Area: Mathematical Biology

Abstract of Research: My background is in the areas of probability theory and functional analysis.  My previous work was focused on stochastic processes, integration and measures in infinite dimensional vector spaces. I have spent the past three years building on my mathematical background to gain knowledge in the area of machine learning and computational science, in particular in its applications to location proteomics. I have extensive programming skills in matlab.

Current Research Projects: Proteomics, the study of proteins their structure and their function, is important in understanding the human body.  The field of proteomics has the potential to advance medicine through a complete understanding of important interactions that help to keep our bodies healthy.  The field of location proteomics seeks to understand protein structure and function by looking at the location pattern of individual proteins.

Novel ideas from optical flow theory and manifold learning techniques can provide new methods for the understanding of protein structure.  When coupled with advances in location proteomics, these methods will advance the understanding of protein motion and the underlying structure of the topological space in which proteins reside.  A thorough understanding of that topological space will be used for generative models or simulations.  These generative models will also provide additional information for understanding protein structure.

The specific aims of this study are (i) to develop and test new numerical descriptors from time sequences of protein images and (ii) to use methods from manifold learning to understand the underlying structure of the space of protein images and develop generative models of the depiction of protein images.  Optical flow calculations, a technique used to quantify motion in the field of computer vision, will be used to develop new descriptors based on protein motion in order to achieve the first aim.  For the second aim, protein images are considered as high dimensional data that are sampled from a low dimensional manifold.  Recent developments in the field of manifold learning, and nonlinear dimensionality reduction will be applied to protein images in order to understand this underlying manifold.  This will then lead to applications for simulating protein images.

This research project will use mathematical and computational methods in order to bring new information to the field of proteomics.

Related Publication: “On Optical Flow of Fluorescent Microscope Protein Images”, Robert C Stolz, Camille A. McKayle, Robert Murphy, Elvira Garcia Osuna and Yanhua Hu, paper number (1014-92-1104), Abstracts of papers presented to the American Mathematical Society, Volume 27, Number 1, Issue 143, Section Mathematical Biology, Year 2006.