论文标题
固定尺寸细胞上人群分布的有限尺寸缩放尺寸及其与分形空间结构的关系
Finite-size scaling of human-population distributions over fixed-size cells and its relation to fractal spatial structure
论文作者
论文摘要
使用欧洲南部一个地区的高空间分辨率的人口统计数据，我们研究了固定尺寸空间细胞的人群。我们发现，违反直觉，当细胞的大小增加时，每个细胞的居民数量的分布会增加其变异性。然而，分布的形状保持恒定，这使我们能够引入缩放定律，类似于有限尺寸的缩放尺寸，其缩放函数与伽马分布相当合理地拟合。这意味着，由于随机变量的明显依赖性，每个细胞的居民数量分布在附近的细胞中（加上重新缩放），违背了中央限制定理，因此每个细胞的居民数量稳定或不变。有限尺寸的缩放量表意味着分布矩与其比例参数之间的幂律关系，发现与人口形成的空间模式的分形特性有关。理论预测与经验结果之间的匹配相当不错。
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases its variability when the size of the cells is increased. Nevertheless, the shape of the distributions is kept constant, which allows us to introduce a scaling law, analogous to finite-size scaling, with a scaling function reasonably well fitted by a gamma distribution. This means that the distribution of the number of inhabitants per cell is stable or invariant under addition with neighboring cells (plus rescaling), defying the central-limit theorem, due to the obvious dependence of the random variables. The finite-size scaling implies a power-law relations between the moments of the distribution and its scale parameter, which are found to be related with the fractal properties of the spatial pattern formed by the population. The match between theoretical predictions and empirical results is reasonably good.
