The deadline for applications is midnight on 28th February 2025. Applications may re-open if all positions are not filled.

Title: EPSRC Doctoral Studentships in Mathematics and Statistics Innovation

Organisation Name: Heriot Watt University

About our Organisation: Heriot-Watt University has established a reputation for world-class teaching and leading-edge, relevant research, which has made it one of the top UK universities for innovation, business and industry.

Heriot-Watt University has five campuses: three in the UK (Edinburgh, Scottish Borders and Orkney), one in Dubai and one in Malaysia. The University offers a highly distinctive range of degree programmes in the specialist areas of science, engineering, design, business and finance. Heriot-Watt is also Scotland’s most international university, boasting the largest international student cohort.

Successful candidates will be affiliated within the School Mathematical and Computer Sciences in Edinburgh and will be working closely with projects stemming from the newly established Mathematics-Driven Innovation Centre (M-DICE).

The Opportunity: EPSRC Doctoral PhD studenships roles are funded by the Engineering and Physical Sciences Research Council (EPSRC) as part of Heriot-Watt University’s Doctoral Training Partnership award.

EPSRC Doctoral Studentships in Mathematics and Statistics Innovation, are fully funded PhD studentships (please check eligibility below) aiming to interface different areas of EPSRC remit within Mathematical Sciences, including Statistics and Data Science. The successful candidates will be working on specific project(s) within the Centre for Mathematics-Driven Innovation, aiming to address industrial and/or applied sciences challenges by employing cutting-edge mathematical and statistical modelling. The duration of the funding is 3.5 years per PhD student.

Specifically, the following potential PhD projects (with short descriptions) are available for starting in September 2025 are given below

Eligibility Essentials: The following eligibility criteria are essential for an application to be evaluated.

Academic conditions:

To receive EPSRC studentship funding, you must have qualifications or experience equal to an honours degree at a first or upper second class level, or a masters from a UK academic research organisation.

Degree qualifications gained outside the UK, or a combination of qualifications and experience that is equivalent to a relevant UK degree, might be accepted in some cases.

Residential eligibility criteria:

Studentships for this call are limited to home students only and will receive a full award of stipend and fees at the home level.

To be treated as a home student, candidates must meet one of these criteria:

  • be a UK national (meeting residency requirements)
  • have settled status
  • have pre-settled status (meeting residency requirements)
  • have indefinite leave to remain or enter.

See the UKRI terms and conditions of training grants for full details.

How to apply

Deadline: The deadline for applications is midnight on 28th February 2025. Applications may re-open if all positions are not filled.

The application process for EPSRC Doctoral Studentships in Mathematics and Statistics Innovation is centred around available research areas/projects, henceforth collectively termed simply as “Projects”. Each Project designates an academic Supervisor and, in some cases, one or more Co-supervisors. Informal enquiries about a project can be addressed to the project’s Supervisor. Enquiries about the application procedure can be addressed to pgadmissions@hw.ac.uk

Each applicant may apply to a maximum of two Projects.

Applicants should apply through the HWU Postgraduate Application Portal for a PhD in Mathematics. Applicants should mention they are applying for EPSRC Doctoral Studentships in Mathematics and Statistics Innovation and state the project(s) they are interested and the Supervisor in the respective fields in the Application Form.

Shortlisted candidates will be invited for an interview. It is anticipated that shortlisted candidates will be invited to interview in March 2025. Successful candidates will be notified as soon as possible thereafter. Applications may reopen in July if not all positions are filled.

All projects have a non-academic/industrial component of varying degree and industrial co-supervisor. It is not possible disclose any specific companies/organisations related to a project at the application stage. Information on specific companies/organisations related to a project may be given during interviews.

Available Projects

Image Classification of Super-resolution ultrasound prostate cancer maps

Supervisor(s): M. Vallejo (MACS, supervisor) & V. Sboros (EPS co-supervisor)

Description: Prostate cancer is a disease with high incidence, high mortality and a high rate of avoidable intervention. It has the highest incidence of cancer in men, with the second highest mortality rate. It is known that the current diagnostic pathway misses up to 22% of significant cancers, leading to nearly 60% of invasive procedures that may be avoided. It is also established that more tumours need to be detected (diagnostic sensitivity) and better classified and localised (specificity) to improve these figures and inform treatment. This relies on the development of better and widely affordable imaging techniques, like super-resolution ultrasound. 

In this project, we will develop machine learning techniques to characterise and classify super-resolution ultrasound images to support more successful prostate cancer detection, especially at its early stage. A combination of medical images with images obtained from numerical simulations of the mathematical model for cancer growth and growth-induced angiogenesis based on characteristics of the blood vessel network will be used to train the machine learning algorithms. The mathematical models will combine partial differential equations for chemical dynamics in a cell tissue with a discrete description of the blood network. The existing mathematical models will be extended to address specific properties of prostate cancer. 

References:

  • Sboros et al. Ultrasound Med Biol 2011, 37.
  • Chaplain et al. In Molecular, Cellular,Tissue Level Aspects & Implications, Ed Jackson 2011,167.   
  • Machado et al, Microcirculation 2011, 18.
  • Wu et al. J Theor Biol 2014, 355.
  • Kanoulas et al. Invest Radiol 2019, 500.
  • Papageorgiou et al. IEEE IUS Symp 2022.

Mathematical Modelling of Wave Energy Converters

Supervisor(s): C. Cummins (MACS, supervisor) 

Description: When you hold a seashell to your ear, the ‘sound of the sea’ you hear is due in part to a phenomenon known as Helmholtz Resonance (HR). This same effect can be heard in a car driving on a motorway with one window slightly open. While these are acoustic examples, a similar resonance happens in water. Harbours, for instance, can face catastrophic damage when the frequency of incoming waves have the same fundamental frequency as the harbour – the Helmholtz mode.

Recently, we discovered that a particular class of device designed to harness wave energy, specifically the wave energy converters (WECs) developed by our project partner, uniquely exhibit this HR. However, the potential power from this resonance has not been fully utilised, because of two main issues. First, there is a lack of deep understanding of this resonance in WECs. Second, “viscous losses” weaken this resonance, much like how placing your hand near the open window arch in the car reduces the thudding sound. The mathematical modelling of viscous losses using computational fluid dynamics (CFD) is computationally challenging, requiring supercomputers and taking many days to complete, which makes it difficult to understand how to mitigate these viscous losses when designing new WECs.

In this project, we will develop a new and efficient mathematical model that takes into account these viscous losses1, but which is several orders of magnitude faster than CFD and does not require the use of supercomputers. While our primary focus is on improving the performance of WECs while they undergo HR, the method is entirely general, so it has a much broader application and it can be used for any underwater structure, not just WECs. By understanding and mitigating these effects, we aim to boost the efficiency of WECs, reducing their costs. Our plan is to share this method with the wider marine engineering community, by creating an open-source code that can benefit numerous marine applications1,2..

References

  1.  Cummins, C. P. & Dias, F. A new model of viscous dissipation for an oscillating wave surge converter. J. Eng. Math. 103, 195–216 (2017).
  2. Cummins, C. P., Scarlett, G. T. & Windt, C. Numerical analysis of wave-structure interaction of regular waves with surface-piercing inclined plates. J. Ocean Eng. Mar. Energy 8, 99–115 (2022).
  3. Ancellin, M. & Dias, F. Capytaine: a Python-based linear potential flow solver. J. Open Source Softw. 4, (2019).

Statistical learning for quantifying meteorological event-related risks

Supervisor(s): G. Tzougas (MACS, supervisor), G. Streftaris (MACS, co-supervisor)

Description: Quantifying meteorological event-related risks has become increasingly important in general insurance as extreme climate events may trigger excess claims that can potentially have detrimental impact on the insurer’s portfolio. On the other hand, it is challenging to model the relation between climate events and claim frequencies, since detailed information on climate events is often not fully recorded. Motivated by the above issues, in this project we will model the number and the cost of claims to characterize meteorological event-related risks.

Multivariate Spatiotemporal Hybrid Neural Networks Regression Models

Supervisor(s): G. Tzougas (MACS, supervisor), G. Streftaris (MACS, co-supervisor)

Description: In this project, we propose a novel approach to modeling multivariate claim frequency data with dependence structures across the claim count responses, which may exhibit different signs and ranges, as well as overdispersion due to unobserved heterogeneity. We will analyze claim rates within a property insurance portfolio of an insurance company, particularly prompted by extreme weather-related events in Greece.

Key drivers in cancer morbidity and mortality disparities: past and future

Supervisor(s): G. Streftaris (MACS, supervisor), G. Tzougas, A. Arik (MACS, co-supervisors)

Description: The aim of this project is to investigate cancer incidence and mortality rates in various sub-national groups, based on demographic/ socio-economic factors (e.g. ethnicity, education, deprivation, country of origin). The research will address whether widening socio-economic differences in some cause-specific deaths are related to are related to migration or other demographic factors by using advanced statistical and machine learning modelling.

Landscape management and the pace of nature recovery: multiscale modelling and simulation

Supervisor(s): Michela Ottobre (MACS, supervisor), Christina Cobbold (University of Glasgow, co-supervisor) Emma Gardner (UK Center for Ecology & Hydrology, industrial co-supervisor)

Description: Human activity has a tremendous impact on shaping our landscapes and the habitats within them. If the rate of landscape change is too fast, for example as a consequence of changing management strategies,  species may not be able to adapt, with consequent biodiversity loss. In this project we will consider this issue for structured, inhomogeneous landscapes, where different patches of land may be used for different purposes (for example mixed rewilding/agricultural). From a mathematical perspective this will entail the use of (stochastic) multiscale modelling and analysis, on spatially inhomogeneous models. 

Holistic Quantitative Risk Management Strategies with Application to Flood Risk Management

Supervisor(s): A. Chong (MACS, supervisor),

Description: Despite tremendous effort being spent, the recent fell short of reducing greenhouse gas emissions to the targets in many countries are evident. If this is going to lead us to a new norm, with more frequent and severe flooding, drought, tropical cyclone, wildfire, and so on, are we prepared to adapt? With limited budget and resources being available, who shall be responsible for enhancing resilience and how? This project aims to develop holistic quantitative risk management strategies to scientifically answer these questions via a probabilistic and game-theoretic approach. The developed theory shall then be applied to flood risk management, and in particular shall provide a systematic analysis on the cost-and-benefit of property flood resilience.