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Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. Here…

物理与社会 · 物理学 2009-11-13 Samuel Arbesman , Jon M. Kleinberg , Steven H. Strogatz

Previous works have shown the universality of allometric scalings under density and total value at city level, but our understanding about the size effects of regions on them is still poor. Here, we revisit the scaling relations between…

物理与社会 · 物理学 2014-12-05 Yuhao Qin , Liang Gao , Lida Xu , Zi-You Gao

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…

Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…

物理与社会 · 物理学 2019-10-16 Marc Barthelemy

A longstanding puzzle in urban science is whether there's an intrinsic match between human populations and the mass of their built environments. Previous findings have revealed various urban properties scaling nonlinearly with population,…

物理与社会 · 物理学 2025-08-11 Kangning Huang , Mingzhen Lu

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…

物理与社会 · 物理学 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…

物理与社会 · 物理学 2019-08-21 Carlos Molinero , Stefan Thurner

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…

物理与社会 · 物理学 2026-05-19 Ulysse Marquis , Marc Barthelemy

Urban outputs often scale superlinearly with city population. A difficulty in understanding the mechanism of this phenomenon is that different outputs differ considerably in their scaling behaviors. Here, we formulate a physics-based model…

物理与社会 · 物理学 2019-09-25 Vicky Chuqiao Yang , Andrew V. Papachristos , Daniel M. Abrams

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…

物理与社会 · 物理学 2015-09-04 Somwrita Sarkar , Peter Phibbs , Roderick Simpson , Sachin Wasnik

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…

物理与社会 · 物理学 2015-09-21 Luiz G. A. Alves , Renio S. Mendes , Ervin K. Lenzi , Haroldo V. Ribeiro

One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\sim x^\beta, \beta \neq 1$. More…

物理与社会 · 物理学 2016-07-20 J. C. Leitao , J. M. Miotto , M. Gerlach , E. G. Altmann

Ecosystems and other naturally resilient systems exhibit allometric scaling in the distribution of sizes of their elements. In this paper we define an allometry inspired scaling indicator for cities that is a first step towards quantifying…

计算机与社会 · 计算机科学 2016-04-19 Fouad Khan , Laszlo Pinter

In this paper we make an attempt to increase our understanding of the urban scaling phenomenon. We investigate how superlinear scaling emerges if a network increases in size and how this scaling depends on the occurrence of elements that…

物理与社会 · 物理学 2023-12-06 Anthony F. J. van Raan

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…

物理与社会 · 物理学 2018-04-18 Jules Depersin , Marc Barthelemy

We study how urban quality evolves as a result of carbon dioxide emissions as urban agglomerations grow. We employ a bottom-up approach combining two unprecedented microscopic data on population and carbon dioxide emissions in the…

物理与社会 · 物理学 2014-09-15 E. A. Oliveira , J. S. Andrade , H. A. Makse

Many outputs of cities scale in universal ways, including infrastructure, crime, and economic activity. Through a mathematical model, this study investigates the interplay between such scaling laws in human organization and governmental…

物理与社会 · 物理学 2025-06-05 Bryce Morsky

Motivated by empirical evidence on the interplay between geography, population density and societal interaction, we propose a generative process for the evolution of social structure in cities. Our analytical and simulation results predict…

物理与社会 · 物理学 2013-06-12 Wei Pan , Gourab Ghoshal , Coco Krumme , Manuel Cebrian , Alex Pentland

Great cities connect people; failed cities isolate people. Despite the fundamental importance of physical, face-to-face social-ties in the functioning of cities, these connectivity networks are not explicitly observed in their entirety.…

物理与社会 · 物理学 2015-07-21 Aaron Sim , Sophia N Yaliraki , Mauricio Barahona , Michael P H Stumpf

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…

物理与社会 · 物理学 2026-05-20 Marc Duran-Sala , Martin Hendrick , Gabriele Manoli
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