Isometric Logratio Transformations for Compositional Data Analysis

Geometry in the simplex has been developed in the last 15 years mainly based on the contributions due to J. Aitchison. The main goal was to develop analytical tools for the statistical analysis of compositional data. Our present aim is to get a further insight into some aspects of this geometry in order to clarify the way for more complex statistical approaches. This is done by way of orthonormal bases, which allow for a straightforward handling of geometric elements in the simplex. The transformation into real coordinates preserves all metric properties and is thus called isometric logratio transformation (ilr). An important result is the decomposition of the simplex, as a vector space, into orthogonal subspaces associated with nonoverlapping subcompositions. This gives the key to join compositions with different parts into a single composition by using a balancing element. The relationship between ilr transformations and the centered-logratio (clr) and additive-logratio (alr) transformations is also studied. Exponential growth or decay of mass is used to illustrate compositional linear processes, parallelism and orthogonality in the simplex.     

BLU Estimators and Compositional Data

One of the principal objections to the logratio approach for the statistical analysis of compositional data has been the absence of unbiasedness and minimum variance properties of some estimators: they seem not to be BLU estimator. Using a geometric approach, we introduce the concept of metric variance and of a compositional unbiased estimator, and we show that the closed geometric mean is a c-BLU estimator (compositional best linear unbiased estimator with respect to the geometry of the simplex) of the center of the distribution of a random composition. Thus, it satisfies analogous properties to the arithmetic mean as a BLU estimator of the expected value in real space. The geometric approach used gives real meaning to the concepts of measure of central tendency and measure of dispersion and opens up a new way of understanding the statistical analysis of compositional data.     

Understanding solubilisation using principles of surfactant self-assembly as geometrical constraintsCompréhension de la solubilisation par utilisation des principes d'auto-association des tensioactifs à partir des contraintes géometriques

Our aim is to give a short introduction of the use of phase diagrams in order to rationalise general principles of surfactant self-assembly. These can be rationalised in terms of geometrical constraints: volume, surface and curvature. Binary (two components: surfactant and water) and ternary systems (surfactants, water, oil) are considered separately. Models for solubilisation, to be understood within the general principles and not as tabulated data, are presented. Finally, some examples of application of solubilisation in formulation are given. To cite this article: F. Testard, T. Zemb, C. R. Geoscience 334 (2002) 649–663.     

基于O-QTM的球面VORONOI图的生成算法

提出了基于“Q－QTM”（Octahedral Quaternary Triangular Mesh）剖分的球面Voronoi图的格网生成算法；首先介绍了球面的QTM格网划发和编码方法，并根据地址码进行邻近球面三角形的探索；然后，参照数学形态学原理，重新定义了球面三角网的膨胀操作和膨胀算子，利用球面实体的递归膨胀来生成球面Voronoi图。应用VC^ 语言在OpenGL3维平台上开发了相应的实验程序，实验结果表明：利用此算法可生成球面上任意实体的Voronoi图，且生成点、弧和曲面Voronoi图的时间复杂度是一样的；而其误差受球面距离的影响较小，主要与球面实体的位置有关。最后给出了本文研究的结论及进一步的工作。     

保持空间分布特征的群点化简方法

群点目标隐含的空间结构化信息是空间分布分析、地图综合感兴趣的内容。对群点目标分布的信息内容区分为存在性、度量结构与拓扑结构，在Delaunay三角网及其对偶Voronoi图模型上对工量结构定义4个在量；分布范围、分布密度、分布中心及分布轴线，顾及视觉识别Gestalt邻近原则，运用三角形“剥皮”法，确立了非凸多边形所表达的群点分布范围，运用图像灰度表达群点分布密度并通过图像处理方法提取分布中心。建立了Voronoi图动态重建进行群点化简的方法，该方法通过边界点和内部点的分开处理，较好地保持了4个空间分布特征。     

伊朗中东部Ghaen-Birjand地区上地壳各向异性研究c

通过对1997年5月10日Zirkuh ( Ghaen-Birjand )破坏性地震若干余震横波分裂现象的观测，研究了该地区上地壳各向异性特征. 采用质点运动图和纵横比两种不同手段获取了横波分裂参数. 所选余震记录显示了明显的横波分裂，说明该地区介质具有强烈的各向异性. 通过质点运动的方法得出:快横波的偏振方向为22N19E；且快、慢横波的延时之差为6516 ms. 用纵横比的方法得到的结果为:快横波的偏振方向35N18E, 且快、慢横波的延时之差为(4910)ms. 对于厚约5 km各向异性均匀分布的水平层， 我们采用了一个沿应力分布的裂纹模型，并采用垂直于N22E排列, 且密度为0.01的裂纹情况来解释本文结果. 由于研究范围是上地壳，因此假设裂纹被水填充. 最后通过Hudson模型，对裂纹密度为0.005, 0.01和0.03的模型，给出横波速度随传播方向与裂纹对称轴夹角的变化曲线. 结果表明，当横波的偏振平行于裂纹表面时波速不随角度变化；而偏振垂直于裂纹表面时，速度曲线则有明显变化.      

基于面向对象的Voronoi图生成算法

面向对象方法是当前较为流行的程序设计方法。针对目前一些生成Voronoi图的算法中所存在的不足，探讨面向对象技术在Voronoi图的生成中的应用。     

含图像资料的气象信息管理系统研制技术

研制含图像资料的气象信息管理系统技术关键是解决气象ＰＣＸ图像格式文件的获取，保存及显示等问题。作者提出通过动态图像保存软件获得气象ＰＣＸ图像格式文件将ＰＣＸ文件保存于气象资料数据加备注字段中，并由ＵＣＤＯＳ特殊显示命令重新显示。