相关论文: Hierarchical Scaling in Systems of Natural Cities
The rank-size regularity known as Zipf's law is one of scaling laws and frequently observed within the natural living world and in social institutions. Many scientists tried to derive the rank-size scaling relation by entropy-maximizing…
The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in…
Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
Urban scaling laws relate socio-economic, behavioral, and physical variables to the population size of cities and allow for a new paradigm of city planning, and an understanding of urban resilience and economies. Independently of culture…
In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear…
Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…
City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States and Japan indicates that the scaling law stems from a…
Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal…
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…
The law of allometric growth is one of basic rules for understanding urban evolution. The general form of this law is allometric scaling law. However, the deep meaning and underlying rationale of the scaling exponents remain to be brought…
City size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from…
Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
Urban scaling and Zipf's law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about…
Over the last decades, in disciplines as diverse as economics, geography, and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using…