A continuous binning for discrete, sparse and concentrated observations.

Discrete observations from data which are obtained from sparse, and yet concentrated events are often observed (e.g. road accidents or murders).

A novel rare event approach to measure the randomness and concentration of road accidents.

Background: Road accidents are one of the main causes of death around the world and yet, from a time-space perspective, they are a rare event. To help us prevent accidents, a metric to determine the level of concentration of road accidents in a city could aid us to determine whether most of the accidents are constrained in a small number of places (hence, the environment plays a leading role) or whether accidents are dispersed over a city as a whole (hence, the driver has the biggest influence).

Methods: Here, we apply a new metric, the Rare Event Concentration Coefficient (RECC), to measure the concentration of road accidents based on a mixture model applied to the counts of road accidents over a discretised space.

Gravity and scaling laws of city to city migration.

Models of human migration provide powerful tools to forecast the flow of migrants, measure the impact of a policy, determine the cost of physical and political frictions and more. Here, we analyse the migration of individuals from and to cities in the US, finding that city to city migration follows scaling laws, so that the city size is a significant factor in determining whether, or not, an individual decides to migrate and the city size of both the origin and destination play key roles in the selection of the destination. We observe that individuals from small cities tend to migrate more frequently, tending to move to similar-sized cities, whereas individuals from large cities do not migrate so often, but when they do, they tend to move to other large cities.

A metric of the difference between perception of security and victimisation rates.

A person's perception of the level of security at a specific location depends on many factors, including past experiences in that location, the actual crime suffered by the population and more. Thus, when the individual perception that a location is insecure becomes the general rule is when the perception of security becomes an attribute of the region rather than the fears of some of its individuals, hence the relevance of aggregating individual perceptions of security into a single regional perception of security. Residents of two different regions, which have the same levels of crime, of a similar nature, may have different perceptions of the level of security.