Figure 2

Crime exhibits temporal regularities that are hidden in city-level aggregated data. To analyse the heterogeneity in cities, we divided each city into regions of same population size and created the time series \(Y^{c}_{i}\) of each region. A pictorial example of San Francisco is shown in (A). With the global wavelet spectrum of the wavelet transform of \(Y^{c}_{i}\), we found that regions in the city might have other rhythms of crime, unseen in the aggregated data. For example, (B) depicts the global wavelet spectrum of selected regions (solid curves) in San Francisco and the null model (dashed curve). To describe these periods in the whole city, we developed the composed spectra \(C_{c}(s)\) that gives us the proportion of regions that exhibit a period s. Each curve in (C) represents \(C_{c}(s)\) of each considered city c in our analysis, showing the signature of criminal periodicity in cities