In the last years, we have extended the concept of visibility graphs to time series analysis. We have provided a topological (graph-theoretical) description for the following type of time series: periodic, chaotic, intermittent, stochastic (with and without linear correlations), self-similar, irreversible, etc. The method has received wide attention and is currently applied across several disciplines, mainly with the aims of making feature extraction. Our current work is based on two lines: (1) push forward the foundations of these methods, and (2) develop applications for graph-theoretical time series and data analysis.

We have explored the onset of this type of emergent phenomena in random phi-4 field models, in combinatoric problems (SAT-like) appearing in number theory, in network models of the air transportation system, in the speech waveforms, etc. We have also developed computational methods for the analysis of disordered systems (the self-overlap method, similar in spirit to damage spreading).

We have applied local bifurcation theory to explore the onset of hierarchy in mathematical models of social interaction. We have investigated the problem of distinguishing noise from chaos using graph-theoretical methods, and have developed alternative descriptions of the onset of chaos via classical routes (period-doubling, intermittency, quasiperiodicity) using graph-theory. We have also extended Grassberger-Procaccia to define a correlation dimension in networks.

Mainly theory, and modelling of stochastic dynamics running on top of networks. We developed a mathematical formulation for time varying graphs that we called scheduled networks (with application in airline networks), which have thereafter been relabeled temporal networks, and have studied the onset of sudden jammings in transportation networks. We have defined a fractal dimension that can be easily calculated only using random walker statistics, that is, only local information. Additionally, we have recently developed a mathematical framework to unfold hidden multiplex networks and reconstruct these from local observation of random walk statistics. This framework turns out to be mathematically equivalent to a stochastic decomposition of non-Markovian dynamics, which we showed enjoy universal properties.

We are interested in complex social and biological problems showing some kind collective phenomena and self-organization, including (i) the onset of social hierarchy, (ii) SOC and the emergence of linguistic laws in the human voice, (iii) the onset of collective intonation in the musical performance of crowds, etc.

Jacopo Iacovacci (graduated 2017, now postoc at Imperial College London & Francis Crisk Institute).

The Complex Systems & Networks group has launched a brand new MSc in Network Science and hosts a weekly seminar in Complex Systems .

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