# Graduate Lectures MT16

**MICHAELMAS TERM 2016**

This lecture series now typically consists of three one and a half hour lectures in each of the following research areas: Computational Statistics; Probability and Bioinformatics/Mathematical Genetics.

The lectures are usually held on Thursdays from 3.30 pm – 5.00 pm in LG.03, Department of Statistics, 24-29 St Giles unless indicated otherwise.

**Week 3 - Wednesday 26th October, 2.00 pm - 3.00 pm ** Large Lecture theatre (LG.01)

**Speaker: ** Paul Chleboun, Department of Statistics, University of Oxford

**Title:** Glassy dynamics of kinetically constrained models (slides available here)

**Abstract: ** I will discuss the dynamics of some intersting interacting particle systems which show rich behaviour in their relaxation to equilibrium and subsequent motion. Specifically we will look at the relaxation to equilibrium of a family of kinetically constrained models (KCMs). KCMs are particle systems on integer lattices, where each vertex is labelled either 0 or 1, which evolve as follows: Each vertex attempts to update at times according to independent rate 1 Poisson processes, every time the Poisson clock rings at x it checks the states of its neighbours, if they satisfy a certain constraint (e.g. left neighbour is zero) then the state at x becomes 1 with probability p and 0 with probability 1-p, otherwise nothing happens. Despite of their apparent simplicity, KCMs pose very challenging and interesting problems due to the hardness of the constraints and lack of monotonicity. Their rich dynamics display many of the key features of real glasses, such as; ageing, huge relaxation times, and dynamic heterogeneity.

**Please note that this talk is joint with the CDT module on Probability and Approximation.**

**Week 5 - Monday 7th November, 10 am - 12 noon **

**Speaker: ** Anthony Lee, Department of Statistics, University of Warwick

**Title:** Stochastic Simulation

**Week 6 - Thursday 17th November, 3.30 pm - 4.30 pm **

**Speaker:** Mike Salter-Townshend, Department of Statistics, University of Oxford

**Title:** Models and Methods for Population Genetics

**Abstract: ** Population genetics is concerned with modelling and understanding patterns of shared genetic variation across sub-populations. Focusing on human populations, I will motivate the importance and utility of the field. Population structure is the result of the stochastic processes of recombination, mutation and, selection which drive genetic diversity. Following a very brief description of the theory behind these mechanisms, I will present methods for clustering individuals into homogeneous sub-groups. Some methods are "global" in that they aggregate information across the whole genome (all of the chromosomes). However, there is strong dependency along each chromosome (linkage). In admixed populations - where two or more diverged groups come together - we can usefully fit "local" models that determine the clustering of segments of DNA along the genome. I will present some methods for inferring this local ancestry and finish with some of my own work on fitting accurate, scalable, multi-way admixture models.

**Week 7 - Thursday 24th November, 3.15 pm - 5.30 pm **

**Third year graduate student talks**

**Week 8 - Thursday 1st December, 3.30 pm - 4.30 pm**

**Speaker:**Jotun Hein, Department of Statistics, University of Oxford

**Title:**A pairwise evolutionary model of protein sequence and structural conformation

**Abstract:**We give a generative evolutionary model of protein sequence and structural conformation. Recently, there have been stochastic models of structural evolution, which have shown that the inclusion of structural information leads to more reliable estimation of evolutionary parameters. We introduce a new pairwise evolutionary model which takes into account local dependencies between sequence and structural evolution. We treat each protein in a pair as random walk in space through the use of angular conformations. A coupling in our model is such that an amino acid change can lead to a jump in angle conformation and a change in diffusion process. This model is comparatively more realistic than previous stochastic models, since it allows improved understanding of the relationship between sequence and structure evolution. The generative nature of our model allows us to provide evidence of it's validity.

Preliminary slides can be found here: http://tinyurl.com/PhiPsiEvolution