Project Ref: NGCM-0082
Supervisor: Dr Ruben Sanchez-Garcia
Academic Unit: Mathematical Sciences
Research Group: Pure & Applied Mathematics
Co-supervisor: Dr Ben MacArthur
Academic Unit: Mathematical Sciences and Medicine
Research Group: Applied Mathematics & Life Sciences
Research Area: Healthcare and Biomedicine
Project Description: Recent technological and methodological advances have increased our data acquisition rate to unprecedented levels, particularly in the biomedical sciences. This very high-dimensional, heterogeneous and noisy data presents crucial analytical challenges. Novel techniques inspired in algebraic topology and combinatorial geometry are being successfully adapted to extract non-trivial high-dimensional information, revealing non-linear relationships among variables and gaining insight from the intrinsic 'shape' of the data.
These methodologies use topological complexes to represent high-dimensional data. Complexes are combinatorial structures that capture the topology, and aspects of the geometry, of a continuous shape. Complexes generalise networks (finite, simple graphs) to higher dimensions however they have not been studied in the same depth computationally or algorithmically, particularly their topological and geometrical aspects, and as models for high-dimensional data.
The main goal of this project is to develop robust and scalable computer models, and efficient computational methods, to effectively manipulate topological complexes as data structures in the emerging field of topological and geometrical data analysis, in a way that can be successfully integrated with more standard bioinformatics tools.
The project dual approach is on one hand the successful translation of concepts and techniques from topology and combinatorial geometry to appropriate computer models and algorithms, and on the other the validation on real-world biomedical data sets.
The project can be roughly subdivided into four parts or objectives:
1. Encoding data as complexes
2. Manipulation and visualization
3. Extracting topological and geometrical features
4. Validation: analysis of biomedical data and comparison with standard techniques
The prospective candidate must have at least an upper second-class degree in Mathematics, Computer Science, Bioinformatics, Physics or related field, with a background and/or interest in topology and discrete mathematics. Programming experience in a numerical computing environment, and an interest in molecular biology, are desirable. An enthusiasm for real-world applications of complex mathematical ideas and a positive attitude towards interdisciplinary research are essential.
If you wish to discuss any details of the project informally, please contact Ruben Sanchez-Garcia, Mathematical Sciences, Email: R.Sanchez-Garcia@soton.ac.uk, Tel: +44 (0) 2380 59 3655.
Keywords: Bioinformatics, Applied Mathematics, Computer Science
Support: All studentships provide access to our unique facilities and training and research support .