Samuel Arbesman, Jon M. Kleinberg, Steven H. Strogatz
Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. Here we provide a network model for the superlinear relationship between population size and innovation found in cities, with a reasonable range for the exponent.
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According to the theory of urban scaling, urban indicators scale with city size in a predictable fashion. In particular, indicators of social and economic productivity are expected to have a superlinear relation. This behavior was verified for many urban systems, but recent findings suggest that this pattern may not be valid for England and Wales (E&W), where income has a linear relation with city size. This finding raises the question of whether the cities of E&W exhibit any superlinear relation with respect to quantities such as the level of education and occupational groups. In this paper, …
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 have urban agglomerations and urban areas defined by the Netherlands Central Bureau of Statistics. For these major cities we investigated the superlinear scaling for three separate modalities: the cities defined as municipalities, their urban agglomerations and their urban areas. We find superlinearity with power-law exponents of around 1.15. But remarkably, b…
Developing a scientific understanding of cities in a fast urbanizing world is essential for planning sustainable urban systems. Recently, it was shown that income and wealth creation follow increasing returns, scaling superlinearly with city size. We study scaling of per capita incomes for separate census defined income categories against population size for the whole of Australia. Across several urban area definitions, we find that lowest incomes grow just linearly or sublinearly ($β= 0.94$ to $1.00$), whereas highest incomes grow superlinearly ($β= 1.00$ to $1.21$), with total income just su…
We investigate the socioeconomic urban scaling behavior in Denmark, Germany, and the Netherlands. In the case of Denmark we examine the scaling of larger cities, municipalities within the Copenhagen agglomeration, and municipalities in rural areas. We also distinguish between municipalities with high and low centrality. Superlinear scaling of the gross urban product with population size is found in all cases, with exponents between 1.14 and 1.24. In Germany we distinguish between major cities of which the surrounding urban region belongs to the municipality of the city, and regions around smal…
The recent quantitative approaches for studing several aspects of urban life and infrastructure have shown that scale properties allow to understand many features of urban infrastructure and of human activity in cities. In this work, an analysis based on the complexity of cities network is performed for data on Brazilian cities firearms homicides. Due to the diversity in Brazilian population and cities, this is an interesting test for theories recently proposed. The superlinear power-law behavior for number of homicides as a function of city population, with exponent $β=1.15$ is obtained. The …
Only a fast and global transformation towards decarbonization and sustainability can keep the Earth in a civilization-friendly state. As hotspots for (green) innovation and experimentation, cities could play an important role in this transition. They are also known to profit from each other's ideas, with policy and technology innovations spreading to other cities. In this way, cities can be conceptualized as nodes in a globe-spanning learning network. The dynamics of this process are important for society's response to climate change and other challenges, but remain poorly understood on a macr…
Validating Urban Scaling Laws through Mobile Phone Data: A Continental-Scale Analysis of Brazil's Largest Cities
本研究利用巴西100个最大城市的31亿条手机通话记录，在大陆尺度上验证了城市标度律，发现通信与出行呈超线性增长，GDP超线性标度而人均天线需求呈次线性标度，揭示了通信与流动性对城市社会经济格局的塑造作用。
We investigate at the subscale of the neighborhoods of a highly populated city the incidence of property crimes in terms of both the resident and the floating population. Our results show that a relevant allometric relation could only be observed between property crimes and floating population. More precisely, the evidence of a superlinear behavior indicates that a disproportional number of property crimes occurs in regions where an increased flow of people takes place in the city. For comparison, we also found that the number of crimes of peace disturbance only correlates well, and in a super…
Sustainable Development Goals are intrinsically competing, but their embedding into urban systems furthermore emphasises such compromises, due to spatial complexity, the non-optimal nature of such systems, and multi-objective aspects of their agents, among other reasons. We propose in this paper to use a stylised simulation model for systems of cities, focused on innovation diffusion and population dynamics, to show how trade-offs may operate at such a scale. We proceed in particular to a bi-objective optimisation of emissions and innovation utilities, and show that no single urban optimum exi…
While great emphasis has been placed on the role of social interactions as driver of innovation growth, very few empirical studies have explicitly investigated the impact of social network structures on the innovation performance of cities. Past research has mostly explored scaling laws of socio-economic outputs of cities as determined by, for example, the single predictor of population. Here, by drawing on a publicly available dataset of the startup ecosystem, we build the first Workforce Mobility Network among US metropolitan areas. We found that node centrality computed on this network acco…
Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community - income inequality. We propose a new method to study the scaling of income distributions by analyzing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city po…
The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be investigated. We propose here such a model for urban dynamics at the macroscopic scale, in which the diffusion of innovations between cities captures transformation processes (mutations) and transmission processes (diffusion), using two coupled spatial interaction models. Explorations of the model on synthetic systems of cities show the role of spatial interac…
This paper attempts to create a first comprehensive analysis of the integrated characteristics of contemporary Indian cities, using scaling and geographic analysis over a set of diverse indicators. We use data at the level of Urban Agglomerations in India from the Census 2011 and from a few other sources to characterize patterns of urban population density, infrastructure, urban services, economic performance, crime and innovation. Many of the results are in line with expectations from urban theory and with the behaviour of analogous quantities in other urban systems in both high and middle-in…
The recent availability of data for cities has allowed scientists to exhibit scalings which present themselves in the form of a power-law dependence with population of various socio-economical and structural indicators. We propose here a dynamical, stochastic theory of urban growth which accounts for some of the observed scalings and we confirm these results on US and OECD empirical data. In particular, we show that the dependence with population size of the total number of miles driven daily, the total length of the road network, the total traffic delay, the total consumption of gasoline, the…
Crime rates per capita are used virtually everywhere to rank and compare cities. However, their usage relies on a strong linear assumption that crime increases at the same pace as the number of people in a region. In this paper, we demonstrate that using per capita rates to rank cities can produce substantially different rankings from rankings adjusted for population size. We analyze the population-crime relationship in cities across 12 countries and assess the impact of per capita measurements on crime analyses, depending on the type of offense. In most countries, we find that theft increases…
How urban scaling and resource distribution shape social welfare and migration dynamics
本文通过数学模型研究城市规模缩放定律与政府资源分配对迁移和社会福利的影响，发现超线性资源驱动效用时城市趋于均衡，而亚线性资源驱动时则导致超大城市与不平等。
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 straightforward method for the identification of network effects in socioeconomic organization, which are the tell-tale of cities and urbanization. For districts, a sub-state regional administrative division in India, we find almost linear scaling of GDP with population, a result quite different from urban functional units in other national contexts. Using deviat…
Evolving spatiotemporal patterns and urban scaling of deaths from external causes
研究通过分析巴西城市近三十年的死亡数据，发现外部死亡原因的规模效应随时间和空间变化，揭示了城市规模与死亡率之间的复杂关系。
Cities are centers for the integration of capital and incubators of invention, and attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and prosperous future. Yet we still lack a quantitative understanding of the relationship between urban characteristics and VC activities. In this paper, we find a clear nonlinear scaling relationship between VC activities and the urban population of Chinese cities. In such nonlinear systems, the widely applied linear per capita indicators would be either biased to large…
Recently humanity has just crossed an important landmark in its history with the majority of people now living in large cities. This population concentration is capable of boosting the growth of positive indicators such as innovation, the production of new patents and supercreative employment, but increases the spread of diseases and the occurrence of crimes. Faced with the realization that crime rates grow year after year in these large urban centers, we sought to understand the dynamics of crime within cities. We investigate at the subscale of the neighborhoods of a highly populated city the…
The size of cities is known to play a fundamental role in social and economic life. Yet, its relation to the structure of the underlying network of human interactions has not been investigated empirically in detail. In this paper, we map society-wide communication networks to the urban areas of two European countries. We show that both the total number of contacts and the total communication activity grow superlinearly with city population size, according to well-defined scaling relations and resulting from a multiplicative increase that affects most citizens. Perhaps surprisingly, however, th…
Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the …
On the Meaning of Urban Scaling
本文指出，通过比较多个城市在某一日期的规模律来解释城市增长轨迹是误导性的，城市规模律反映的是不同城市历史、约束和增长路径的统计模式，而非单一城市的发展轨迹。
We explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948-2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single parameter only, and one of the parties always shows superlinear scaling and drives the process, while the sublinear exponent of the other party is merely the consequence of probability conservation. Based on the recently developed model of urban scaling, we give a microscopic model of voter behavior in which we replace diversity characterizing humans in creativ…
Multifractal analysis of racially-constrained population patterns and residential segregation in the US cities
本文提出一种基于多重分形分析的方法，量化美国城市中种族受限人口的居住模式与隔离程度，并在十四个城市中识别出三类不同的隔离特征。
Intercity connectivity and urban innovation
本研究通过绘制中美两国城际通信、人口流动与科研合作网络，发现城际连通性可提升城市专利活动预测效果，且两国驱动创新的核心网络类型存在差异，凸显城市网络位置对创新的重要性。
The prevalence of many urban phenomena changes systematically with population size. We propose a theory that unifies models of economic complexity and cultural evolution to derive urban scaling. The theory accounts for the difference in scaling exponents and average prevalence across phenomena, as well as the difference in the variance within phenomena across cities of similar size. The central ideas are that a number of necessary complementary factors must be simultaneously present for a phenomenon to occur, and that the diversity of factors is logarithmically related to population size. The …
Understanding demographic and migrational patterns constitutes a great challenge. Millions of individual decisions, motivated by economic, political, demographic, rational, and/or emotional reasons underlie the high complexity of demographic dynamics. Significant advances in quantitatively understanding such complexity have been registered in recent years, as those involving the growth of cities [Bettencourt LMA, Lobo J, Helbing D, Kuehnert C, West GB (2007) Growth,. Innovation, Scaling, and the Pace of Life in Cities, Proc Natl Acad Sci USA 104 (17) 7301-7306] but many fundamental issues stil…
The Evolution of Eco-routing under Population Growth: Evidence from Six U.S. Cities
本研究提出时间仅和时间-碳用户均衡模型，分析人口增长下生态路线的演变及城市动态，发现排放随人口超线性增长，针对性扩容可减少排放和出行时间。
We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting i…
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 their growth has long been of interest, yet fundamental debates about the effects of firm size on growth have persisted. Here we develop a scaling framework that focuses on company size as the critical feature determining a variety of tradeoffs, and use this to reveal novel systematic behavior across the diversity of publicly-traded companies. Using a large da…
Networks of agglomeration: how population density rewires social networks and reshapes contagion dynamics
通过最小主体模型，发现人口密度单独变化即可重构社交网络结构，稀疏人口形成局部集群，密集人口形成全局集成网络，并影响简单与复杂传染的传播速度与范围。
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