In the 21st century ongoing rapid urbanization highlights the need to gain deeper insights into the social structure of cities. While work on this challenge can profit from abundant data sources, the complexity of this data itself proves to be a challenge. In this paper we use diffusion maps, a manifold learning method, to discover hidden manifolds in the UK 2011 census data set. The census key statistics and quick statistics report 1450 different statistical features for each census output area. Here we focus primarily on the city of Bristol and the surrounding countryside, comprising 3490 of these output areas. Our analysis finds the main variables that span the census responses, highlighting that university student density and poverty are the most important explanatory variables of variation in census responses.
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 and climate, almost all cities exhibit two fundamental scaling exponents, one sub-linear and one super-linear that are related. Here we show that based on fundamental fractal geometric relations of cities we derive both exponents and their relation. Sub-linear scaling arises as the ratio of the fractal dimensions of the road network and the distribution of the…
Recent advances in the urban science make broad use of the notion of scaling. We focus here on the important scaling relationship between the gross metropolitan product (GMP) of a city and its population (pop). It has been demonstrated that GMP $\propto$ Y pop $^β$ with $β$ always greater than 1 and close to 1.2. This fundamental finding highlights a universal rule that holds across countries and cultures and might explain the very nature of cities. However, in an increasingly connected world, the hypothesis that the economy of a city solely depends on its population might be questionable. Usi…
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…
Bidirectional yet asymmetric causality between urban systems and traffic dynamics in 30 cities worldwide
ETH Zurich（苏黎世联邦理工学院）；University College London（伦敦大学学院）；Singapore-ETH Centre, ETH Zurich（新加坡-苏黎世联邦理工学院中心，苏黎世联邦理工学院）；Department of Geography, University of Wisconsin-Madison（威斯康星大学麦迪逊分校地理系）
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale systematically with population sizes across cities, also known as urban scaling laws. However, at the mesoscopic level, we lack an understanding of whether the simple scaling relationship holds within cities, which is a fundamental question regarding the spatial origin of scaling in urban systems. Here, by analyzing four extensive datasets covering millions of …
The ideal Renaissance city is designed as a star-shaped fortress, where the streets and squares are organized to speed the movement of people and soldiers. Symmetry and accessibility represent the key features for the organization of the urban space. The resulting city is hierarchized and does not always guarantee an optimal degree of connectivity. Taking the baton from the work done by space syntax in the definition of properties of spatial graph representation, we introduce a method to compute urban graphs from the Euclidean representation, the corresponding line graph and the contraction of…
Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realisations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. T…
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of C…
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, …
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between entropy and fractal dimension, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurement into fractal dimension for the spatial analysis of scale-free urban phenomena using ideas from scaling. Urban systems proved to be random prefractal and multifractals systems. The entropy o…
Beijing Jiaotong University（北京交通大学）；Leibniz Institute of Ecological Urban and Regional Development (IOER)（莱布尼茨生态城市与区域发展研究所）；Federal University of Lavras (UFLA)（拉夫拉斯联邦大学）；University College London（伦敦大学学院）
The development of public transportation networks and associated transit oriented development policies are efficient tools to mitigate urban sprawl and its negative environmental impacts, especially in terms of commuting emissions. We study in this paper the trajectories in terms of sprawl and public transport accessibility of the nine largest Chinese megacities, from 2000 to 2030 with projected transportation networks and populations. Using the radial profile methodology, we compare the evolution of population distribution with the evolution of accessibility profiles. We show a rebalancing of…
The difference of a city's artificial land use (ALU) radial profile to the average ALU profile is examined for 585 European cities. Using Urban Atlas 2012 data, a radial (or monocentric) approach is used to calculate a city's land use profile in relation to distance to the city centre. A scaling law is used which controls for city size and population. As a consequence, cities of varying degrees of size can be contrasted in a comparable way. Utilising the mean ALU profile for the entire sample of 585 cities, the difference to the mean profile is calculated for each city. Using these differences…
The percentage of urban areas dedicated to streets and public spaces is a crucial feature of the spatial planning of cities. By 2050 urban mobility will be one of the biggest confronts for global cities. This study has been carried out to assess the ratio of public space allocated to the streets in some cities of Bangladesh. The length, width, area, and number of street crossings have been counted for the city core and its suburban area as an indicator of the form and pattern of the street layout. This exercise does not consider the rest of the public spaces, like gardens and general public sp…
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…
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 define urban settlements beyond their administrative boundaries through a bottom-up approach that takes into account geographical biases intrinsically associated with most societies around the world, and reflected in their different regional growing dynamics. The generality of the model allows to study the scaling laws of cities at all geographical levels: coun…
The emergence of India as an urbanized nation is one of the most significant socioeconomic and political processes of the 21st century. An essential feature of India's urbanization has been the growth and persistence of informal settlements (slums) in its fast-developing cities. Whether living conditions in Indian urban slums constitute a path to human development or a poverty trap is therefore an issue of vital importance. Here, we characterize census data using the framework of urban scaling to systematically characterize the relative properties of Indian urban slums, focusing on attributes …
We examined the effect of social distancing on changes in visits to urban hotspot points of interest. Urban hotspots, such as central business districts, are gravity activity centers orchestrating movement and mobility patterns in cities. In a pandemic situation, urban hotspots could be potential superspreader areas as visits to urban hotspots can increase the risk of contact and transmission of a disease among a population. We mapped origin-destination networks from census block groups to points of interest (POIs) in sixteen cities in the United States. We adopted a coarse-grain approach to s…
We compare the structural properties of the street networks of ten different European cities using their primal representation. We investigate the properties of the geometry of the networks and a set of centrality measures highlighting differences and similarities among cases. In particular, we found that cities share structural similarities due to their quasi planarity but that there are also several distinctive geometrical proprieties. A Principal Component Analysis is also performed on the distributions of centralities and their respective moments, which is used to find distinctive characte…
We study centrality in urban street patterns of different world cities represented as networks in geographical space. The results indicate that a spatial analysis based on a set of four centrality indices allows an extended visualization and characterization of the city structure. Planned and self-organized cities clearly belong to two different universality classes. In particular, self-organized cities exhibit scale-free properties similar to those found in the degree distributions of non-spatial networks.
We analyze the anonymous communication patterns of 2.5 million customers of a Belgian mobile phone operator. Grouping customers by billing address, we build a social network of cities, that consists of communications between 571 cities in Belgium. We show that inter-city communication intensity is characterized by a gravity model: the communication intensity between two cities is proportional to the product of their sizes divided by the square of their distance.
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…
Cities are complex systems comprised of socioeconomic systems relying on critical services delivered by multiple physical infrastructure networks. Due to interdependencies between social and physical systems, disruptions caused by natural hazards may cascade across systems, amplifying the impact of disasters. Despite the increasing threat posed by climate change and rapid urban growth, how to design interdependencies between social and physical systems to achieve resilient cities have been largely unexplored. Here, we study the socio-physical interdependencies in urban systems and their effect…
Seen from a satellite, observing land use in the daytime or at night, most cities have circular shapes, organised around a city centre. A radial analysis of artificial land use growth is conducted in order to understand what the recent changes in urbanisation are across Europe and how it relates to city size. We focus on the most fundamental differentiation regarding urban land use: has it been artificialised for human uses (residence or roads for instance) or is it natural, or at least undeveloped? Using spatially detailed data from the EU Copernicus Urban Atlas, profiles of artificial land u…
Mobility energetic balance frames spatial configuration of cities
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB)（综合物理与复杂系统研究所）；Human Openware Research Lab (HOWLab), Engineering Research Institute of Aragon (I3A), University of Zaragoza (UZ)（萨拉戈萨大学阿拉贡工程研究院）；Arquitecturas Open Source (AOS) Research Group, School of Architecture and Technology, Universidad San Jorge（圣乔治大学建筑与技术学院）
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 relationships that urban built-up area sub-linearly scales with population across cities, but super-linearly scales with population over time in most individual cities because urban land expands faster than population grows. Different cities have diverse temporal scaling exponents and one city even has opposite temporal scaling regimes during two periods, strongl…
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 thesis we apply some ideas from statistical physics to the study of cities. We first present a stochastic, out-of-equilibrium model of city growth that describes the structure of the mobility pattern of individuals. The model explains the appearance of secondary subcenters as an effect of traffic congestion, and predicts a sublinear increase of the number of …
Given the importance of urban sustainability and resilience to the future of our planet, there is a need to better understand the interconnectedness between the social, economic, environmental, and governance outcomes that underline these frameworks. Here, we propose a synthesis of the independent scientific frameworks of economic complexity and urban scaling into a consistent mechanism - termed 'city complexity' - to measure the fitness of cities across multiple dimensions. Essentially, we propose the use of urban scaling as the basis to construct and populate a bipartite city-outcome matrix,…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal parameters can be employed to characterize scale-free phenomena. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on different entropy concepts. Three representa…
The city reading proposed is a modern postmodern urbanism approach which quantifies but by passing through subjectivism. The isobenefit lines shown translate cities into benefit landscapes, subjective and continually changeable according to personal moods needs preferences and urban transformations. They read attractiveness and how they flow throughout the city. Doing it for each urban point and for each urban attraction, we obtain the isobenefit orography of the city, namely a map of its urban attractions and of their flows. This is a liquid surface rather than solid, as it varies across time…
Cities are physical manifestations of our competitive and cooperative behaviours. The tension between these two forces generates dynamic equilibriums whose material expressions are cities and their evolutions. In a Darwinian cooperative view, as Darwinism does not involve only competition, the public benefit obtained by cooperation, return in terms of private benefit too. An urban genetic code is proposed, according to which cities emerge connecting nature and urbanity, and as sum of multiuse, independent micro-areas, each one with its centrality, job locations, parks and daily shops-services …
We propose a phenomenological non-equilibrium framework for modelling the evolution of cities which describes the intra-urban resettlement as an irreversible diffusive process. We validate this framework using the actual migration data for the Australian capital cities. With respect to the residential relocation, the population is shown to be composed of two distinct groups, exhibiting different relocation frequencies. In the context of the developed framework, these groups can be interpreted as two components of a binary mixture, each with its own diffusive relaxation time. Using this approac…
Bus transportation is considered as one of the most convenient and cheapest modes of public transportation in Indian cities. Due to their cost-effectiveness and wide reachability, they help a significant portion of the human population in cities to reach their destinations every day. Although from a transportation point of view they have numerous advantages over other modes of public transportation, they also pose a serious threat of contagious diseases spreading throughout the city. The presence of numerous local spatial constraints makes the process and extent of epidemic spreading extremely…
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 characteristics of urban environments and the built form of cities is essential to achieve local and global sustainability goals. Here, we compile and analyze the most extensive data set of building shapes to date, covering more than 4.8 million individual buildings across several major cities in North America. We show that average building height increases syst…
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 same territory, time and attribute, depending on the criteria used to delineate cities. The aim of this paper is to present new insights concerning this variation, coupled with a sensitivity analysis of urban scaling in France, for several socio-economic and infrastructural attributes from data collected exhaustively at the local level. The sensitivity analys…
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 …
Understanding the relationship between spatial structures of cities and environmental hazard exposures (such as urban heat) is essential for urban health and sustainability planning. However, a critical knowledge gap exists in terms of the extent to which socio-spatial networks shaped by human mobility exacerbate or alleviate urban heat exposures of populations in cities. In this study, we utilize location-based data to construct human mobility networks in twenty metropolitan areas in the U.S. The human mobility networks are analyzed in conjunction with the urban heat characteristics of spatia…
Systems of cities at the macroscopic scale have their trajectories conditioned by the evolution of infrastructure networks. This leads to complex planning and management situations in the particular case of international transportation infrastructure projects. To understand such dynamics and anticipate future sustainable trajectories, we introduce a co-evolution model between cities and transportation networks at the international scale, which simulates network growth by including transportation governance. The model is applied to synthetic systems of cities and the parameter space systematica…
We show that the definition of the city boundaries can have a dramatic influence on the scaling behavior of the night-time light (NTL) as a function of population (POP) in the US. Precisely, our results show that the arbitrary geopolitical definition based on the Metropolitan/Consolidated Metropolitan Statistical Areas (MSA/CMSA) leads to a sublinear power-law growth of NTL with POP. On the other hand, when cities are defined according to a more natural agglomeration criteria, namely, the City Clustering Algorithm (CCA), an isometric relation emerges between NTL and population. This discrepanc…
Multilayer networks describing interactions in urban systems: a digital twin of five cities in Spain
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), CSIC-UIB（复杂系统与跨学科物理研究所（IFISC），CSIC-UIB）；CA UNED Illes Balears（巴利阿里群岛开放大学学院）；Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza（萨拉戈萨大学复杂系统生物计算与物理研究所（BIFI））；CENTAI Institute（CENTAI研究所）
In this paper, we develop a novel approach to measuring urban sprawl based on street nodes and naturally defined urban boundaries, both extracted from massive volunteered geographic information OpenStreetMap databases through some data-intensive computing processes. The street nodes are defined as street intersections and ends, while the naturally defined urban boundaries constitute what we call natural cities. We find that the street nodes are significantly correlated with population of cities. Based on this finding, we set street nodes as a proxy of population to measure urban sprawl. We fur…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial correlation function of cities. Suppose that the spatial correlation follows the power law. It can be proved that the correlation exponent is the second order generalized dimension. The spatial correlation model is applied to the system of cities in China. The results show that the Chinese urban system can be described by the correlation dimension ranging from 1.3 t…
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 characterizing the urban form have been introduced in the literature, often with the risk of redundancy. Here, we argue that two measures are enough to capture a wealth of different forms of the population density. First, fluctuations of the local density can be very important and we should distinguish almost homogeneous cities from highly heterogeneous ones…
The area-perimeter allometric scaling is a basic and important approach for researching fractal cities and has been studied for a long time. However, the boundary dimension of a city is always numerically overestimated by the traditional formula. An adjusting formula has been derived to revise the overestimated boundary dimension and estimate the form dimension, but the association between the global and local fractal parameters is not clear. This paper is devoted to describing the urban evolution by using the improved fractal parameters based on the area-perimeter measure relation. A system o…
