美国城市中种族受限人口模式与居住隔离的多重分形分析
Multifractal analysis of racially-constrained population patterns and residential segregation in the US cities
AI总结：
本文提出一种基于多重分形分析的方法，量化美国城市中种族受限人口的居住模式与隔离程度，并在十四个城市中识别出三类不同的隔离特征。
摘要：
美国城市中的种族隔离现象是一个多方面的研究领域。该领域近期的一项进展是开发了一种方法，将人口普查中按种族统计的人口数据转换为单一族裔单元格的网格。这种格式能够评估城市内部隔离的异质性。本文利用这种网格来量化种族受限的人口模式，从而能够在任意区域内计算和绘制二元隔离模式。一个关键创新是应用多重分形分析（MFA）来量化种族受限人口的居住模式。居住模式通过多重分形谱函数来表征，其中自变量是模式“间隙度”的局部度量，因变量与由所有具有相同该度量值的位置组成的子模式的大小成正比。在二元人口的背景下，种族受限人口模式的间隙度与其隔离程度有着内在联系。本文对该方法进行了全面描述，并以华盛顿特区中心地区黑人人口的居住模式为例进行说明。此外，该方法还通过美国十四个大城市中黑人人口居住模式的样本进行了演示。通过用多重分形谱对每种模式进行数值描述，这十四种模式被聚类为三个具有各自独特特征的类别。提供了每个城市的局部间隙度和隔离地图，以展示多重分形谱的性质与相应的居住和隔离模式之间的联系。该方法为美国城市内种族受限的居住和居住隔离模式提供了极好的量化手段。
英文摘要：
A phenomenon of racial segregation in U.S. cities is a multifaceted area of study. A recent advancement in this field is the development of a methodology that transforms census population count-by-race data into a grid of monoracial cells. This format enables assessment of heterogeneity of segregation within a city. This paper leverages such a grid for the quantification of race-constrained population patterns, allowing for the calculation and mapping of binary segregation patterns within arbitrary region. A key innovation is the application of Multifractal Analysis (MFA) to quantify the residency patterns of race-constrained populations. The residency pattern is characterized by a multifractal spectrum function, where the independent variable is a local metric of pattern's "gappiness", and the dependent variable is proportional to the size of the sub-pattern consisting of all locations having the same value of this metric. In the context of binary populations, the gappiness of the race-constrained population's pattern is intrinsically linked to its segregation. This paper provides a comprehensive description of the methodology, illustrated with examples focusing on the residency pattern of Black population in the central region of Washington, DC. Further, the methodology is demonstrated using a sample of residency patterns of Black population in fourteen large U.S. cities. By numerically describing each pattern through a multifractal spectrum, the fourteen patterns are clustered into three distinct categories, each having unique characteristics. Maps of local gappiness and segregation for each city are provided to show the connection between the nature of the multifractal spectrum and the corresponding residency and segregation patterns. This method offers an excellent quantification of race-restricted residency and residential segregation patterns within U.S. cities.
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