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New methods of Geometry and Topology for solving Computer Vision problems in Materials Science

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  • Full or part time
    Dr V Kurlin
  • Application Deadline
    No more applications being accepted
  • Funded PhD Project (European/UK Students Only)
    Funded PhD Project (European/UK Students Only)

Project Description

This project will help the multi-billion company Unilever to design better washing products for people and homes. A typical colloidal product is a mixture of two or more substances whose concentrations determine physical properties and customers’ perceptions. It is slow to physically test many combinations one by one, hence a fast analysis of outputs from computer simulations is needed.
One potential direction of this PhD is to link geometric configurations of colloidal particles with physical properties, e.g. by using machine learning. The first example is the microbial growth, i.e. tracking how colonies of bacterias grow and merge. The second example is predicting stability of products faster than simply waiting for months. Another possible direction is to quantify clusters or more complicated structures of active components on fabric in microscopic images.

The student will be based in the Department of Computer Science or the new £68M research institute MIF (Materials Innovation Factory) within the University of Liverpool, UK. The main supervisor is Dr Vitaliy Kurlin ( The project can be considered as a part of the new Centre for Topological Data Analysis (, joint with the Universities of Oxford and Swansea) funded by the recent £2.8 EPSRC grant "Application-driven Topological Data Analysis" (EP/R018472/1,

The Centre for Topological Data Analysis will study the shape of data, through the development of new mathematics and algorithms, and build on existing data science techniques in order to obtain and interpret the shape of data. Modern science and technology generates data at an unprecedented rate. A major challenge is that this data is often complex, high dimensional, may include temporal and/or spatial information. The "shape" of the data can be important but it is difficult to extract and quantify it using standard machine learning or statistical techniques. For example, an image of blood vessels near a tumour looks very different than an image of healthy blood vessels; statistics alone cannot quantify this difference and the new methods are required.

A theoretical field of mathematics that enables the study of shapes is geometry and topology. The ability to quantify the shape of complicated objects is only possible with advanced mathematics and algorithms. Topological Data Analysis (TDA), enables one to use methods of topology and geometry to study the shape of data. In particular, a method known as persistent homology, provides a summary of the shape of the data (e.g., features such as holes) at multiple scales. A key success of persistent homology is the ability to provide robust results, even if the data are noisy. There are theoretical and computational challenges in the application of these algorithms to large scale, real-world data. The aim is to build on current persistent homology tools, extending it theoretically, computationally, and adapting it for applications. Our team is composed of experts in pure and applied mathematicians, computer scientists, and statisticians.

Prior Experience.
Applications are welcomed from students with a 2:1 or higher (60% grade point average) masters or BSc degree or equivalent in Mathematics, Statistics, Computer Science or Computational Chemistry. The essential requirements are programming experiences (preferably C/C++, or Python, Java, Matlab, R) and excellent communication skills to work in a large team. The project will involve a close collaboration with colleagues from different areas and industry partners, e.g. Unilever, IBM Research UK (Hartree centre in the Daresbury lab), STFC (Science and Technology Facilities Council).

Funding Notes

The PhD is funded for 3 years from October 2018 by the School of Electrical Engineering, Electronic and Computer Science at the University of Liverpool (UK). The funding of 20K GBP per year covers the tuition fees for UK/EU students (about 4.2K GBP per year) and a tax-free bursary. Additional travel funds can be available from various grants in the university for presenting research work at top conferences.

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