土壤偏贫瘠,植物体通过提高一定幅度的抗氧化酶活性和抗氧化剂含量以清除干旱导致的氧化伤害。     

应用代数重建法编程重建数字图像

对已知和未知数字图像分别沿射线作Radon变换(线积分),用同一种布置射线特殊方法布置射线,每条射线积分步长易知皆为常数。从而,得到已知数字图像每条射线的线积分近似值(“观测值”);易建立未知数字图像线性代数方程组。应用“代数重建法”加法修正迭代编制Matlab程序,用此程序处理“观测值”数据,重建未知数字图像,其数值计算结果较好,与已知数字图像相对误差不超过2%。本文是ART加法修正迭代的基础工作,可为有关部门提供研究“代数重建法”实际应用参考。      

Kaczmarz算法收敛解的性态分析

Kaczmarz算法作为一种重要的代数重建技术(ART)在医学成像及诊断研究中起着很重要的作用。随着计算机硬件技术的发展,诸如ART、SIRT等迭代算法由于其良好的抗干扰性能及数据缺失情况下良好的成像能力逐渐受到人们的重视。本文主要基于矩阵广义逆的定义和性质证明,当x(0)∈R(AT)⊥时Kaczmarz算法迭代序列的极限为Moore-Penrose广义解的性质。理论表明Kaczmarz方法求解相容性和不相容性问题都是适定方法,本文从数值实验的角度验证了Kaczmarz方法的“适定”性和求解扰动问题时的“半收敛”性。另外,Kaczmarz方法当x(0)∈R(AT)⊥时还是一类正则化方法。      

高斯投影复变换的数值计算方法

高斯投影复变换的数值计算简单快捷,具有重要的工程应用价值.从数值计算角度出发,使用计算机代数系统Mathcad,Matlab以及Mathematica对高斯投影复变换进行了改进:只需建立正算变换计算式而不再需要建立反算变换计算式.对于复方程,利用系统的求根函数直接求解.对于复积分,研究了积分级数分析法、椭圆积分函数法及...     

大型稀疏法方程组的代数多重网格解法

测量平差中经常会遇到大型稀疏法方程组的求解。传统的线性方程组迭代解法能够很快平滑误差分量中的高频分量;但对于低频分量衰减很慢。代数多重网格算法通过建立多重网格,并在不同的网格层上分别处理高低频误差分量,将所有层相互协调起来求解同一问题。这对于大规模稀疏线性方程组的求解,具有高效性。这里介绍了代数多重网格算法,并进行了改进,得到了AMG-CG算法。数值算例表明,代数多重网格算法(AMG)以及改进的AMG-CG算法对求解大型稀疏法方程组具有高效性和数值稳定性,改进后的AMG-CG算法在计算效率上进一步提高,对于大型稀疏法方程组的求解是可行有效的算法。