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There are many benefits and costs that come from people and firms clustering together in space. Agglomeration economies, in particular, are the manifestation of centripetal forces that make larger cities disproportionately more wealthy than…

Physics and Society · Physics 2024-04-23 Andres Gomez-Lievano , Michail Fragkias

The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature, many issues remain unclear. In particular, all definitions of…

Physics and Society · Physics 2016-06-22 Rémi Louf , Marc Barthelemy

Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…

General Economics · Economics 2019-08-27 Tomoya Mori

Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the…

Physics and Society · Physics 2016-06-15 Clementine Cottineau , Erez Hatna , Elsa Arcaute , Michael Batty

Cities are some of the most intricate and advanced creations of humanity. Most objects in cities are perfectly synchronised to coordinate activities such as jobs, education, transportation, entertainment, and waste management. Although each…

Physics and Society · Physics 2026-04-01 Rafael Prieto-Curiel

Over the last decades, in disciplines as diverse as economics, geography, and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using…

Physics and Society · Physics 2015-10-06 Luis M. A. Bettencourt , Jose Lobo

Estimating the capabilities, or inputs of production, that drive and constrain the economic development of urban areas has remained a challenging goal. We posit that capabilities are instantiated in the complexity and sophistication of…

Physics and Society · Physics 2021-09-17 Andres Gomez-Lievano , Oscar Patterson-Lomba

The city has proven to be the most successful form of human agglomeration and provides wide employment opportunities for its dwellers. As advances in robotics and artificial intelligence revive concerns about the impact of automation on…

Computers and Society · Computer Science 2018-02-08 Morgan R. Frank , Lijun Sun , Manuel Cebrian , Hyejin Youn , Iyad Rahwan

Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phenomena, which tend to be either too aggregated or too local, depending on the…

Physics and Society · Physics 2025-09-30 Luís M. A. Bettencourt , Ivanna Rodriguez , Jordan T. Kemp , José Lobo

The amount of data that is being gathered about cities is increasing in size and specificity. However, despite this wealth of information, we still have little understanding of what really drives the processes behind urbanisation. In this…

Physics and Society · Physics 2015-11-30 Rémi Louf

Why do some economic activities agglomerate more than others? And, why does the agglomeration of some economic activities continue to increase despite recent developments in communication and transportation technologies? In this paper, we…

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

Agglomeration economies drive urban growth at different spatial scales by enabling productivity gains, knowledge spillovers, and shared inputs among proximate firms and amenities. To develop a unified science of cities it is thus important…

Physics and Society · Physics 2026-05-12 Jianrui Wu , Baiyue He , Alec Kirkley

Although the average population density of a city is an extremely simple indicator, it is often used as a determinant factor for describing various aspects of urban phenomena. On the other hand, a plethora of different measures that aim at…

Physics and Society · Physics 2018-04-04 Valerio Volpati , Marc Barthelemy

Thanks to the use of geolocated big data in computational social science research, the spatial and temporal heterogeneity of human activities are increasingly being revealed. Paired with smaller and more traditional data, this opens new…

Physics and Society · Physics 2019-01-16 Clementine Cottineau , Maarten Vanhoof

We investigated the socioeconomic scaling behavior of all cities with more than 50,000 inhabitants in the Netherlands and found significant superlinear scaling of gross urban product with population size. Of these cities, 22 major cities…

Physics and Society · Physics 2016-02-17 Anthony F. J. van Raan , Gerwin van der Meulen , Willem Goedhart

The shape of urban settlements plays a fundamental role in their sustainable planning. Properly defining the boundaries of cities is challenging and remains an open problem in the Science of Cities. Here, we propose a worldwide model to…

Physics and Society · Physics 2018-05-24 Erneson A. Oliveira , Vasco Furtado , José S. Andrade , Hernán A. Makse

How does transport cost affect the spatial organization of economic activities? This study develops a theoretical framework that distinguishes between two types of dispersion forces in spatial models: "local" dispersion forces acting within…

General Economics · Economics 2026-03-02 Takashi Akamatsu , Tomoya Mori , Minoru Osawa , Yuki Takayama

In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear…

Applications · Statistics 2015-03-19 Cosma Rohilla Shalizi

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
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