Title: Spatio-temporal variations in the urban rhythm: the travelling waves of crime,
Abstract: In the last decades, the notion that cities are in a state of equilibrium
with a centralised organisation has given place to the viewpoint of cities in
disequilibrium and organised from bottom to up. In this perspective, cities are
evolving systems that exhibit emergent phenomena built from local decisions.
While urban evolution promotes the emergence of positive social phenomena such
as the formation of innovation hubs and the increase in cultural diversity, it
also yields negative phenomena such as increases in criminal activity. Yet, we
are still far from understanding the driving mechanisms of these phenomena. In
particular, approaches to analyse urban phenomena are limited in scope by
neglecting both temporal non-stationarity and spatial heterogeneity. In the
case of criminal activity, we know for more than one century that crime peaks
during specific times of the year, but the literature still fails to
characterise the mobility of crime. Here we develop an approach to describe the
spatial, temporal, and periodic variations in urban quantities. With crime data
from 12 cities, we characterise how the periodicity of crime varies spatially
across the city over time. We confirm one-year criminal cycles and show that
this periodicity occurs unevenly across the city. These `waves of crime' keep
travelling across the city: while cities have a stable number of regions with a
circannual period, the regions exhibit non-stationary series. Our findings
support the concept of cities in a constant change, influencing urban
phenomena---in agreement with the notion of cities not in equilibrium.