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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

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.…

Physics and Society · Physics 2015-07-21 Aaron Sim , Sophia N Yaliraki , Mauricio Barahona , Michael P H Stumpf

Are there multiple equilibria in the spatial economy? This paper develops a unified framework that integrates systems of cities and regional models to address this question within a general geographic space. A key feature is the endogenous…

Theoretical Economics · Economics 2025-05-01 Gianandrea Lanzara , Matteo Santacesaria

Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding…

Physics and Society · Physics 2019-09-04 Hoai Nguyen Huynh

Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…

Physics and Society · Physics 2024-04-04 Fabiano L. Ribeiro , Vinicius M. Netto

The concept of hierarchy in complex systems is tightly linked to co-evolutionary processes. We propose here to explore it in the case of the co-evolution between transportation networks and territories. More precisely, we extend a…

Physics and Society · Physics 2020-02-03 Juste Raimbault

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

Urbanization has been the dominant demographic trend in the entire world, during the last half century. Rural to urban migration, international migration, and the re-classification or expansion of existing city boundaries have been among…

Physics and Society · Physics 2013-12-19 Philippe Blanchard , Dimitri Volchenkov

Urban space is highly heterogeneous, with population and human activities concentrating in localized centers. However, the global organization of such intra-urban centers remains poorly understood due to the lack of consistent, comparable…

Physics and Society · Physics 2026-01-21 Shuai Pang , Junlong Zhang , Yu Liu , Lei Dong

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

Understanding the long-term impact that changes in a city's transportation infrastructure have on its spatial interactions remains a challenge. The difficulty arises from the fact that the real impact may not be revealed in static or…

Physics and Society · Physics 2014-11-27 Lijun Sun , Jian Gang Jin , Kay W. Axhausen , Der-Horng Lee , Manuel Cebrian

Urban cultures and architectural styles vary significantly across cities due to geographical, chronological, historical, and socio-political factors. Understanding these differences is essential for anticipating how cities may evolve in the…

Computer Vision and Pattern Recognition · Computer Science 2025-08-05 Jun Yin , Jing Zhong , Peilin Li , Ruolin Pan , Pengyu Zeng , Miao Zhang , Shuai Lu

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

Growth is a multi-layered phenomenon in human societies, composed of socioeconomic and demographic change at many different scales. Yet, standard macroeconomic indicators average over most of these processes, blurring the spatial and…

Physics and Society · Physics 2025-11-11 Jordan T Kemp , Laura Fürsich , Luís M A Bettencourt

Characterizing the structure of cities constitutes an important task since the identification of similar cities can promote sharing of respective experiences. In the present work, we consider 20 European cities from 5 respective countries…

Physics and Society · Physics 2022-09-28 Luciano da F. Costa , Eric K. Tokuda

Entropy relates the fast, microscopic behaviour of the elements in a system to its slow, macroscopic state. We propose to use it to explain how, as complexity theory suggests, small scale decisions of individuals form cities. For this, we…

Physics and Society · Physics 2017-11-28 Martin Barner , Clémentine Cottineau , Carlos Molinero , Hadrien Salat , Kiril Stanilov , Elsa Arcaute

Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…

Physics and Society · Physics 2024-06-11 Chenxin Liu , Yu Yang , Bingsheng Chen , Tianyu Cui , Fan Shang , Jingfang Fan , Ruiqi Li

Large-scale networks of human interaction, in particular country-wide telephone call networks, can be used to redraw geographical maps by applying algorithms of topological community detection. The geographic projections of the emerging…

Social and Information Networks · Computer Science 2013-12-23 Stanislav Sobolevsky , Michael Szell , Riccardo Campari , Thomas Couronné , Zbigniew Smoreda , Carlo Ratti

Urban economic vitality is a crucial indicator of a city's long-term growth potential, comprising key metrics such as the annual number of new companies and the population employed. However, modeling urban economic vitality remains…

Artificial Intelligence · Computer Science 2025-12-01 Xiaofeng Li , Xiangyi Xiao , Xiaocong Du , Ying Zhang , Haipeng Zhang

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
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