# Research lines

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My research is focused on ***complex systems** science, where I address both fundamental and applied questions. The tools I use include statistical physics, nonlinear dynamics, stochastic processes and networks. If you want to take a look at my publications, go here.
My works can be somehow distributed among the following topics

**Graph-theoretical time series analysis: visibility graph theory**

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.

**Phase transitions, critical phenomena and self-organized criticality**

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).

**Applied nonlinear dynamics and chaos**

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.

**Complex 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 recently defined a fractal dimension that can be easily calculated only using random walker statistics, that is, only local information.

**Complexity in living systems **

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.

## Research group

My research group is currently composed by:

*PhD students:* Ryan Flanagan , Jacopo Iacovacci (graduated June 2017, now postdoc at Imperial College London).

*Phd students (second supervisor)*: Owen Courtney, Andrea Santoro, Oliver Williams.

*Current MSc students:* Oliver Richardson, Damien Cathro, Ivan Sokolenko.

Previous students (both at UPM and QMUL) include:

*PhD students:* Angel NuĂ±ez (UPM, graduated 2014, now postdoc at Universidad Autonoma de Madrid)

* MSc students * Simon Wiggins (QMUL), Bernat Serra (UPM), Alvaro de la Fuente (UPM), David Sepulveda (UPM)

Our research group is part of the wider Complex Systems & Networks group . I am also affiliated with the Dynamical Systems & Statistical Physics group.

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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