The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2016 (funded students) or at any point in the academic year (self-funded students).
The last decade has witnessed the development of a new branch within complexity science, the so called complex network theory, from the crossroads of graph theory, statistical physics and data analysis. Within this branch, in the last years we have developed a brand new collection of techniques, generally quoted visibility graph algorithms, whose target is the systematic study of time series (and their underlying dynamics) using the tools of complex network theory. The methodology can be straightforwardly outlined: by making use of an algorithm that we have labeled as ’visibility’, we can map a time series into an associated complex network, allowing the use of the powerful tools of complex network theory in the tasks of signal processing and signal analysis.
Several recent studies suggest that such a network inherits in its topology the series information and hidden structure. A complex network description can thereby fully characterize the time series and the underlying dynamical process that generated such a series from a novel angle: the visibility methods stand as a new paradigm for time series analysis. Preliminary results include the topological characterization of self-similar series or irreversible processes, and the discrimination between noise and chaos.
In this project, we will take this methodology to the next level, moving from a somewhat disconnected collection of validated techniques towards a coherent and mathematically sound general theory that describes complex systems dynamics in terms of graph theoretical representations. In short, the project objective is twofold:
(1) Theoretical foundations: develop a mathematically sound theory of visibility methods, as a bridge between time series analysis, nonlinear dynamics and complex network theory. Several possible approaches will be considered.
(2) Applications to complex systems and signals for which a complete and meaningful description has remained elusive to date by traditional time
This project will be supervised by Dr Lucas Lacasa. For full details, see the project abstract: http://www.maths.qmul.ac.uk/sites/default/files/phd%20projects%202015/Complex%20Systems/lacasa.pdf
The application procedure is described on the School website. For further enquiries please contact Dr Lucas Lacasa ([email protected]
This project is eligible for several sources of full funding for the 2016/17 academic year, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process. The best candidates will be eligible to receive a prestigious Ian Macdonald Postgraduate Award of £1000, for which you will be considered alongside your application. The application deadline for full funding is January 31st 2016.
There is also 50% funding scheme available for students who are able to find the matching 50 % of the cost of their studies. Competition for these half-funded slots will be less intensive, and eligible students should mention their willingness to be considered for them in their application. The application deadline for 50 % funding is January 31st 2016.
This project can be also undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.