论文标题
城市系统的主要树方法
A dominance tree approach to systems of cities
论文作者
论文摘要
表征城市系统的空间组织是一个挑战，它指出了描述空间统计中明显的点过程的更一般问题。我们提出了一种非参数方法，该方法超出了点模式分析的标准工具，并且基于点与“优势树”之间的映射，该方法是由对其Voronoi Tessellation的递归分析构建的。使用玩具模型，我们表明该树中的节点的高度既编码其标记和邻域的结构，从而反映了其在系统中的重要性。我们使用法国（1876-2018）和美国（1880-2010）的历史人口数据，并表明该方法突出了这些国家所经历的多尺度城市动态。这些包括美国在树上的高度演变所揭示的美国的非单调城市轨迹。我们表明，树上的城市的高度对城市的统计定义的敏感性不如城市等级的等级。该方法还捕获了连续尺度上城市的吸引力盆地，尽管在这两个国家，这些盆地的尺寸在较大的尺度上变得更加均匀，但法国也比在美国更加异质。最后，我们介绍了一个简单的图形表示 - 高度时钟 - 监视每个城市在其国家中的作用的演变。
Characterizing the spatial organization of urban systems is a challenge which points to the more general problem of describing marked point processes in spatial statistics. We propose a non-parametric method that goes beyond standard tools of point pattern analysis and which is based on a mapping between the points and a "dominance tree", constructed from a recursive analysis of their Voronoi tessellation. Using toy models, we show that the height of a node in this tree encodes both its mark and the structure of its neighborhood, reflecting its importance in the system. We use historical population data in France (1876-2018) and the US (1880-2010) and show that the method highlights multiscale urban dynamics experienced by these countries. These include non-monotonous city trajectories in the US, as revealed by the evolution of their height in the tree. We show that the height of a city in the tree is less sensitive to different statistical definitions of cities than its rank in the urban hierarchy. The method also captures the attraction basins of cities at successive scales, and while in both countries these basin sizes become more homogeneous at larger scales, they are also more heterogeneous in France than in the US. Finally, we introduce a simple graphical representation - the height clock - that monitors the evolution of the role of each city in its country.
