Zipf’s law for all the natural cities around the world

Two fundamental issues surrounding research on Zipf’s law regarding city sizes are whether and why this law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf’s law holds in a global setting, thus involving all cities around the world. Unlike previous studies, which have mainly relied on conventional census data such as populations and census-bureau-imposed definitions of cities, we adopt naturally (in terms of data speak for itself) delineated cities, or natural cities, to be more precise, in order to examine Zipf’s law. We find that Zipf’s law holds remarkably well for all natural cities at the global level, and it remains almost valid at the continental level except for Africa at certain time instants. We further examine the law at the country level, and note that Zipf’s law is violated from country to country or from time to time. This violation is mainly due to our limitations; we are limited to individual countries, or to a static view on city-size distributions. The central argument of this paper is that Zipf’s law is universal, and we therefore must use the correct scope in order to observe it. We further find Zipf’s law applied to city numbers; the number of cities in the largest country is twice as many as that in the second largest country, three times as many as that in the third largest country, and so on. These findings have profound implications for big data and the science of cities.     

Wholeness as a hierarchical graph to capture the nature of space

According to Christopher Alexander’s theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks, can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented, which enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating built and natural environments of beauty or with a high degree of wholeness.     

CRG Index: A More Sensitive Ht-Index for Enabling Dynamic Views of Geographic Features

The ht-index is a recently proposed tool for capturing dynamic views of the evolution process of geographic features, but the ht-index is not sensitive to small changes during this process. To address this problem, an improved ht-index, a cumulative rate of growth (CRG) index, was proposed. Compared to the ht-index, the CRG index is more sensitive to changes during the evolution process of geographic features, and the process is better captured by the CRG index as a result. In addition, the head/tail breaks method (used to derive the ht-index) was adjusted, making the CRG index a universal tool for capturing the dynamic views of both increasingly heterogeneous and increasingly homogeneous geographic features.     

社会感知视角下基于“头尾划分”的游憩热点识别新方法

作为游憩空间的核心研究对象,游憩热点在研判居民游憩偏好、落实城市游憩规划等方面具有重要作用。该文从“社会感知”视角,结合“头尾划分”理论,提出基于时空轨迹数据识别城市游憩热点的新方法。首先基于个人轨迹数据识别停留点,然后基于“头尾划分”理论划定游憩停留点簇群,最后整合停留点簇群并赋值于邻近道路形成游憩热点;以广州市老城区为例进行实证分析,并与两种既有点数据聚类方法进行对比。结果显示:1)广州市老城区的游憩热点整体集中于中、西部,热点类型可分为蓝绿空间、历史风貌、商业街区、批发市场和新兴网红场所5类;2)相比DBSCAN和CFSFDP算法,该文方法在识别游憩热点数量、捕捉游憩热点核心、明确游憩热点边界和运行简洁程度等方面表现更好,有利于后续游憩热点的深度分析与整合。研究成果可为城市游憩热点的识别提供新思路,也可为国土空间规划语境下游憩系统的重塑与提升提供重要分析基础。     

辅以NDVI/DEM的面向对象木薯提取方法研究——以广西壮族自治区武鸣县为例

木薯作为重要的非粮能源作物,因其种植分散、与易混淆作物缺乏生长时相差,从而导致其种植分布信息难以正确获取,一直是困扰木薯乙醇资源正确评估的技术问题。该研究以广西壮族自治区武鸣县为研究区,应用高分辨率RapidEye影像数据,探讨利用面向对象分类方法合理提取木薯种植面积及其空间分布信息。研究表明,将归一化植被指数(NDVI)和数字高程数据(DEM)应用于遥感影像的多尺度分割,并结合基于隶属度函数和阈值的面向对象分类方法,提取木薯种植面积的精度达85%,分类精度(以Kappa系数表示)为0.9。相比最大似然监督分类方法和未辅以NDVI/DEM的面向对象分类方法,该方法的总精度分别提高了5%和12%,Kappa系数分别提高了0.2和0.3。因此,NDVI和DEM数据参与影像分割的面向对象的信息提取方法,可以有效地提高遥感图像分类的精度,并为提取种植分散、与相关植被时相差异小的作物的空间分布提供了有效的技术借鉴。