arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.05725physics.soc-phphysics.app-ph
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城市宏观经济动力学的Hamilton模型

Hamiltonian Modeling of Macro-Economic Urban Dynamics

Bernardo Monechi, Miguel Ibáñez-Berganza, and Vittorio Loreto

摘要:

持续的快速城市化现象使得了解城市环境的演变对于改善福祉和引导社会走向更美好的未来至关重要。许多研究集中于城市的新特性,从而发现了反映社会经济指标对城市规模的依赖性的比例法则。虽然标度律允许定义独立于城市规模的社会经济指标,但只有少数努力致力于通过社会经济变量及其相互影响来反映城市的动态演变。在这项工作中,我们提出了一个最大熵(ME),非线性,生成模型的城市。我们写特别是一个哈密顿函数的几个宏观经济变量,其耦合参数,我们推断从实际数据对应的法国城镇。我们首先发现,不同的指标之间的非线性依赖关系需要一个完整的统计描述的非高斯相关性。此外,虽然个别城市的动态是远离平稳,我们表明,对应于不同年份的耦合参数是相当强大的。准时间不变性的哈密顿模型允许提出一个分析模型的演变的宏观经济变量的时间,朗之万方程的基础上。尽管没有时间信息的演变城市已被用来推导出这个模型,其预测精度的时间演变的系统是兼容的模型推断,明确使用这样的信息。

英文摘要:

The ongoing rapid urbanization phenomena make the understanding of the evolution of urban environments of utmost importance to improve the well-being and steer societies towards better futures. Many studies have focused on the emerging properties of cities, leading to the discovery of scaling laws mirroring, for instance, the dependence of socio-economic indicators on city sizes. Though scaling laws allow for the definition of city-size independent socio-economic indicators, only a few efforts have been devoted to the modeling of the dynamical evolution of cities as mirrored through socio-economic variables and their mutual influence. In this work, we propose a Maximum Entropy (ME), non-linear, generative model of cities. We write in particular a Hamiltonian function in terms of a few macro-economic variables, whose coupling parameters we infer from real data corresponding to French towns. We first discover that non-linear dependencies among different indicators are needed for a complete statistical description of the non-Gaussian correlations among them. Furthermore, though the dynamics of individual cities are far from being stationary, we show that the coupling parameters corresponding to different years turn out to be quite robust. The quasi time-invariance of the Hamiltonian model allows proposing an analytic model for the evolution in time of the macro-economic variables, based on the Langevin equation. Despite no temporal information about the evolution of cities has been used to derive this model, its forecast accuracy of the temporal evolution of the system is compatible to that of a model inferred using explicitly such information.

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