Projects
Symmetry Breaking In X-Chromosome Inactivation
(MPhys Dissertation)
In female mammalian cells one of the two X chromosomes must be silenced in order to prevent over expression of X-linked gene products and cell death. The mechanism of counting and choice is a complex task which must be achieved in all cells if they are to be viable. We investigated a statistical mechanics inspired model: the spontaneous symmetry breaking model. Extensive Monte-Carlo simulations undertaken indicated that the phase-transition observed was abrupt in nature. Finite size effects were examined, the metastabilitiy of the system was probed and the critical temperature was measured to be 1.68(1) E0kB/T. The project resulted in the publication of a paper in Physica A and a poster summarising the results, see below.
- D. Barker & A. Griffiths, Physica A, Volume 388 No. 6 - 2009 (link)
- Poster (784 KB)
Fast Mixing Monte-Carlo For Biological Networks
(MSc Project 1)
Inferring biological networks from data is currently an area of much interest. Understanding novel biology based upon these networks has important implications for studying many diseases. This project, which was supervised by Sach Mukherjee and Mario Nicodemi, aimed to find a speed up over a widely used Metropolis-Hastings scheme for inferring the networks. Tempering (both simulated and parallel) and a novel `Tunnelling' scheme were examined. Analysis and empirical results provide a clearer understanding of the nature of the MCMC problem and insight into the computational exploration of network space. A parallel variant of Simulated Tempering called Parallel Tempering is found to provide gains relative to other schemes on a 10 node problem with a vast state space.
- Poster detailing initial results (853 KB)
- Final report (587 KB)
Coupling And Feedback In The Manna Universality Class
(MSc Project 2)
This project was supervised by Prof. Haye Hinrichsen who is based at Universitaet Wuerzburg in Bavaria, Germany. We aimed to discover which salient features of non-equillibrium statistical mechanical models placed them into either the Directed Percolation (DP) or Manna (CDP) universality class. To investigate this we constructed a variant of the well studied contact process where by the active field (infection density) is coupled to a conserved background field. The critical properties of this model were then investigated. In addition the properties of a novel quantity representing the current flow were investigated for the manna model and were found to have interesting correlations and possible non-Gaussian distributions.
- Final report (408 KB)
- Presentation (664 KB)