Integrative Study of Voronoi-Delaunay Spatial Tessellation and Spatial Statistics

Voronoi-Delaunay空间细分与空间统计的综合研究

• 批准号: 17500188
• 负责人: TANEMURA Masaharu
• 金额: $ 2.37万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17500188/
• 关键词: Voronoi-Delaunay analysis; Aftershock activity; Spatial-temporal data; Langerhans cell; Spatial tessellation of a sphere; Morphological analysis; Map data of trees; Super-computer system; 全地球規模余震活動; 球面ボロノイ・デローネイ分割; MCMCによる近似尤度; 第k近接距離; ポアソン・ボロ

When a number of particles are distributed in a finite region in the space, it is the important role of spatial statistics to extract the information of statistical properties of the given spatial data and to provide an appropriate result which is useful to the scientific field corresponding to the observed data. On the other hand, there is a method of analyzing spatial data, called Voronoi-Delaunay analysis, which produces the spatial information of a given configuration of particles as a statistical distribution of the shape of Voronoi cells or Delaunay cells which are obtained by the tessellation of observed area. But, hitherto, Voronoi-Delaunay analysis was limited as a supplementary tool of the spatial statistics. In this research project, however, we aimed to positively integrate the Voronoi-Delaunay analysis to the spatial statistics by utilizing the former as a tool for extracting detailed information about the spatial data and by utilizing the results of the analysis as means … More of constructing various statistical models.In the study of statistical distribution of Poisson Voronoi cells, we obtained accurate statistical distributions of several characteristics of Poisson Voronoi cells in 4-D and 5-D spaces, and presented them as prototypes of multivariate spatial statistics. Then, we performed computations of Voronoi-Delaunay tessellation of a large scale spatial-temporal data. This is concerned with records of aftershocks of earthquakes in Japan, and the data is composed of latitude, longitude and time (3-dimensional) for each event. Data size is about 560, 000, and in order to perform the computation of 3-D Voronoi-Delaunay tessellation for such a big size of data, we used the Super-Computer system Altix of ISM for main computation and the UNIX workstation which was introduced by this project for implementing and checking computer programs.In order to make a list of Delaunay cells for such a big data, we have developed an efficient program. Further, we have prepared the Voronoi-Delaunay analysis of aftershocks of earthquakes for whole of the earth. For this computation, we need a computer program of Voronoi-Delaunay tessellation on the sphere. We have already devised such a program.Finally, we have performed Voronoi-Delaunay tessellation for spatial point patterns of Langerhans cells in a skin tissue of mouse and for spatial point patterns of pine trees in a wild situation. Less

空间统计学的重要作用是，当多个粒子分布在空间的有限区域内时，提取给定空间数据的统计特性信息，并给出与观测数据相对应的、对科学领域有用的结果。另一方面，存在一种分析空间数据的方法，称为Voronoi-Delaunay分析，其产生给定粒子配置的空间信息，作为通过观察区域的镶嵌获得的Voronoi单元或Delaunay单元的形状的统计分布。但是，迄今为止，Voronoi-Delaunay分析仅限于作为空间统计的辅助工具。然而，在本研究项目中，我们的目标是通过将Voronoi-Delaunay分析用作提取空间数据详细信息的工具，并将分析结果用作手段，将Voronoi-Delaunay分析积极整合到空间统计学中 ...更多信息 在Poisson Voronoi胞的统计分布研究中，我们得到了Poisson Voronoi胞的若干特征在四维和五维空间中的精确统计分布，并将其作为多元空间统计的原型。然后，我们进行了大规模时空数据的Voronoi-Delaunay曲面细分的计算。这是关于日本地震余震的记录，数据由每个事件的纬度、经度和时间（三维）组成。数据量约为560，000，为了对如此大的数据量进行三维Voronoi-Delaunay网格划分的计算，我们采用ISM的Altix超级计算机系统作为主计算系统，采用本项目引进的UNIX工作站作为计算机程序的实现和校验系统，并编制了一个高效的程序，以便对如此大的数据量进行Delaunay网格划分。此外，我们还准备了全球地震余震的Voronoi-Delaunay分析。对于这个计算，我们需要一个计算机程序的Voronoi-Delaunay曲面细分的领域。最后，我们对小鼠皮肤组织中朗格汉斯细胞的空间点模式和野生松树的空间点模式进行了Voronoi-Delaunay曲面细分。少

项目成果

細胞インターカーレーションによる形態形成

细胞嵌入的形态发生

• 发表时间: 2007
• 期刊: 形の科学会誌 22巻,2号
• 作者: Kentaro Tanaka;Akimichi Takemura;宮川雅巳;H.Honda;H. Honda;T.Sugimoto;M.Tanemura;沼原 利彦;本多 久夫
• 通讯作者: 本多 久夫

2x2分割表を利用した南極蘇類群落と微地形の関係評価法

利用2x2列联表评估南极亚种群落与微地形关系的方法

• 发表时间: 2007
• 期刊: 2007年度統計関連学会連合大会報告集 2007
• 作者: Kentaro Tanaka;Akimichi Takemura;宮川雅巳;H.Honda;H. Honda;T.Sugimoto;M.Tanemura;沼原 利彦;本多 久夫;M.Okuda;奥田 将己
• 通讯作者: 奥田 将己

On some aspects of random packing: dissymmetry in the packing process

关于随机装箱的一些方面：装箱过程中的不对称性

• 发表时间: 2007
• 期刊: Symmetry: Art and Science Vol.2007,No.2-4
• 作者: Kentaro Tanaka;Akimichi Takemura;宮川雅巳;H.Honda;H. Honda;T.Sugimoto;M.Tanemura;沼原 利彦;本多 久夫;M.Okuda;奥田 将己;T. Sugimoto;M. Tanemura;T. Numahara;M. Okuda;T. Sugimoto;M. Tanemura
• 通讯作者: M. Tanemura

On tilings whose tiles have many facets

在瓷砖有很多面的瓷砖上

• 发表时间: 2005
• 期刊: Romanian Journal of Pure and Applied Mathematics Vol.50
• 作者: 沼原利彦;沼原紀予;種村正美 他;M.Tanemura;N.Dolbilin
• 通讯作者: N.Dolbilin

Density and spatial structure of random packing by spheres…cases of 2-, 3-, and 4-D spaces…

球体随机堆积的密度和空间结构...2-、3-和 4-D 空间的情况...

• 发表时间: 2005
• 期刊: Bulletin of the Society for Science on Form 20
• 作者: 沼原利彦;沼原紀予;種村正美 他;M.Tanemura;N.Dolbilin;M.Tanemura;N.Dolbilin;種村 正美;M. Tanemura;N. Dolbilin;M. Tanemura;N. Dolbilin;M. Tanemura
• 通讯作者: M. Tanemura