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NGCM-0082: Computer models and algorithms for topological complexes with applications to biomedical data.

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  • Full or part time
    Dr R Sanchez-Garcia
    Dr B MacArthur
  • Application Deadline
    Applications accepted all year round
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

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 isy 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: [email protected], Tel: +44 (0) 2380 59 3655.

This project is run through participation in the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling ( For details of our 4 Year PhD programme, please see

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