Mathematical Framework for Multiplex Networks (PLEXMATH)
European Commission. FET Proactive STREP Project number 317614Summary of the project: Complex systems are made up by many interacting, non-identical components, whose individual dynamics is usually governed by simple rules that operate at multiple levels. The structure of interactions between the system’s components is defined through networks, the study of which represent one of the most fascinating topics in modern science. Network science has revolutionized our classical understanding of physical, biological, social and technological systems. Nevertheless, there are several challenges hindering significant advances in the theoretical and computational characterization of complex networks, the most important one being the lack of a mathematical formalism for coping with the multi-level (both in space and time) nature of many real systems. The vision of PLEXMATH relies on formulating a brand new mathematical framework for the analysis of multi-level networks in terms of tensors, in particular 4th-rank tensors that represent with four indices the most general structure of possible connections. We therefore will accommodate current and future theoretical and algorithmic needs by adopting a radically new point of view. Capitalizing on tensorial algebra we will reformulate all network descriptors and will propose dynamical equations to represent diffusive processes on multiplex networks. In doing this, we will generate new mathematical models that will be validated on unparallel amounts of ICT data that describes relevant socioeconomic and techno-social systems. PLEXMATH constitutes a vital step towards a more general formalism for complex networked systems, as the generated knowledge will substantially improve our understanding of complex systems, and will directly impact the way we deal with structural and dynamical patterns in many systems, including ICT systems.