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Urban scaling and Zipfs 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 the connection between these two laws using population and GDP data from almost five thousand consistently-defined cities in 96 countries. We empirically demonstrate that both laws are tied to each other and derive an expression relating the urban scaling and Zipf exponents. This expression captures the average tendency of the empirical relation between both exponents, and simulations yield very similar results to the real data after accounting for random variations. We find that while the vast majority of countries exhibit increasing returns to scale of urban GDP, this effect is less pronounced in countries with fewer small cities and more metropolises (small Zipf exponent) than in countries with a more uneven number of small and large cities (large Zipf exponent). Our research puts forward the idea that urban scaling does not solely emerge from intra-city processes, as population distribution and scaling of urban GDP are correlated to each other.
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Urban areas play an unprecedented role in potentially mitigating climate change and supporting sustainable development. In light of the rapid urbanisation in many parts on the globe, it is crucial to understand the relationship between settlement size and CO2 emission efficiency of cities. Recent literature on urban scaling properties of emissions as a function of population size have led to contradictory results and more importantly, lacked an in-depth investigation of the essential factors and causes explaining such scaling properties. Therefore, in analogy to the well-established Kaya Identity, we develop a relation combining the involved exponents. We demonstrate that application of this Urban Kaya Relation will enable a comprehensive understanding about the intrinsic factors determining emission efficiencies in large cities by applying it to a global dataset of 61 cities. Contrary to traditional urban scaling studies which use Ordinary Least Squares (OLS) regression, we show that the Reduced Major Axis (RMA) is necessary when complex relations among scaling exponents are to be investigated. RMA is given by the geometric mean of the two OLS slopes obtained by interchanging the dependent and independent variable. We discuss the potential of the Urban Kaya Relation in main-streaming local actions for climate change mitigation.
We report on the existing connection between power-law distributions and allometries. As it was first reported in [PLoS ONE 7, e40393 (2012)] for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.
In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear power-scaling with total population, while measures of resource use show sub-linear power-law scaling. Re-analysis of the gross economic production and personal income for cities in the United States, however, shows that the data cannot distinguish between power laws and other functional forms, including logarithmic growth, and that size predicts relatively little of the variation between cities. The striking appearance of scaling in previous work is largely artifact of using extensive quantities (city-wide totals) rather than intensive ones (per-capita rates). The remaining dependence of productivity on city size is explained by concentration of specialist service industries, with high value-added per worker, in larger cities, in accordance with the long-standing economic notion of the hierarchy of central places.
Understanding cities is central to addressing major global challenges from climate and health to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is only now accessible to comprehensive analyses with the availability of large datasets. Here, we study abundances of business categories across U.S. metropolitan statistical areas to investigate how diversity of economic activities depends on city size. A universal structure common to all cities is revealed, manifesting self-similarity in internal economic structure as well as aggregated metrics (GDP, patents, crime). A derivation is presented that explains universality and the observed empirical distribution. The model incorporates a generalized preferential attachment process with ceaseless introduction of new business types. Combined with scaling analyses for individual categories, the theory quantitatively predicts how individual business types systematically change rank with city size, thereby providing a quantitative means for estimating their expected abundances as a function of city size. These results shed light on processes of economic differentiation with scale, suggesting a general structure for the growth of national economies as integrated urban systems.
Mitigating traffic congestion on urban roads, with paramount importance in urban development and reduction of energy consumption and air pollution, depends on our ability to foresee road usage and traffic conditions pertaining to the collective behavior of drivers, raising a significant question: to what degree is road traffic predictable in urban areas? Here we rely on the precise records of daily vehicle mobility based on GPS positioning device installed in taxis to uncover the potential daily predictability of urban traffic patterns. Using the mapping from the degree of congestion on roads into a time series of symbols and measuring its entropy, we find a relatively high daily predictability of traffic conditions despite the absence of any a priori knowledge of drivers origins and destinations and quite different travel patterns between weekdays and weekends. Moreover, we find a counterintuitive dependence of the predictability on travel speed: the road segment associated with intermediate average travel speed is most difficult to be predicted. We also explore the possibility of recovering the traffic condition of an inaccessible segment from its adjacent segments with respect to limited observability. The highly predictable traffic patterns in spite of the heterogeneity of drivers behaviors and the variability of their origins and destinations enables development of accurate predictive models for eventually devising practical strategies to mitigate urban road congestion.
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