Abstract
The rapid urbanization makes the understanding of the evolution of urban environments of utmost importance to steer societies towards better futures. Many studies have focused on the emerging properties of cities, leading to the discovery of scaling laws mirroring the dependence of socio-economic indicators on city sizes. However, few efforts have been devoted to the modelling of the dynamical evolution of cities, as reflected through the mutual influence of socio-economic variables. Here, we fill this gap by presenting a maximum entropy generative model for cities written in terms of a few macro-economic variables, whose parameters (the effective Hamiltonian, in a statistical-physical analogy) are inferred from real data through a maximum-likelihood approach. This approach allows for establishing a few results. First, nonlinear dependencies among indicators are needed for an accurate statistical description of the complexity of empirical correlations. Second, the inferred coupling parameters turn out to be quite robust along different years. Third, the quasi time-invariance of the effective Hamiltonian allows guessing the future state of a city based on a previous state. Through the adoption of a longitudinal dataset of macro-economic variables for French towns, we assess a significant forecasting accuracy.
Highlights
One of the significant challenges humanity is currently facing is accelerated urbanization
Many studies have focused on the emerging properties of cities, leading to the discovery of scaling laws mirroring the dependence of socio-economic indicators on city sizes
We fill this gap by presenting a maximum entropy generative model for cities written in terms of a few macro-economic variables, whose parameters are inferred from real data through a maximum-likelihood approach
Summary
One of the significant challenges humanity is currently facing is accelerated urbanization. While the identification of the mechanisms behind the emergence of scaling laws is essential to understand the evolution of cities, the current research is still lacking studies aimed at understanding how different indicators influence each other To fill this gap, we present here a maximum entropy (ME) generative model for cities written in terms of a few macro-economic variables, whose parameters (the effective Hamiltonian, in a statistical-physical analogy) are inferred from real data through a maximum-likelihood approach. Though in the literature cities are often described as out-of-equilibrium systems [5,20], we observe that assuming a quasi-equilibrium dynamical evolution of rescaled indicators allows to forecast with high precision their future value in individual cities To this end, we assume that the vector of indicators obeys the solution of a discretized Langevin equation whose stationary state is given by the previously inferred Hamiltonian.
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