Related papers: Association between population distribution and ur…
Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…
Crime rates per capita are used virtually everywhere to rank and compare cities. However, their usage relies on a strong linear assumption that crime increases at the same pace as the number of people in a region. In this paper, we…
Two classical hypotheses are examined about the population growth in a system of cities: Hypothesis 1 pertains to Gibrat's and Zipf's theory which states that the city growth-decay process is size independent; Hypothesis 2 pertains to the…
While there has been an extended discussion concerning city population distribution, little has been said about administrative units. Even though there might be a correspondence between cities and administrative divisions, they are…
This work studies the Zipf Law for cities in Brazil. Data from censuses of 1970, 1980, 1991 and 2000 were used to select a sample containing only cities with 30,000 inhabitants or more. The results show that the population distribution in…
Challenges due to the rapid urbanization of the world -- especially in emerging countries -- range from an increasing dependence on energy, to air pollution, socio-spatial inequalities, environmental and sustainability issues. Modelling the…
Urban-induced microclimate variations, such as urban heat islands and air pollution, scale with city size, producing distinctive relations between average climate variables and city-scale quantities (e.g., total population). However, these…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
Developing a scientific understanding of cities in a fast urbanizing world is essential for planning sustainable urban systems. Recently, it was shown that income and wealth creation follow increasing returns, scaling superlinearly with…
We have assembled CO2 emission figures from collections of urban GHG emission estimates published in peer reviewed journals or reports from research institutes and non-governmental organizations. Analyzing the scaling with population size…
Combining global gridded population and fossil fuel based CO2 emission data at 1km scale, we investigate the spatial origin of CO2 emissions in relation to the population distribution within countries. We depict the correlations between…
We present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration. In most cases, the Boltzmann-type kinetic description allows to obtain, within an asymptotic procedure, a…
We investigate spatial dependence in Zipf's law for cities among the OECD countries. The aim is to identify an upper tail of the distribution that follows a power law (Pareto) but is perturbed by spatial autocorrelation, as indicated by a…
Analysis of the urban population fraction data for sixteen populous countries over the last fifty years reveals a universal increase in urbanization, exhibiting four qualitatively distinct temporal patterns: (i) continuously accelerating…
Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes…
This article investigates scaling laws within language families using data from over six thousand languages and analyzing emergent patterns observed in Zipf-like classification graphs. Both macroscopic (based on number of languages by…
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…
The share of the world population living in cities with more than one million people rose from 11% in 1975 to 24% in 2025 (our estimates). Will this trend towards greater concentration in large cities continue or level off? We introduce two…
The Zipf's law establishes that if the words of a (large) text are ordered by decreasing frequency, the frequency versus the rank decreases as a power law with exponent close to $-1$. Previous work has stressed that this pattern arises from…
Voting data from city-councillors, state and federal deputies elections are analyzed and considered as a response function of a social system with underlying dynamics leading to complex behavior. The voting results from the last two general…