Neave O'Clery

Daniel Straulino, Juan C. Saldarriaga, Jairo A. Gómez et al.

Knowledge of the spatial organisation of economic activity within a city is key to policy concerns. However, in developing cities with high levels of informality, this information is often unavailable. Recent progress in machine learning together with the availability of street imagery offers an affordable and easily automated solution. Here we propose an algorithm that can detect what we call 'visible firms' using street view imagery. Using Medellín, Colombia as a case study, we illustrate how this approach can be used to uncover previously unseen economic activity. Applying spatial analysis to our dataset we detect a polycentric structure with five distinct clusters located in both the established centre and peripheral areas. Comparing the density of visible and registered firms, we find that informal activity concentrates in poor but densely populated areas. Our findings highlight the large gap between what is captured in official data and the reality on the ground.

Michael T. Schaub, Neave O'Clery, Yazan N. Billeh et al.

Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges, and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators.