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During the last years, the new science of municipalities has been established as a fertile quantitative approach to systematically understand the urban phenomena. One of its main pillars is the proposition that urban systems display…

\abstract{Urban scaling theories posit that larger cities exhibit disproportionately higher levels of socioeconomic activity and human interactions. Yet, evidence from developing contexts (especially those marked by stark socioeconomic…

Numerous urban indicators scale with population in a power law across cities, but whether the cross-sectional scaling law is applicable to the temporal growth of individual cities is unclear. Here we first find two paradoxical scaling…

Physics and Society · Physics 2019-10-18 Gang Xu , Zhengzi Zhou , Limin Jiao , Ting Dong , Ruiqi Li

Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…

Physics and Society · Physics 2018-04-18 Jules Depersin , Marc Barthelemy

The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of…

Physics and Society · Physics 2023-01-31 Keith Burghardt , Johannes H. Uhl , Kristina Lerman , Stefan Leyk

Despite the rapid growth of cities in the past century, our quantitative, in-depth understanding of how cities grow remains limited due to a consistent lack of historical data. Thus, the scaling laws between a city's features and its…

Physics and Society · Physics 2024-12-18 Keith Burghardt , Johannes H. Uhl , Kristina Lerman , Stefan Leyk

We report on a quantitative analysis of relationships between the number of homicides, population size and other ten urban metrics. By using data from Brazilian cities, we show that well defined average scaling laws with the population size…

Physics and Society · Physics 2013-09-26 Luiz G. A. Alves , Haroldo V. Ribeiro , Ervin K. Lenzi , Renio S. Mendes

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…

Physics and Society · Physics 2026-05-19 Ulysse Marquis , Marc Barthelemy

Urban scaling theory posits that urban indicators follow power-law relations with population, yet the evolution of these patterns - and the role of regional differences in settings marked by social inequalities and unplanned urbanization -…

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…

Physics and Society · Physics 2022-11-18 Haroldo V. Ribeiro , Milena Oehlers , Ana I. Moreno-Monroy , Jurgen P. Kropp , Diego Rybski

Urban scaling laws reveal how cities evolve as their populations grow, yet the role of street network accessibility in this process remains underexplored. We analyze over 5,000 Brazilian cities to establish a scaling law linking average…

Physics and Society · Physics 2025-02-19 R. L. Fagundes , G. G. Piva , A. S. Mata , F. L. Ribeiro

The increasing number of crimes in areas with large concentrations of people have made cities one of the main sources of violence. Understanding characteristics of how crime rate expands and its relations with the cities size goes beyond an…

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…

Physics and Society · Physics 2021-01-26 Lei Dong , Zhou Huang , Jiang Zhang , Yu Liu

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…

Physics and Society · Physics 2019-08-21 Carlos Molinero , Stefan Thurner

More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of…

Physics and Society · Physics 2015-09-21 Luiz G. A. Alves , Renio S. Mendes , Ervin K. Lenzi , Haroldo V. Ribeiro

Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures…

Physics and Society · Physics 2015-12-22 Elsa Arcaute , Erez Hatna , Peter Ferguson , Hyejin Youn , Anders Johansson , Michael Batty

Is there a general economic pathway recapitulated by individual cities over and over? Identifying such evolution structure, if any, would inform models for the assessment, maintenance, and forecasting of urban sustainability and economic…

Physics and Society · Physics 2020-08-27 Inho Hong , Morgan R. Frank , Iyad Rahwan , Woo-Sung Jung , Hyejin Youn

Evidences are presented concerning tantalizing regularities in cities' population-flows in what regards to space and time correlations. The former exhibit a distance-behavior (for large distances) compatible with the inverse square law,…

Applications · Statistics 2012-07-30 A. Hernando , A. Plastino

There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…

Physics and Society · Physics 2013-01-28 Luis M. A. Bettencourt , Jose Lobo , Hyejin Youn

The size of cities is known to play a fundamental role in social and economic life. Yet, its relation to the structure of the underlying network of human interactions has not been investigated empirically in detail. In this paper, we map…

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