Vincenzo (KatolaZ) Nicosia
Since I was a child, I have had a genuine curiosity about anything that exhibits patterns, regularities, self-organisation, non-trivial interconnections and an overall unexpected structure. This interest is probably the reason that led me to start an academic career, driving my research towards the study of complex systems. In particular, my current research interests include:
Structure of complex networksA large number of experimental evidences have confirmed that many real systems are can be represented as sets of elementary units interacting through non-trivial networks of relationships. In the last fifteen years the theory of complex networks has provided a comprehensive framework to model and study these systems. The systematic analysis of the structural properties of a complex network can reveal important information about the overall organisation of a system and about the role and function of each of its elementary units. One of my major contributions in this field is the extension of the modularity function for graphs with overlapping communities. I have worked on the controllability of centrality in complex networks, on the analysis of functional human brain networks, on the problem of defining three-body correlations and on the characterisation of the evolution of road networks. I am also interested in the analysis of the evolution of neural networks and in the characterisation of symmetries in complex networks.
Processes on complex topologiesThe diffusion of a rumour on Facebook, the spread of a disease in a country and of a virus in a corporate computer network, the anomalous synchronisation of large areas of the brain observed during an epileptic seizure, the formation of consensus and the evolution of trends and tendencies on Twitter are all examples of processes which evolve over a complex network. I have worked on the characterisation of different processes occurring on complex topologies, including biased random walks, evolution of competing species, synchronisation of mobile agents, spreading of diseases and diffusion of information. In particular, I am interested in the characterisation of first passage times for different classes of independent random walks on networks and in quantifying the impact of network structure on the evolution of interacting random walks.
Time-varying graphsReal networked systems, e.g. online social networks, contact networks, functional networks of areas in the human brain, are inherently dynamic, since the relationships among the nodes are not persistent and usually fluctuate over time. However, up until recently the studies on complex networks have been entirely based on static graphs, where the connections among the nodes are given once and for all. In the last few years, the concept of time-varying graph has been proposed as a model to incorporate time in the description of complex networks. I have worked on the extension of centrality metrics (including closeness and betweenness) and on the definition of connectedness and connected components for time-varying graphs, and I am currently working on the problem of defining and detecting temporal communities. I am also interested in the development of models of temporal graphs, and on the study of dynamical processes on time-varying graphs, including disease spreading, synchronisation and cooperative games.