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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

Complex networks are commonly used to explore human behavior. However, previous studies largely overlooked the geographical and economic factors embedded in collective attention. To address this, we construct attention networks from…

Physics and Society · Physics 2025-08-13 Ke-ke Shang , Jiangli Zhu , Junfan Yi , Liwen Zhang , Junjie Yang , Ge Guo , Zixuan Jin , Michael Small

Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal…

Physics and Society · Physics 2009-09-29 Michael Batty , Rui Carvalho , Andy Hudson-Smith , Richard Milton , Duncan Smith , Philip Steadman

The spatial distribution of population and activities within urban areas, or urban form at the mesoscopic scale, is the outcome of multiple antagonist processes. We propose in this paper to benchmark different models of urban morphogenesis,…

Physics and Society · Physics 2020-09-01 Juste Raimbault

Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…

Statistical Mechanics · Physics 2007-05-23 G. Malescio , N. V. Dokholyan , S. V. Buldyrev , H. Eugene Stanley

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…

Physics and Society · Physics 2019-10-16 Marc Barthelemy

Urban land cover doubled between 1985 and 2015, yet the spatial dynamics of urban form remain under-quantified, despite its importance for sustainability, infrastructure planning, and climate risk. Urban expansion is a non-equilibrium…

Physics and Society · Physics 2026-03-10 Marc Barthelemy , Ulysse Marquis

The shape of buildings plays a critical role in the energy efficiency, lifestyles, land use and infrastructure systems of cities. Thus, as most of the world's cities continue to grow and develop, understanding the interplay between the…

Physics and Society · Physics 2015-12-04 Markus Schläpfer , Joey Lee , Luís M. A. Bettencourt

Large scale simulations of the movements of people in a ``virtual'' city and their analyses are used to generate new insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these…

Physics and Society · Physics 2016-09-08 Gerardo Chowell , James M. Hyman , Stephen Eubank , Carlos Castillo-Chavez

This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…

Physics and Society · Physics 2020-10-29 Juste Raimbault , Denise Pumain

Understanding scaling relations of social and environmental attributes of urban systems is necessary for effectively managing cities. Urban scaling theory (UST) has assumed that population density scales positively with city size. We…

Subway systems span most large cities, and railway networks most countries in the world. These networks are fundamental in the development of countries and their cities, and it is therefore crucial to understand their formation and…

Physics and Society · Physics 2014-07-18 Rémi Louf , Camille Roth , Marc Barthelemy

Although the cluster theory literature is bountiful in economics and regional science, there is still a lack of understanding of how the geographical scales of analysis (neighbourhood, city, region) relate to one another and impact the…

Physics and Society · Physics 2019-05-14 Clémentine Cottineau , Elsa Arcaute

Since the industrial revolution, accelerated urban growth has overflown administrative divisions, merged cities into large built extensions, and blurred the boundaries between urban and rural land-uses. These traits, present in most of…

Social and Information Networks · Computer Science 2017-09-21 Francisco J. Humeres , Horacio Samaniego

We undertake an exploration of the economic income (Gross Domestic Product, GDP) of Indian districts and cities based on scaling analyses of the dependence of these quantities on associated population size. Scaling analysis provides a…

Physics and Society · Physics 2020-03-25 Anand Sahasranaman , Luis M. A. Bettencourt

Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…

Physics and Society · Physics 2022-07-11 Qing Yao , Bingsheng Chen , Tim S. Evans , Kim Christensen

Easy and intuitive navigability is of central importance in cities. The actual scale-free networking of urban street networks in their topological space, where navigation information is encoded by mapping roads to nodes and junctions to…

Physics and Society · Physics 2019-10-03 Jerome Benoit , Saif Eddin Jabari

Publicly traded companies are fundamental units of contemporary economies and markets and are important mechanisms through which humans interact with their environments. Understanding the general properties that underlie the processes of…

Physics and Society · Physics 2022-07-07 Jiang Zhang , Christopher P. Kempes , Marcus J. Hamilton , Ruyi Tao , Geoffrey B. West

The city is a complex system that evolves through its inherent social and economic interactions. Mediating the movements of people and resources, urban street networks offer a spatial footprint of these activities; consequently their…

Physics and Society · Physics 2018-04-19 Minjin Lee , Hugo Barbosa , Hyejin Youn , Petter Holme , Gourab Ghoshal

The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban…

Methodology · Statistics 2018-05-10 L. Ellam , M. Girolami , G. A. Pavliotis , A. Wilson