标度律的可检测性极限
Detectability limits of scaling laws
- University of Hong Kong（香港大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文推导了标度指数的分辨率极限，指出赫斯特指数决定区分竞争标度理论所需的数据记录长度，并发现许多现有数据集不足以进行可靠的模型选择。
AI中文摘要：
规模与产出之间的幂律标度关系是城市、生物体及其他复杂系统定量理论的核心。相互竞争的理论所预测的标度指数差异很小，但目前尚无理论可用于验证给定数据集是否能够以所需分辨率区分这些指数，以解决此类分歧。在此，我们推导出标度指数的分辨率极限，给出了任何分析方法所能检测到的最小指数差异。我们发现，控制系统规模演化及偏离标度律的赫斯特指数决定了增长系统的记录需要多长才能区分相互竞争的标度理论。实证结果表明，许多现有的数据面板不足以进行可靠的标度模型选择。
英文摘要：
Power law scaling relations between size and output are central to quantitative theories of cities, organisms, and other complex systems. Competing theories predict scaling exponents that differ by small fractions, but there is no existing theory for verifying whether a given dataset can even distinguish exponents at the required resolution to address such discrepancies. Here we derive a resolution limit for scaling exponents, giving the smallest exponent difference that any method of analysis can detect. We find that the Hurst exponents governing the evolution of systems' sizes and deviations from the scaling law determine how long a record of growing systems must be before it can separate competing scaling theories. Empirical results suggest that many available data panels are insufficient for reliable scaling model selection.
