Many complex systems exhibit universal scaling laws, for example, the famous Kleiber law in biology, and the scaling law in cities. On one side, by discovering scaling laws on the aggregated level from the data, scaling analysis can characterize the macroscopic universal patterns of complex systems, on the other side, scaling laws can provide some insights for the micro-level mechanisms. I have done several works on scaling laws, for example, in urban system, firms, web forums, and so on.
By a simple model mainly based on spatial attraction and matching growth mechanisms, we reveal that the spatial scaling rules of these three elements are in a consistent framework, which allows us to use any single observation to infer the others. All numerical and theoretical results are consistent with empirical data from ten representative cities. In addition, our model can also provide a general explanation of the origins of the universal super- and sub-linear aggregate scaling laws and accurately predict kilometre-level socioeconomic activity. Our work opens a new avenue for uncovering the evolution of cities in terms of the interplay among urban elements, and it has a broad range of applications
Two classes of scaling behaviours, namely the super-linear scaling of links or activities and the sub-linear scaling of area, diversity, or time elapsed with respect to size have been found to prevail in the growth of complex networked systems. Despite some pioneering modelling approaches proposed for specific systems, whether there exists some general mechanisms that account for the origins of such scaling behaviours in different contexts, especially in socioeconomic systems, remains an open question. We address this problem by introducing a geometric network model without free parameter, finding that both super-linear and sub-linear scaling behaviours can be simultaneously reproduced and that the scaling exponents are exclusively determined by the dimension of the Euclidean space in which the network is embedded.
In comparison with patterns of city systems found in traditional census data, we examined the allometric scaling, size distribution and fractal geometry of natural cities. It can be concluded from our empirical analysis on regional, country and continental scales that a super-linear scaling between lightness and area with a stable exponent across different low light threshold levels generally holds for natural cities. But Zipf’s Law does not always apply over the whole range of lightness thresholds. Furthermore, we build a model based on the simple geometric matching mechanism to reproduce the self-organized formation process of nighttime light patterns. The statistical properties including allometries, size distributions and fractal geometries generated by our model are in good agreement with empirical evidence. These findings have profound implications for understanding the effects of simple aggregation behaviour in primitive stages of city formation and the urbanization process
Our study shows that the power law relationship T ∝ Pγ (γ > 1) is in fact ubiquitous in online activities such as microblogging, news voting, and photo tagging. We call the pattern “accelerating growth” and find it relates to a type of distribution that changes with system size. We show both analytically and empirically how the growth rate γ associates with a scaling parameter b in the size-dependent distribution. As most previous studies explain accelerating growth by power law distribution, the model of size-dependent distribution is worth further exploration.