Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics

We report on a quantitative analysis of relationships between the number of homicides, population size and ten other urban metrics. By using data from Brazilian cities, we show that well-defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. This approach has proved to be robust and useful for unveiling relationships/behaviors that were not properly carried out by the regression analysis, such as the non-explanatory potential of the elderly population when the number of homicides is much above or much below the scaling law, the fact that unemployment has explanatory potential only when the number of homicides is considerably larger than the expected by the power law, and a gender difference in number of homicides, where cities with female population below the scaling law are characterized by a number of homicides above the power law.     

Urban scaling and its deviations: revealing the structure of wealth, innovation and crime across cities

With urban population increasing dramatically worldwide, cities are playing an increasingly critical role in human societies and the sustainability of the planet. An obstacle to effective policy is the lack of meaningful urban metrics based on a quantitative understanding of cities. Typically, linear per capita indicators are used to characterize and rank cities. However, these implicitly ignore the fundamental role of nonlinear agglomeration integral to the life history of cities. As such, per capita indicators conflate general nonlinear effects, common to all cities, with local dynamics, specific to each city, failing to provide direct measures of the impact of local events and policy. Agglomeration nonlinearities are explicitly manifested by the superlinear power law scaling of most urban socioeconomic indicators with population size, all with similar exponents (1.15). As a result larger cities are disproportionally the centers of innovation, wealth and crime, all to approximately the same degree. We use these general urban laws to develop new urban metrics that disentangle dynamics at different scales and provide true measures of local urban performance. New rankings of cities and a novel and simpler perspective on urban systems emerge. We find that local urban dynamics display long-term memory, so cities under or outperforming their size expectation maintain such (dis)advantage for decades. Spatiotemporal correlation analyses reveal a novel functional taxonomy of U.S. metropolitan areas that is generally not organized geographically but based instead on common local economic models, innovation strategies and patterns of crime.     

Urban Scaling of Cities in the Netherlands

We investigated the socioeconomic scaling behavior of all cities with more than 50,000 inhabitants in the Netherlands and found significant superlinear scaling of the 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, both types of agglomerations underperform if we compare for the same size of population an agglomeration with a city as a municipality. In other words, an urban system as one formal municipality performs better as compared to an urban agglomeration with the same population size. This effect is larger for the second type of agglomerations, the urban areas. We think this finding has important implications for urban policy, in particular municipal reorganizations. A residual analysis suggests that cities with a municipal reorganization recently and in the past decades have a higher probability to perform better than cities without municipal restructuring.     

Impact of the Economic Structure of Cities on Urban Scaling Factors: Implications for Urban Material and Energy Flows in China

We explore the population‐scaling and gross domestic product (GDP)‐scaling relationships of material and energy flow (MEF) parameters in different city types based on economic structure. Using migration‐corrected population data, we classify 233 Chinese city propers (Shiqu) as “highly industrial” (share of secondary GDP exceeds 63.9%), “highly commercial” (share of tertiary GDP exceeds 52.6%), and “mixed‐economy” (the remaining cities). We find that, first, the GDP population‐scaling factors differ in the different city types. Highly commercial and mixed‐economy cities exhibit superlinear GDP population‐scaling factors greater than 1, whereas highly industrial cities are sublinear. Second, GDP scaling better correlates with city‐wide MEF parameters in Chinese cities; these scaling relationships also show differences by city typology. Third, highly commercial cities are significantly different from others in demonstrating greater average per capita household income creation relative to per capita GDP. Further, highly industrial cities show an apparent cap in population. This also translates to lower densities in highly industrial cities compared to other types, showing a size effect on urban population density. Finally, a multiple variable regression of total household electricity showed significant and positive correlation with population, income effect, and urban form effect. With such multivariate modeling, the apparent superlinearity of household electricity use with respect to population is no longer observed. Our study enhances understanding of MEFs associated with Chinese cities and provides new insights into the patterns of scaling observed in different city types by economic structure. Results recommend dual scaling by GDP and by population for MEF parameters and suggest caution in applying universal scaling factors to all cities in a country.     

Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities

More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of data, academics have recently immersed in this topic and one of the most striking and universal finding was the discovery of robust allometric scaling laws between several urban indicators and the population size. Despite that, most governmental reports and several academic works still ignore these nonlinearities by often analyzing the raw or the per capita value of urban indicators, a practice that actually makes the urban metrics biased towards small or large cities depending on whether we have super or sublinear allometries. By following the ideas of Bettencourt et al. [PLoS ONE 5 (2010) e13541], we account for this bias by evaluating the difference between the actual value of an urban indicator and the value expected by the allometry with the population size. We show that this scale-adjusted metric provides a more appropriate/informative summary of the evolution of urban indicators and reveals patterns that do not appear in the evolution of per capita values of indicators obtained from Brazilian cities. We also show that these scale-adjusted metrics are strongly correlated with their past values by a linear correspondence and that they also display crosscorrelations among themselves. Simple linear models account for 31%–97% of the observed variance in data and correctly reproduce the average of the scale-adjusted metric when grouping the cities in above and below the allometric laws. We further employ these models to forecast future values of urban indicators and, by visualizing the predicted changes, we verify the emergence of spatial clusters characterized by regions of the Brazilian territory where we expect an increase or a decrease in the values of urban indicators.     

Modeling fractal structure of city-size distributions using correlation functions

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.     

Scaling in urban building energy use and its influencing factors

Several studies have reported scaling relationships for energy consumption with respect to city size and other indicators. However, such scaling relationships have rarely been reported at the suburban level. This study explored the scaling relationships between energy use (EU) and building size (gross floor area [GFA]) at the building level in 16 urban regions in the United States from 2011 to 2019. We found that the scaling exponents of most of the examined regions changed from either super-linear or sub-linear to linear (β = 1) over the years. The scaling exponents of some cities (e.g., New York City) fluctuated around 1. These scaling exponents are negatively correlated with regional climate. This study reports that the scaling relationships between energy consumption and GFA at the building level in heterogeneous cities are evolving toward linear scaling. This study also found that different building types and building energy structures significantly impact building energy consumption. Hotels in New York City had the highest scaling exponent (β = 1.02), and strong correlations were observed between the scaling exponents and the share of electricity in building EU. These insights reveal the common nature of the relationships between building EU and GFA and the intersections between scaling exponents and building attributes. Our study highlights the importance of energy efficiency management in hotels and electricity-dominated buildings.     

Fitness distributions in evolutionary computation: motivation and examples in the continuous domain

Evolutionary algorithms are, fundamentally, stochastic search procedures. Each next population is a probabilistic function of the current population. Various controls are available to adjust the probability mass function that is used to sample the space of candidate solutions at each generation. For example, the step size of a single-parent variation operator can be adjusted with a corresponding effect on the probability of finding improved solutions and the expected improvement that will be obtained. Examining these statistics as a function of the step size leads to a 'fitness distribution', a function that trades off the expected improvement at each iteration for the probability of that improvement. This paper analyzes the effects of adjusting the step size of Gaussian and Cauchy mutations, as well as a mutation that is a convolution of these two distributions. The results indicate that fitness distributions can be effective in identifying suitable parameter settings for these operators. Some comments on the utility of extending this protocol toward the general diagnosis of evolutionary algorithms is also offered.     

Universities Scale Like Cities

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 distribution of the ‘gross university income’ in terms of total number of citations over ‘size’ in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities -the top-100 European universities- we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment.     

Some Mathematical Models for Line Transect Sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to an estimator with interesting characteristics. This work was given a uniform mathematical framework in BURNHAM and ANDERSON (1976). In this paper we extend that mathematical framework to several different sampling models, and a number of interesting discrete probability distributions emerge.     

Does Size Matter? Scaling of CO2 Emissions and U.S. Urban Areas

Urban areas consume more than 66% of the world’s energy and generate more than 70% of global greenhouse gas emissions. With the world’s population expected to reach 10 billion by 2100, nearly 90% of whom will live in urban areas, a critical question for planetary sustainability is how the size of cities affects energy use and carbon dioxide (CO₂) emissions. Are larger cities more energy and emissions efficient than smaller ones? Do larger cities exhibit gains from economies of scale with regard to emissions? Here we examine the relationship between city size and CO₂ emissions for U.S. metropolitan areas using a production accounting allocation of emissions. We find that for the time period of 1999–2008, CO₂ emissions scale proportionally with urban population size. Contrary to theoretical expectations, larger cities are not more emissions efficient than smaller ones.     

Emergent Systems Energy Laws for Predicting Myosin Ensemble Processivity

In complex systems with stochastic components, systems laws often emerge that describe higher level behavior regardless of lower level component configurations. In this paper, emergent laws for describing mechanochemical systems are investigated for processive myosin-actin motility systems. On the basis of prior experimental evidence that longer processive lifetimes are enabled by larger myosin ensembles, it is hypothesized that emergent scaling laws could coincide with myosin-actin contact probability or system energy consumption. Because processivity is difficult to predict analytically and measure experimentally, agent-based computational techniques are developed to simulate processive myosin ensembles and produce novel processive lifetime measurements. It is demonstrated that only systems energy relationships hold regardless of isoform configurations or ensemble size, and a unified expression for predicting processive lifetime is revealed. The finding of such laws provides insight for how patterns emerge in stochastic mechanochemical systems, while also informing understanding and engineering of complex biological systems.     

Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic susceptible-infectious-removed (SIR) epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because undirected edges disappear in the limit of a large population. In a series of simulations, we show that epidemic percolation networks accurately predict the mean outbreak size and probability and final size of an epidemic for a variety of epidemic models in homogeneous and heterogeneous populations. Finally, we show that epidemic percolation networks can be used to re-derive classical results from several different areas of infectious disease epidemiology. In an Appendix, we show that an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model in a closed population and prove that the distribution of outbreak sizes given the infection of any given node in the SIR model is identical to the distribution of its out-component sizes in the corresponding probability space of epidemic percolation networks. We conclude that the theory of percolation on semi-directed networks provides a very general framework for the analysis of stochastic SIR models in closed populations.     

The scaling of green space coverage in European cities

Most people on the planet live in dense aggregations, and policy directives emphasize green areas within cities to ameliorate some of the problems of urban living. Benefits of urban green spaces range from physical and psychological health to social cohesion, ecosystem service provision and biodiversity conservation. Green space coverage differs enormously among cities, yet little is known about the correlates or geography of this variation. This is important because urbanization is accelerating and the consequences for green space are unclear. Here, we use standardized major axis regression to explore the relationships between urban green space coverage, city area and population size across 386 European cities. We show that green space coverage increases more rapidly than city area, yet declines only weakly as human population density increases. Thus, green space provision within a city is primarily related to city area rather than the number of inhabitants that it serves, or a simple space-filling effect. Thus, compact cities (small size and high density) show very low per capita green space allocation. However, at high levels of urbanicity, the green space network is robust to further city compaction. As cities grow, interactions between people and nature depend increasingly on landscape quality outside formal green space networks, such as street plantings, or the size, composition and management of backyards and gardens.     

Everyday Encounters in the Shopping Mall: (Un)Making Boundaries in the Divided Cities of Johannesburg and Mostar

ABSTRACT

The many studies that see shopping malls as places of power, control and exclusion have often neglected the potential of malls as places of encounters. Drawing on ethnographic data from the divided cities of Johannesburg in South Africa and Mostar in Bosnia–Herzegovina, we examine the ways in which urban dwellers who enter the mall from a marginalised position – poor black urban dwellers at a regional, middle class and white-dominated mall in Johannesburg and Bosniak city dwellers at a mall located in the Croat part of Mostar – use the mall, what kind of relations they build to others and how they rework boundaries of race, class, religion and ethnicity at the mall. Rather than being spaces that strengthen and reproduce centre–margins relations, urban dwellers appropriate them as places where these relations become reworked.     

Dynamic sampling bias and overdispersion induced by skewed offspring distributions

Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population expansions. The resulting allele-frequency fluctuations are large and, therefore, challenge standard models of population genetics, which assume sufficiently narrow offspring distributions. While the neutral dynamics backward in time can be readily analyzed using coalescent approaches, we still know little about the effect of broad offspring distributions on the forward-in-time dynamics, especially with selection. Here, we employ an asymptotic analysis combined with a scaling hypothesis to demonstrate that over-dispersed frequency trajectories emerge from the competition of conventional forces, such as selection or mutations, with an emerging time-dependent sampling bias against the minor allele. The sampling bias arises from the characteristic time-dependence of the largest sampled family size within each allelic type. Using this insight, we establish simple scaling relations for allele-frequency fluctuations, fixation probabilities, extinction times, and the site frequency spectra that arise when offspring numbers are distributed according to a power law.     

How should we grow cities to minimize their biodiversity impacts?

Urbanization causes severe environmental degradation and continues to increase in scale and intensity around the world, but little is known about how we should design cities to minimize their ecological impact. With a sprawling style of urban development, low intensity impact is spread across a wide area, and with a compact form of development intense impact is concentrated over a small area; it remains unclear which of these development styles has a lower overall ecological impact. Here, we compare the consequences of compact and sprawling urban growth patterns on bird distributions across the city of Brisbane, Australia. We predicted the impact on bird populations of adding 84 642 houses to the city in either a compact or sprawling design using statistical models of bird distributions. We show that urban growth of any type reduces bird distributions overall, but compact development substantially slows these reductions at the city scale. Urban‐sensitive species particularly benefited from compact development at the city scale because large green spaces were left intact, whereas the distributions of nonnative species expanded as a result of sprawling development. As well as minimizing ecological disruption, compact urban development maintains human access to public green spaces. However, backyards are smaller, which impacts opportunities for people to experience nature close to home. Our results suggest that cities built to minimize per capita ecological impact are characterized by high residential density, with large interstitial green spaces and small backyards, and that there are important trade‐offs between maintaining city‐wide species diversity and people's access to biodiversity in their own backyard.     

Probabilistic measures of persistence and extinction in measles (meta)populations

Persistence and extinction are fundamental processes in ecological systems that are difficult to accurately measure due to stochasticity and incomplete observation. Moreover, these processes operate on multiple scales, from individual populations to metapopulations. Here, we examine an extensive new data set of measles case reports and associated demographics in pre‐vaccine era US cities, alongside a classic England & Wales data set. We first infer the per‐population quasi‐continuous distribution of log incidence. We then use stochastic, spatially implicit metapopulation models to explore the frequency of rescue events and apparent extinctions. We show that, unlike critical community size, the inferred distributions account for observational processes, allowing direct comparisons between metapopulations. The inferred distributions scale with population size. We use these scalings to estimate extinction boundary probabilities. We compare these predictions with measurements in individual populations and random aggregates of populations, highlighting the importance of medium‐sized populations in metapopulation persistence.     

Global patterns of city size distributions and their fundamental drivers

Urban areas and their voracious appetites are increasingly dominating the flows of energy and materials around the globe. Understanding the size distribution and dynamics of urban areas is vital if we are to manage their growth and mitigate their negative impacts on global ecosystems. For over 50 years, city size distributions have been assumed to universally follow a power function, and many theories have been put forth to explain what has become known as Zipf's law (the instance where the exponent of the power function equals unity). Most previous studies, however, only include the largest cities that comprise the tail of the distribution. Here we show that national, regional and continental city size distributions, whether based on census data or inferred from cluster areas of remotely-sensed nighttime lights, are in fact lognormally distributed through the majority of cities and only approach power functions for the largest cities in the distribution tails. To explore generating processes, we use a simple model incorporating only two basic human dynamics, migration and reproduction, that nonetheless generates distributions very similar to those found empirically. Our results suggest that macroscopic patterns of human settlements may be far more constrained by fundamental ecological principles than more fine-scale socioeconomic factors.