Quentin S. Hanley

Considerable efforts have been made to explore ways to prevent crime by studying how and where it arises. Much less is known about what happens after a crime has been reported. Here, we analysed a cohort of crimes from an outcome database released monthly by the UK Home Office. The data documents the disposition of a crime report through a range of outcomes beginning with “under investigation” and converting to other outcomes (e.g. “unable to prosecute”) over a 39-month period. We found that the reduction in the number of “under investigation” reports and the appearance of new designations follow either a one- or two-component exponential decay process. The rates of decay vary by police force, crime type, and new outcome designation. Crimes like bicycle theft (0.472 month^-1) and vehicle crime (0.478 month^-1) tend to be resolved quickly while investigation of violence and sexual offences proceed more slowly (0.207 month^-1). The crime type consisting of violence and sexual offences shows low variability across the 42 forces investigated indicating a more standardized approach to these crimes. When looking at the rate processes, the different rates are not competing to act on all crimes together. Rather, there are different pools of crimes and outcomes which are acted upon separately. Metrics obtained from the dynamic process of investigating crimes provide unprecedented insight into policing once a crime report is made.

This chapter revisits an attempt to incorporate rural and urban regions into a coherent and unified approach based on scaling relationships between indicator density and population density. We apply this approach across regions spanning a wide range of human settlements, finding that some types of indicators follow a single scaling law with population density, while others undergo transitions in urban environments such that the density scaling exponent may increase (accelerated scaling), decrease (inhibited scaling), or even become negative (collapsed scaling) in high-density regions. These urban scaling transitions occur at critical densities between 10 and 70 people per hectare in England and Wales, which may suggest the existence of an underlying universal mechanism. We further use this approach to define density scale-adjusted metrics, an extension of the concept of scale-adjusted metrics which allow an unbiased comparison of urban and non-urban indicators across regions with different population densities.

We investigated daily COVID-19 cases and deaths in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 15-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening coincided with increased variance indicative of conditions with local impact and country scale heterogeneity. University reopening and December holidays reduced variance indicative of country scale homogenisation which reached a minimum in mid-January 2021. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of “cold-spots” and “super-isolation” dominated for approximately 8 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales. Regional positions relative to density scaling laws were remarkably persistent after the first 5–9 days of the available data set. The determinants of this persistent behaviour probably precede the pandemic and remain unchanged.

We investigated daily COVID-19 cases and deaths in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 15-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening triggered increased variance indicative of outbreaks with local impact and country scale heterogeneity. University reopening and December holidays triggered reduced variance indicative of country scale homogenisation which reached a minimum in mid-January 2021. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of cold-spots and super-isolation dominated for approximately 8 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales. Regional positions relative to density scaling laws were remarkably persistent after the first 5-9 days of the available data set. The determinants of this persistent behaviour probably precede the pandemic and remain unchanged.

We investigated daily COVID-19 cases and death in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 10-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening triggered increased variance indicative of outbreaks with local impact and country scale heterogeneity. University reopening and December holidays triggered reduced variance indicative of country scale homogenisation which reached a minimum after New Year. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of “cold-spots” and “super-isolation” dominated for approximately 4 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales.

High throughput screening (HTS) interrogates compound libraries to find those that are “active” in an assay. To better understand compound behavior in HTS, we assessed an existing binomial survivor function (BSF) model of “frequent hitters” using 872 publicly available HTS data sets. We found large numbers of “infrequent hitters” using this model leading us to reject the BSF for identifying “frequent hitters.” As alternatives, we investigated generalized logistic, gamma, and negative binomial distributions as models for compound behavior. The gamma model reduced the proportion of both frequent and infrequent hitters relative to the BSF. Within this data set, conclusions about individual compound behavior were limited by the number of times individual compounds were tested (1–1613 times) and disproportionate testing of some compounds. Specifically, most tests (78%) were on a 309,847-compound subset (17.6% of compounds) each tested ≥ 300 times. We concluded that the disproportionate retesting of some compounds represents compound repurposing at scale rather than drug discovery. The approach to drug discovery represented by these 872 data sets characterizes the assays well by challenging them with many compounds while each compound is characterized poorly with a single assay. Aggregating the testing information from each compound across the multiple screens yielded a continuum with no clear boundary between normal and frequent hitting compounds.

The urban scaling hypothesis has improved our understanding of cities; however, rural areas have been neglected. We investigated rural–urban population density scaling in England and Wales using 67 indicators of crime, mortality, property, and age. Most indicators exhibited segmented scaling about a median critical density of 27 people per hectare. Above the critical density, urban regions preferentially attract young adults (25–40 years) and lose older people (> 45 years). Density scale adjusted metrics (DSAMs) were analysed using hierarchical clustering, networks, and self-organizing maps (SOMs) revealing regional differences and an inverse relationship between excess value of property transactions and a range of preventable mortality (e.g. diabetes, suicide, lung cancer). The most striking finding is that age demographics break the expected self-similarity underlying the urban scaling hypothesis. Urban dynamism is fuelled by preferential attraction of young adults and not a fundamental property of total urban population.

Quantitative real-time PCR methods have been used to perform approximately 278 million tests for COVID-19 up to mid-July 2020. Real-time PCR involves a rate limiting step where the samples are measured in situ during each PCR amplification cycle. This creates a bottleneck limiting scalability and as a consequence reducing access to inexpensive reliable testing at national and international scales. We investigated endpoint PCR for the qualitative detection of SARS-CoV-2 sequences on synthetic RNA standards and hospital patient samples. The endpoint PCR detection limit is constrained only by the stochastics of low copy numbers and reliably detected single copies of synthetic RNA standards. On a set of 30 patient samples, endpoint PCR found one additional positive sample and was able to confirm an indeterminate sample as negative. These results were found using 4 μl reagent and 1 μl of sample representing an 80% reduction in required RNA extract input and PCR reagent volumes relative to the NHS protocol (20 μl reagent and 5 μl sample). These results indicate that endpoint PCR should be the method of choice for large scale testing programmes. Based on the experience from ultra-high throughput genotyping efforts a single workflow using 384-well plates has similar PCR capacity (250 Million) to that required for all testing done worldwide during the first 7 month of the pandemic.