Aims of the project
The project focuses on the exploration of long-time properties of
random walks on graphs for the characterisation of heterogeneity in
spatial systems. The main hypothesis is that the trajectories of
random walks on graphs embedded in 2-dimensional and 3-dimensional
Euclidean spaces preserve a lot of information about the presence and
importance of spatial correlations in the system. The main aim is to
provide new graph-based methods to quantify correlations and
heterogeneity in large-scale spatial data sets, and to devise
appropriate null-models for the normalisation of those measures and
the comparison of heterogeneity across different systems. The project
has both a mathematical and a data-oriented component. It will most
probably require the ability to simulate simple dynamics processes on
graphs, and will provide extensive opportunities to deal with
real-world data sets.
The ideal candidate is a UK/EU national with a Master-level degree in
Mathematics, Physics, or Computer Science (with a strong maths
component), and a strong interest in networks. Previous
experience/knowledge in one or more of graph theory, network science,
processes on graphs, discrete mathematics, combinatorics, matrix
theory, dynamical systems, stochastic processes, random walks,
time-series analysis, numerical simulations, is desirable but not
The research group
The student will be part of the Complex Systems and Networks Research
Group at Queen Mary University of London. The group consists of 8
academics, 3 PDRAs and about 12 PhD students conducting world-leading
research in complex networks, complex systems, time series analysis,
stochastic processes, statistical physics, nonlinear dynamics,
mathematical modelling of biological systems, with applications to
biology, ecology, neuroscience, urbanism, finance, engineering.
The School of Mathematical Sciences is committed to the equality of
opportunities and to advancing women’s careers. As holders of a Bronze
Athena SWAN award we offer family friendly benefits and support
part-time study. We strongly encourage applications from women as they
are underrepresented within the School.
This project is eligible for full funding, including support for 3.5
years’ study, additional funds for conference and research visits and
funding for relevant IT needs.
|Keywords||spatial systems; random walks; graphs;|
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