Paradoxical Interpretations of Urban Scaling Laws

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 analysis considers different aggregations of local units for which data are given by the Population Census. We produce a large variety of definitions of cities (approximatively 5000) by aggregating local Census units corresponding to the systematic combination of three definitional criteria: density, commuting flows and population cutoffs. We then measure the magnitude of scaling estimations and their sensitivity to city definitions for several urban indicators, showing for example that simple population cutoffs impact dramatically on the results obtained for a given system and attribute. Variations are interpreted with respect to the meaning of the attributes (socio-economic descriptors as well as infrastructure) and the urban definitions used (understood as the combination of the three criteria). Because of the Modifiable Areal Unit Problem and of the heterogeneous morphologies and social landscapes in the cities internal space, scaling estimations are subject to large variations, distorting many of the conclusions on which generative models are based. We conclude that examining scaling variations might be an opportunity to understand better the inner composition of cities with regard to their size, i.e. to link the scales of the city-system with the system of cities

On the problem of boundaries and scaling for urban street networks

Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling laws have been observed in urban studies, including Zipf's law and Gibrat's law, rendering cities attractive systems for analysis within statistical physics. Nevertheless, a broad consensus on how cities and their boundaries are defined is still lacking. Applying an elementary clustering technique to the street intersection space, we show that growth curves for the maximum cluster size of the largest cities in the UK and in California collapse to a single curve, namely the logistic. Subsequently, by introducing the concept of the condensation threshold, we show that natural boundaries of cities can be well defined in a universal way. This allows us to study and discuss systematically some of the regularities that are present in cities. We show that some scaling laws present consistent behaviour in space and time, thus suggesting the presence of common principles at the basis of the evolution of urban systems

Constructing cities, deconstructing scaling laws

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. The analysis shows that population size alone does not provide enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size regardless of the definition of the urban boundaries. However, when non-linear correlations are present, the exponent fluctuates considerably.Comment: Accepted for publication, Journal of the Royal Society Interfac

Evidence for localization and urbanization economies in urban scaling

We study the scaling of (i) numbers of workers and aggregate incomes by occupational categories against city size, and (ii) total incomes against numbers of workers in different occupations, across the functional metropolitan areas of Australia and the US. The number of workers and aggregate incomes in specific high income knowledge economy related occupations and industries show increasing returns to scale by city size, showing that localization economies within particular industries account for superlinear effects. However, when total urban area incomes and/or Gross Domestic Products are regressed using a generalised Cobb-Douglas function against the number of workers in different occupations as labour inputs, constant returns to scale in productivity against city size are observed. This implies that the urbanization economies at the whole city level show linear scaling or constant returns to scale. Furthermore, industrial and occupational organisations, not population size, largely explain the observed productivity variable. The results show that some very specific industries and occupations contribute to the observed overall superlinearity. The findings suggest that it is not just size but also that it is the diversity of specific intra-city organization of economic and social activity and physical infrastructure that should be used to understand urban scaling behaviors.Comment: 17 pages, 3 table

Defining localities of inadequate treatment for childhood asthma: A GIS approach

BACKGROUND: The use of Geographic Information Systems (GIS) has great potential for the management of chronic disease and the analysis of clinical and administrative health care data. Asthma is a chronic disease associated with substantial morbidity, mortality, and health care use. Epidemiologic data from all over the world show an increasing prevalence of asthma morbidity and mortality despite the availability of effective treatment. These facts led to the emergence of strategies developed to improve the quality of asthma care. THE OBJECTIVE: To develop an efficient tool for quality assurance and chronic disease management using a Geographic Information System (GIS). GEOGRAPHIC LOCATION: The southern region of Israel. January 1998 – October 2000. DATABASES: Administrative claims data of the largest HMO in Israel: drug dispensing registry, demographic data, Emergency Room visits, and hospitalization data bases. METHODS: We created a list of six markers for inadequate pharmaceutical treatment of childhood asthma from the Israeli clinical guidelines. We used this list to search the drug dispensing registry to identify asthmatic children who received inadequate treatment and to assess their health care utilization and bad outcomes: emergency room visits and hospitalizations. Using GIS we created thematic maps on which we located the clinics with a high percentage of children for whom the treatment provided was not in adherence with the clinical guidelines. RESULTS: 81% of the children were found to have at least one marker for inadequate treatment; 17.5% were found to have more than one marker. Children with markers were found to have statistically significant higher rates of Emergency Room visits, hospitalizations and longer length of stay in hospital compared with children without markers. The maps show in a robust way which clinics provided treatment not in accord with the clinical guidelines. Those clinics have high rates of Emergency Room visits, hospitalizations and length of stay. CONCLUSION: Integration of clinical guidelines, administrative data and GIS can create an efficient interface between administrative and clinical information. This tool can be used for allocating sites for quality assurance interventions

Building a city in vitro: the experiment and the simulation model

All current urban models accept the ‘first-order recursion’ view, namely, that the state of an urban system at time t is sufficient for predicting its state at t+1 . This assumption is not at all evident in the case of urban development, where the behavior of developers and planners is defined by the complex interaction between long-term and short-term plan guidelines, local spatial and temporal conditions, and individual entrepreneurial activity and cognition. In this paper we validate the first-order recursion approach in an artificial game environment: thirty geography students were asked to construct a ‘city’ on the floor of a large room, with each student using the same set of fifty-two building mock-ups. Based on the analysis of game outcomes, the first-order recursive set of behavioral rules shared by all the participants is estimated and further employed for computer generation of artificial cities. Comparison between the human-built and model patterns reveals that the constructed set of rules is sufficient for representing the dynamics of the majority of experimental patterns; however, the behavior of some participants differs and we analyze these differences. We consider this experiment as a preliminary yet important step towards the adequate modeling of decision-making behavior among real developers and planners.