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Register a new userZipfs law and urban scaling: Hypotheses towards a Unified Urban Theory
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We propose hypotheses describing the empirical finding of an association between the exponents of urban GDP scaling and Zipfs law for cities. These hypotheses represent various combinations of directional or reciprocal causal links between the two phenomena and include inter- and intra-city processes. Future theories and models can be motivated with and categorized according to these hypotheses. This paper intends to stimulate the discussion around the processes behind these phenomena and pave the way to a Unified Urban Theory.
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Urban theorists, social reformists and philosophers have considered the city as a living organism since Plato. However, despite extraordinary advancements in evolutionary biology, now being used to explain social and cultural phenomena, a proper science of evolution in cities has never been established since Geddes work at the dawn of the Town Planning discipline. Commencing in the tradition of Urban Morphology, this research develops and validates a statistically reliable and universally applicable urban taxonomy. The research solidifies existing definitions of built form at the scale of the urban fabric and identifies the constituent elements of form in 40 contemporary UK cities. Quantifiable measurements of these elements allow mathematical descriptions of their organization and mutual relationships. Further, an optimized list of indices with maximum discriminatory potential distinguishes between cases from four historically characterised categories: 1) Historical, 2) Industrial, 3) New Towns, 4) Sprawl. Finally, a dendrogram is produced that shows the tree of similarity between cases, where the great divide between pre and post WWII war urban form is demonstrated. This work shows that: a) it is conceptually sound and viable to measure urban fabric utilizing public, big-data repositories, b) the proposed urban morphometrics system accurately characterises the structure of urban form and clusters cases properly based on their historical origins, c) scientific models of biological evolution can be applied to urban analysis to understand underlying structural similarities.
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.
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 population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyze the shapes of income distributions. First, we find that mean, variance, skewness, and kurtosis of income distributions all increase with city size. Second, the Kullback-Leibler divergence between a citys income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.
Assessing the resilience of a road network is instrumental to improve existing infrastructures and design new ones. Here we apply the optimal path crack model (OPC) to investigate the mobility of road networks and propose a new proxy for resilience of urban mobility. In contrast to static approaches, the OPC accounts for the dynamics of rerouting as a response to traffic jams. Precisely, one simulates a sequence of failures (cracks) at the most vulnerable segments of the optimal origin-destination paths that are capable to collapse the system. Our results with synthetic and real road networks reveal that their levels of disorder, fractions of unidirectional segments and spatial correlations can drastically affect the vulnerability to traffic congestion. By applying the OPC to downtown Boston and Manhattan, we found that Boston is significantly more vulnerable than Manhattan. This is compatible with the fact that Boston heads the list of American metropolitan areas with the highest average time waste in traffic. Moreover, our analysis discloses that the origin of this difference comes from the intrinsic spatial correlations of each road network. Finally, we argue that, due to their global influence, the most important cracks identified with OPC can be used to pinpoint potential small rerouting and structural changes in road networks that are capable to substantially improve urban mobility.
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.
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