ArticleRoyal Society open science2016
Is this scaling nonlinear?
Article in Royal Society open science, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 43 papers, 1 of them a synthesis that pooled it.
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Who cites it
43 citing papers in PubMed, 1 synthesis or guideline pooled it, 117 citations in OpenAlex.
- Recent advances in urban system science: Models and data.PloS one · 2022Pooled it
- Comprehensive indicators and fine granularity refine density scaling laws in rural-urban systems.Scientific reports · 2026Article
- The coherence of US cities.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Scaling COVID-19 rates with population size in the United States.Journal of the Royal Society, Interface · 2025Article
- Impact of inter-city interactions on disease scaling.Scientific reports · 2025Article
- Scaling behavior for electric vehicle chargers and road map to addressing the infrastructure gap.PNAS nexus · 2023Article
- Effects of municipal boundaries measured by combining urban scaling and spatial interaction.Journal of the Royal Society, Interface · 2023Article
- Lognormals, power laws and double power laws in the distribution of frequencies of harmonic codewords from classical music.Scientific reports · 2022Article
- Non-trivial relationship between scaling behavior and the spatial organization of GDP in Indonesian cities.PloS one · 2022Article
- Modelling virus spreading in ride-pooling networks.Scientific reports · 2021Article
- How the geometry of cities determines urban scaling laws.Journal of the Royal Society, Interface · 2021Article
- Article
- Urban population size and road traffic collisions in Europe.PloS one · 2021Article
- The effect of dragon-kings on the estimation of scaling law parameters.Scientific reports · 2020Article
- Rural-urban scaling of age, mortality, crime and property reveals a loss of expected self-similar behaviour.Scientific reports · 2020Article
- Hamiltonian modelling of macro-economic urban dynamics.Royal Society open science · 2020Article
- Urban growth and the emergent statistics of cities.Science advances · 2020Article
- The universal pathway to innovative urban economies.Science advances · 2020Article
- The impact of news exposure on collective attention in the United States during the 2016 Zika epidemic.PLoS computational biology · 2020Article
- Evidence for localization and urbanization economies in urban scaling.Royal Society open science · 2020Article
Corrections and comments
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Authors and funding
4 authors at 1 institution in 1 country.
Funding
No grant is acknowledged in the PubMed record.
Abstract
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼x (β) ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)-(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.