# Publications

We show how increasing returns to scale in urban scaling can artificially emerge, systematically and predictably, without any sorting or positive externalities. We employ a model where individual productivities are independent and identically distributed lognormal random variables across all cities. We use extreme value theory to demonstrate analytically the paradoxical emergence of increasing returns to scale when the variance of log-productivity is larger than twice the log-size of the population size of the smallest city in a cross-sectional regression. Our contributions are to derive an analytical prediction for the artificial scaling exponent arising from this mechanism and to develop a simple statistical test to try to tell whether a given estimate is real or an artifact. Our analytical results are validated analyzing simulations and real microdata of wages across municipalities in Colombia. We show how an artificial scaling exponent emerges in the Colombian data when the sizes of random samples of workers per municipality are 1% or less of their total size.

*per capita*income. The inferred model predicts that diversification drives growth in income, that diversified middle-income countries will grow the fastest, and that countries will converge onto intermediate levels of income and specialization. PriSDA is generalizable and may illuminate dynamics of elusive quantities such as diversity and complexity in other natural and social systems.

### Background

Several past studies have found that media reports of suicides and homicides appear to subsequently increase the incidence of similar events in the community, apparently due to the coverage planting the seeds of ideation in at-risk individuals to commit similar acts.

### Methods

Here we explore whether or not contagion is evident in more high-profile incidents, such as school shootings and mass killings (incidents with four or more people killed). We fit a contagion model to recent data sets related to such incidents in the US, with terms that take into account the fact that a school shooting or mass murder may temporarily increase the probability of a similar event in the immediate future, by assuming an exponential decay in contagiousness after an event.

### Conclusions

We find significant evidence that mass killings involving firearms are incented by similar events in the immediate past. On average, this temporary increase in probability lasts 13 days, and each incident incites at least 0.30 new incidents (*p* = 0.0015). We also find significant evidence of contagion in school shootings, for which an incident is contagious for an average of 13 days, and incites an average of at least 0.22 new incidents (*p* = 0.0001). All *p*-values are assessed based on a likelihood ratio test comparing the likelihood of a contagion model to that of a null model with no contagion. On average, mass killings involving firearms occur approximately every two weeks in the US, while school shootings occur on average monthly. We find that state prevalence of firearm ownership is significantly associated with the state incidence of mass killings with firearms, school shootings, and mass shootings.

**Objectives** Rampant urbanisation rates across the globe demand that we improve our understanding of how infectious diseases spread in modern urban landscapes, where larger and more connected host populations enhance the thriving capacity of certain pathogens.

**Methods** A data-driven approach is employed to study the ability of sexually transmitted diseases (STDs) to thrive in urban areas. The conduciveness of population size of urban areas and their socioeconomic characteristics are used as predictors of disease incidence, using confirmed-case data on STDs in the USA as a case study.

**Results** A *superlinear* relation between STD incidence and urban population size is found, even after controlling for various socioeconomic aspects, suggesting that doubling the population size of a city results in an expected increase in STD incidence larger than twofold, provided that all other socioeconomic aspects remain fixed. Additionally, the percentage of African–Americans, income inequalities, education and per capita income are found to have a significant impact on the incidence of each of the three STDs studied.

**Conclusions** STDs disproportionately concentrate in larger cities. Hence, larger urban areas merit extra prevention and treatment efforts, especially in low-income and middle-income countries where urbanisation rates are higher.