Two talks: Statistical shape analysis of helices; and Modelling heterogeneity and discontinuities using Voronoi tessellations

Mai Alfahad and Chris Pope, University of Leeds. Part of the statistics seminar series.

Mai Alfahad: Proteins are biomolecule compounds that consist of a chain of amino acid, which can be found in every living organism. The shape of protein plays an important role in its function. A chain of amino acids forms a 3-dimensional shape, and we are interested only in a common shape, alpha-helix. The alpha-helix is a right-handed helix. We study the shape of a helix and, more generally, a helix with change point, since change point are functionally important in membrane proteins. Consider change point as a point where the helix axis changes direction. We are developed a new algorithm, OptLS, to fit a regular helix for maximum likelihood estimation (MLE). In addition, we developed a hypothesis testing to determine if a given protein alpha-helix has a change point or not.  If it is, then we estimate the change point position and study 6 test statistics to investigate the nature of this change point.

Chris Pope: Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities. The problem of non-stationarity is dealt with by using a combination of Voronoi tessellation to partition the input space, and a separate Gaussian process to model the data on each region of the partitioned space. Our method is highly flexible as we allow the Voronoi cells to form relationships with each other, which can enable non-convex and disconnected regions to be considered. In such problems, identifying the borders between regions is often of great importance and we propose an adaptive sampling method to gain extra information along such borders. The method is illustrated in this talk with a simulation study and application to real data.