Members of the team are engaged in interdisciplinary research in applied mathematics with applications in a number of interlinking industries.
Research Contact: Professor Nadia Chuzhanova
Research is an important activity, ensuring the vitality and health of our academic subjects, and underpins the teaching of our courses. Members of the mathematics team are engaged in interdisciplinary research in applied mathematics with applications to biomedical, health and life sciences, engineering, computing and industry, specifically in the following areas of mathematics:
- biomathematics, bio- and neuro-informatics
- statistical learning theory and applications
- industrial mathematics
- quantum information science
- graph theory and combinatorics
- machine learning and optimisation
The research of Mathematical Aspects of Computer Science group focusses on the developing mathematical and statistical foundation for a range of computational techniques and approaches. It aligns with the Computing and Informatics subject area.
- Quantum computing research, undertaken by Dr Wilmott, is conducted in Quantum Algorithms, Quantum Circuits, Quantum Cryptography, and Quantum Error-correction – all of which drives new work in the area of quantum technologies. Quantum technologies will be profound and far-reaching: secure communication networks for consumers, corporations and government; precision sensors for biomedical technology; quantum simulators for the design of new materials; and ultra-powerful quantum computers for addressing otherwise impossibly large datasets for machine learning and artificial intelligence applications.
- However, engineering quantum systems and controlling them is an immense technological challenge: they are inherently fragile; and information extracted from a quantum system necessarily disturbs the system itself. Of the various approaches to quantum technologies, photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level.
- We here at Nottingham Trent have developed a novel approach to photonic quantum circuits for high performance, miniaturisation and scalability, which makes great use of mathematical aspects from combinatorics and number theory. Our investigations are based on innovative, award-winning research into the implications of weak random processes on quantum cryptography pioneered by Wilmott, and the research project is supported by Swiss-based quantum technologies specialist ID-Quantique. Areas of growing activity include application of genetic algorithms for the constructing quantum circuitry, investigations of genetic and Monte-Carlo algorithms for quantum data-mining, possible application of graph-theoretic approaches to classical and quantum computing.
- The focus of Dr Shahtahmassebi's research is on the development and application of methodology of Statistical Learning Theory and Bayesian Inference to modelling non-Gaussian and non-linear data. Application areas include multispectral image analysis with application to art history and conservation and quality control (defect or crack detection); remote sensing studies (land cover information extraction from satellite images); modelling high latitude ionosphere plasma structure in atmosphere.
- Dr Hetherington’s research interests include graph theory and combinatorics, in particular colourings and list-colourings.
- Dr McCollin works on identifying latent structure within systems reliability data. He attempts to identify structure on the basis of physical relationships and systems structure. Any complex system with many failure times where previous analysis has identified the exponential distribution as fitting the data is therefore a candidate for further analysis. Current work involves modelling with Lévy processes. He is currently applying the methods to dementia data.
- Dr Archontis Giannakidis’s research lies in developing novel techniques for the intelligent processing of visual information, with a particular focus on biomedical applications. His research includes using machine learning and deep learning techniques for extracting clinically useful information from cardiovascular MRI datasets. Another main research area of his is in diffusion tensor MRI. His research is linked to Allied Health Professions, Dentistry, Nursing and Pharmacy subject area.
The research of the Biomathematics and Bioinformatics group focuses on the development of novel mathematical and statistical approaches for analysis of data emerging from various disciplines, including Biosciences. It aligns with the Allied Health Professions, Dentistry, Nursing and Pharmacy subject area and Health and Wellbeing strategic research theme.
- Prof Chuzhanova's research interests include in silico modelling of mechanisms of mutations underlying inherited disease and cancer, based upon computational statistics and DNA complexity measures. She is particularly interested in the role of repetitive sequences, epigenetic factors and 3D architecture of the human genome in mutagenesis.
- Dr Crofts' research is in computational and applied mathematics with strong interests in computational neuroscience. In particular, his current research focuses on developing new mathematical approaches that combine techniques from network science, data-mining and dynamical systems in order to understand complex self-organising systems such as the brain.
- Dr Nelson's research is primarily in the area of Mathematical Biology, with particular focus on biomechanical models and models of complex many-cell systems. Applications to date include morphogenesis of soft tissues, tissue engineering, and sexually-transmitted infections. Current projects include modelling spatial aspects of the anti-inflammatory response via both partial differential equations and cellular automata models, and using techniques from network science and dynamical systems theory to elucidate the mechanisms underlying certain neurological conditions.
- Dr Chappell's research interests surround mathematical modelling and numerical analysis with industrial applications. Areas of current interest include time-dependent wave propagation problems, boundary integral and boundary element methods, convolution quadrature methods, inverse problems, fluid-structure interaction problems, high frequency wave modelling in complex industrial and engineering structures, numerical methods for phase space flow equations, uncertainty modelling and multi-scale methods. In 2016, Dr Chappell was awarded the Vice Chancellor’s Outstanding Researcher Award (early career). Dr Chappell is a member of Computation and Simulation group; his research is aligned with the Engineering subject area.