Objectives

Thanks to modern ICT, a new generation of large data sets of social, biological, and man-made systems are now available. Many more will be produced at an ever–increasing rate in the near future. Such data contain high precision and integrated information on the nature and the evolution -in space and time- of the state of each single component, together with information on different types of interactions between them. Unfortunately, it is extremely difficult to extract meaningful information from this new generation of high-integrated data, since current network theory provides not much more than a static description of single, independent networks. The aim of this project is to provide a novel and coherent theoretical framework for analyzing and modeling these dynamic and multi-layer networks in terms of multi-graphs embedded in space and time. To do this, we will treat time, space and the nature of interactions not as additional dimensions of the problem, but as natural, inherent components of the very same generalized network (GNE) description. The first goal of the project is to devise novel metrics and models, able to capture the interactions between different layers and across different spatio-temporal scales. The second goal is to understand the combined role of spatial distance, time and inter-layer interactions on the dynamics of processes running on GNEs, and on the emergence of collective behaviors, such as synchronization. The third goal is to investigate cases where GNEs are co-evolving with the processes they facilitate. The theory will be validated on real-world applications involving large and heterogeneous data sets of brain networks, on- and off-line social systems, healthcare systems, and transportation flows in cities. Our project will provide new quantitative opportunities in different fields, ranging from the prediction of pathologies to the diffusion of ideas and trends in societies, and for the management of socio-technological systems.

In our GNE formulation, the position of the nodes might change in time, and the links can be embedded in space and fluctuate in time. We suppose that the GNE formulation is mathematically more treatable, and rich enough to completely describe a large variety of real systems:

• In online social systems, the nodes are the different users with a geographical position, and the links represent different layers of interaction (family ties, work collaborations, friends)

• In the human brain, the nodes are different areas of the brain, the time-varying links are

extracted from functional correlations, and the different layers represent various modalities

of acquisition (MEG, EEG, fMRI and DTI).

• In transportation networks, the nodes are different areas of the city and the different layers

represent different public transportation means (bus, underground, bike, car), and links/connections are time-dependent.