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Neural scaling laws establish a predictable relationship between model performance and data or compute, offering crucial guidance for resource allocation in new domains and tasks. Yet such laws are most needed precisely where they are…

Machine Learning · Computer Science 2026-05-11 Xing Han , Ziyin Liu , Suchi Saria , Paul Pu Liang

The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international…

Physics and Society · Physics 2020-05-21 Juste Raimbault , Eric Denis , Denise Pumain

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

We analyze a scaling law for the consumption of agricultural soil by cities. The nonlinear dependence of the size of the city on the number of inhabitants gives rise to an equation for population dynamics. We found the asymptotic limit of…

Physics and Society · Physics 2014-11-18 Roberto D'Autilia , Ilaria D'Ambrosi

The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of…

Physics and Society · Physics 2023-01-31 Keith Burghardt , Johannes H. Uhl , Kristina Lerman , Stefan Leyk

Numerous urban indicators scale with population in a power law across cities, but whether the cross-sectional scaling law is applicable to the temporal growth of individual cities is unclear. Here we first find two paradoxical scaling…

Physics and Society · Physics 2019-10-18 Gang Xu , Zhengzi Zhou , Limin Jiao , Ting Dong , Ruiqi Li

The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most…

Physics and Society · Physics 2021-10-14 Vincent Verbavatz , Marc Barthelemy

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

Combining global gridded population and fossil fuel based CO2 emission data at 1km scale, we investigate the spatial origin of CO2 emissions in relation to the population distribution within countries. We depict the correlations between…

Physics and Society · Physics 2018-10-03 Bin Zhou , Stephan Thies , Ramana Gudipudi , Matthias K. B. Lüdeke , Jürgen P. Kropp , Diego Rybski

The interaction of all mobile species with their environment hinges on their movement patterns: the places they visit and how frequently they go there. In human society, where the prevalent form of cohabitation is in cities, the highly…

Physics and Society · Physics 2020-02-17 Markus Schläpfer , Michael Szell , Hadrien Salat , Carlo Ratti , Geoffrey B. West

Urban scaling and Zipf's law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about…

Physics and Society · Physics 2022-11-18 Haroldo V. Ribeiro , Milena Oehlers , Ana I. Moreno-Monroy , Jurgen P. Kropp , Diego Rybski

Sustainability has over the past two decades emerged as a key concern in human-computer interaction, with a much critiqued focus on quantification and eco-feedback. This approach fits within a modernist framing of sustainability, treating…

Human-Computer Interaction · Computer Science 2023-04-28 Aksel Biørn-Hansen

Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based…

Dynamical Systems · Mathematics 2022-03-29 Xiong Ying , Si-Yang Leng , Huan-Fei Ma , Qing Nie , Ying-Cheng Lai , Wei Lin

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…

Physics and Society · Physics 2019-08-21 Carlos Molinero , Stefan Thurner

The study of spacetime, and its role in understanding functional systems has received little attention in information science. Recent work, on the origin of universal scaling in cities and biological systems, provides an intriguing insight…

Computers and Society · Computer Science 2016-02-22 Mark Burgess

We report on a quantitative analysis of relationships between the number of homicides, population size and other ten urban metrics. By using data from Brazilian cities, we show that well defined average scaling laws with the population size…

Physics and Society · Physics 2013-09-26 Luiz G. A. Alves , Haroldo V. Ribeiro , Ervin K. Lenzi , Renio S. Mendes

Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare…

Machine Learning · Computer Science 2025-06-04 Leshem Choshen , Yang Zhang , Jacob Andreas

Transportation systems can be conceptualized as an instrument of spreading people and resources over the territory, playing an important role in developing sustainable cities. The current rationale of transport provision is based on…

Physics and Society · Physics 2019-08-05 J. Siqueira-Gay , M. A. Giannotti , M. Sester

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship…

Machine Learning · Computer Science 2025-02-27 Margaret Li , Sneha Kudugunta , Luke Zettlemoyer

The scaling of urban characteristics with total population has become an important research field since one needs to better understand the challenges of urban densification. Yet urban scaling research is largely disconnected from…

Physics and Society · Physics 2018-01-24 Justin Delloye , Rémi Lemoy , Geoffrey Caruso