Networks, graphs and spreading processes
Network effects can have a significant impact on the propagation of diseases, memes and information in populations. I am interested in describing such impact using computer simulations and analytical methods. In addition to this, I am interested in mathematical properties of graphs and spreading processes taking place on graphs.
With Mason A. Porter I have investigated how a few individuals may lead the formation of anti-establishment majorities when competing products, opinions etc. are spreading in the same network. We also investigated how synergistic effects may affect spreading processes on networks.
I am currently interested in statistical distributions of descendants in epidemics, rumour spreading and other spreading processes. An 'epidemic descendant' of a person is any person who this person can influence in relation to the spreading process. The statistical distributions of descendants tell us whether most people can exert no influence at all, or whether a lot of people can exert influence on a large fraction of the population. So these distributions are very important, but surprisingly little is known about them.
Oscillators can synchronise with each other, they can drive each other or oscillate without being influenced by other oscillators. I am interested in the mathematical theory describing coupled oscillators, and how systems of coupled oscillators can create spatial patterns in e.g. biological systems.
Together with Mogens H. Jensen (NBI, Copenhagen) and Sandeep Krishna (NCBS, Bangalore) I have examined the mathematical theory behind a mechanism for scaling vertebrae precursors in mice embryos. We are currently interested how the these oscillators form intricate spatial patterns, even while being subject to noise.