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As urban critic Jane Jacobs conceived, a city is essentially the problem of organized complexity. What underlies the complexity refers to a structural factor, called living structure, which is defined as a mathematical structure composed of…

Physics and Society · Physics 2024-10-03 Andy Jingqian Xue , Chenyu Huang , Bin Jiang

The growth of cities has traditionally been studied from a population perspective, while urban expansion-its spatial growth-has often been approached qualitatively. However, characterizing and modeling this spatial expansion is crucial,…

Physics and Society · Physics 2026-03-31 Ulysse Marquis , Marc Barthelemy

Disparity in spatial accessibility is strongly associated with growing inequalities among urban communities. Since improving levels of accessibility for certain communities can provide them with upward social mobility and address social…

Physics and Society · Physics 2022-03-28 Leonardo Nicoletti , Mikhail Sirenko , Trivik Verma

A large proportion of Africa's infrastructure is yet to be built. Where and how these new buildings are constructed matters since today's decisions will last for decades. The resulting morphology of cities has lasting implications for a…

Physics and Society · Physics 2022-08-12 Rafael Prieto Curiel , Jorge E. Patino , Brilé Anderson

It is traditionally assumed that Zipf's law implies the power-law growth of the number of different elements with the total number of elements in a system - the so-called Heaps' law. We show that a careful definition of Zipf's law leads to…

Physics and Society · Physics 2015-06-17 Francesc Font-Clos , Alvaro Corral

Given the importance of urban sustainability and resilience to the future of our planet, there is a need to better understand the interconnectedness between the social, economic, environmental, and governance outcomes that underline these…

Physics and Society · Physics 2019-04-15 Anand Sahasranaman , Henrik Jeldtoft Jensen

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…

Physics and Society · Physics 2025-06-05 Bryce Morsky

We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth…

Disordered Systems and Neural Networks · Physics 2009-10-31 Hernan A. Makse , Jose S. Andrade , Michael Batty , Shlomo Havlin , H. Eugene Stanley

Cities are centers for the integration of capital and incubators of invention, and attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and…

Physics and Society · Physics 2022-02-15 Ruiqi Li , Lingyun Lu , Weiwei Gu , Shaodong Ma , Gang Xu , H. Eugene Stanley

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…

Physics and Society · Physics 2026-05-20 Marc Duran-Sala , Martin Hendrick , Gabriele Manoli

Cities are complex systems, their complexity manifests itself through fractality of their spatial structures and by power law distributions (scaling) of multiple urban attributes. Here we report on the previously unreported manifestation of…

Physics and Society · Physics 2021-02-03 Tomasz F. Stepinski , Anna Dmowska

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…

Physics and Society · Physics 2022-03-17 Marcos Oliveira

Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility and freight transportation. However, despite their importance, the…

Physics and Society · Physics 2026-03-09 Xu-Jie Lin , Yitao Yang , Wei-Peng Nie , Xiao-Yong Yan

The question of whether urbanization contributes to increasing carbon dioxide emissions has been mainly investigated via scaling relationships with population or population density. However, these approaches overlook the correlations…

Physics and Society · Physics 2019-07-23 Haroldo V. Ribeiro , Diego Rybski , Jürgen P. Kropp

The law of allometric growth originated from biology has been widely used in urban research for a long time. Some conditional research conclusions based on biological phenomena have been erroneously transmitted in the field of urban…

Physics and Society · Physics 2025-02-28 Yanguang Chen

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…

Physics and Society · Physics 2021-01-21 Eduardo G. Altmann

We study the scaling of (i) numbers of workers and aggregate incomes by occupational categories against city size, and (ii) total incomes against numbers of workers in different occupations, across the functional metropolitan areas of…

Physics and Society · Physics 2019-10-17 Somwrita Sarkar , Elsa Arcaute , Erez Hatna , Tooran Alizadeh , Glen Searle , Michael Batty

Map generalization is a process of producing maps at different levels of detail by retaining essential properties of the underlying geographic space. In this paper, we explore how the map generalization process can be guided by the…

Data Analysis, Statistics and Probability · Physics 2013-10-22 Bin Jiang , Xintao Liu , Tao Jia

The study addresses the patterns of ground sealing for two different types of German cities during 2006 to 2018. By using urban scaling law and corresponding panel regressions, it can be shown that sealing of ground in the distribution of…

Physics and Society · Physics 2024-09-06 Rolf Bergs

The quest for a theory of cities that could offer a quantitative and systematic approach to manage cities is at the top priority, given the challenges humanity faces due to the increasing urbanization and densification of cities. If such a…

Physics and Society · Physics 2021-11-17 Fabiano L. Ribeiro , Diego Rybski