Third molar development in a London population of White British and Black British or other Black ethnicity.

Population differences in dental development between Black and White ethnic groups have been debated but not previously studied in the UK. Using inappropriate data for dental age estimation (DAE) could lead to erroneous results and injustice. Data were collected from dental panoramic radiographs of 5590 subjects aged 6-24 years in a teaching hospital archive. Demirjian stages were determined for left-sided teeth and third molars and data collected regarding hypodontia and third molar agenesis. Third molar development in self-assigned Black British, including other self-assigned Black ethnicity, was compared with that of self-assigned White British subjects. Data were compared for males and females in the two ethnic groups using T-tests for Demirjian Stages A-G of third molar development and Mann-Whitney tests for Stage H once a cut-off age at the maximum age for Stage G had been imposed. Third molar development occurred earlier in subjects of Black ancestry compared to those of White ancestry. While both ethnic groups showed large age ranges for every third molar stage, in female subjects these generally occurred at least 1.5 years earlier, and in males at least one year earlier. Hypodontia and third molar agenesis were more prevalent in White British, but the ethnic difference in third molar development persisted in subjects with complete dentitions. This is a large study that confirms ethnic differences in a London population, emphasises the difficulties of establishing the 18-year-old threshold using DAE, and confirms the risk of overestimating the age of individuals of Black ethnicity using White ethnic reference data.

Entropy, complexity, and spatial information.

We pose the central problem of defining a measure of complexity, specifically for spatial systems in general, city systems in particular. The measures we adopt are based on Shannon's (in Bell Syst Tech J 27:379-423, 623-656, 1948) definition of information. We introduce this measure and argue that increasing information is equivalent to increasing complexity, and we show that for spatial distributions, this involves a trade-off between the density of the distribution and the number of events that characterize it; as cities get bigger and are characterized by more events-more places or locations, information increases, all other things being equal. But sometimes the distribution changes at a faster rate than the number of events and thus information can decrease even if a city grows. We develop these ideas using various information measures. We first demonstrate their applicability to various distributions of population in London over the last 100 years, then to a wider region of London which is divided into bands of zones at increasing distances from the core, and finally to the evolution of the street system that characterizes the built-up area of London from 1786 to the present day. We conclude by arguing that we need to relate these measures to other measures of complexity, to choose a wider array of examples, and to extend the analysis to two-dimensional spatial systems.