Postgraduate research opportunities

We welcome enquiries from prospective PhD students. Here is a list of potential research topics, but we are also happy to discuss other projects.

 

Evaluating the collective resilience of animal social groups to changing environments – Colin Torney

Increasingly animal groups are seen as collectively functioning systems. To perform the tasks that are essential for their survival they must respond to their environment, and their ability to do this is determined not only by individual-level characteristics, but also by the collective properties of the social group. Collective behaviour and emergent group-level phenomena are known to play a role in activities relating to information processing, such as foraging, predator avoidance, or migration. While it has been assumed that the emergent properties of systems are robust and resilient, to date it remains unclear how these systems will respond to environmental disturbances. Since a social group may function as a collective, individuals within the group are often assumed to be non-essential and interchangeable. However adaptation and learning are processes that occur at the individual level, thus the mechanisms by which groups can modify their collective behaviour are complex and potentially subject to multilevel conflicts of interest. The purpose of this project will be to investigate, within an experimental and theoretical framework, how social structure develops and how resilient the collective properties of animal social groups are to changes in their environment.

Dynamical modelling and adaptation strategies for changing eco-systems – Markus Mueller, Ilya Maclean (ESI)

Dynamical models are relatively successfully predicting the possible implications of increasing carbon and GHG emissions on our climate. Because the climate is global, systems and models have to incorporate many processes and operate on a very large scale and hence do not have the capacity to make local and regional predictions. Most organisms experience climate on scales of millimetres to meters and many land-use decisions are also made on a local/regional level. For example, it might be that an increase of the average global temperature is locally amplified or does not play any crucial role in the ecosystem. This project aims to develop dynamical and predictive models, with a focus on the fine scale, which will allow us to predict local processes and interactions. Based on the prediction, we also aim to develop control and adaptation strategies to achieve pre-specified objectives. Finally, we aim to apply and test the models on environmental, ecological and micro-climate data collected in various regions in Cornwall like the Lizard Peninsula. The project would be in collaboration with colleagues in Exeter’s Environment and Sustainability Institute and is an ideal opportunity to apply mathematical knowledge to real world problems.

Density dependent population dynamics: Feedback loops and small gain theorems – Stuart Townley

Density dependence in a population can often be viewed as a nonlinear feedback. For example, seedling establishment is a nonlinear feedback on seed production. Adopting a feedback interpretation of such density dependent effects we can appeal to classical and more recent developments in feedback control theory, for example Popov and Circle Criteria and small gain theorems. These feedback control theory results lead to criteria for global stability. Using specific density dependent population projection models for plants as motivation, we will develop novel small gain type results as a generic tool for analysing density dependent population dynamics. These results in turn will provide a framework for assessing, for example, the effect of fitting different density dependencies to observed data.

Robustness tools for integral projection models – Stuart Townley

We have developed several robust control based techniques for studying the dynamics of stage structured populations, modelled in terms of uncertain population projection matrices. In this project we will extend these quantitative techniques to populations described by integral projection models. Integral projection models use a continuum state (e.g. height, weight) and are defined via integro-difference equations. A key component of these models is an integral operator defined in terms of a kernel function. In most applications the kernel will be uncertain. We will develop techniques for modelling this uncertainty as a perturbation and then analyse how various indicators of asymptotic and transient dynamics (growth bound, systems reactivity) respond to p;erturbations.

The effects of spatio-temporal heterogeneities on the spread and persistence of vector-borne diseases – Mario Recker

Vector-borne diseases are a growing risk to human and animal health, exemplified by the world-wide (re-)emergence of dengue, the current threat of bluetongue and Schmallenberg virus, or the recent epidemic spread of West Nile and Rift Valley fever. Standard epidemic models are inadequate to capture the complex interactions between the pathogen, the insect vector and the human or animal host. Furthermore, the dependencies of vector ecologies on environmental attributes, such as temperature, ra;infall, or host density, introduce strong heterogeneities both in time and space that have important consequences for the disease’s local and global epidemiology. This project aims to develop a new mathematical frameworks to investigate the epidemiological effects of population structure and spatio-temporal heterogeneities in host and vector ecologies. These frameworks will be applied to understand and predict the epidemic behaviour of emerging pathogens as well as the outcome of intervention measures. 

A systems biological approach to understand malaria immunity: from high-throughput sequence data to predictive modelling – Mario Recker

Malaria still poses a significant burden on the lives of millions of people, with children under the age of 5 years in sub-Saharan Africa being at the highest risk of severe morbidity and mortality. In contrast to many childhood diseases, such as measles, even repeated infections with the human malaria pathogen Plasmodium falciparum will not lead to immunity against further infections. However, a level of protection against life-threatening illness is usually acquire after few infections only. New sequencing technologies (including genomics and transcriptomics) in combination with mathematical approaches will allow us to get a more detailed picture of how individuals build up immunity under repeated challenge and what really constitutes immunity to malaria. This project aims to develop new mathematical models to integrate genomic, transcriptional, immunological and epidemiological data in a multi-scale, systems biological approach.

Evolutionary dynamics of multi-strain pathogens – Mario Recker

Many important human pathogens, such as malaria, influenza or HIV, show a high degree of diversity, which enables them to maintain chronic infections and achieve high rates of re-infection. On the other hand, the co-circulation and constant emergence of novel pathogen strains severely hinder our efforts to develop effective control strategies, such as vaccines. The evolutionary trajectories of these pathogens are significantly influenced by the interactions between individual strains, which commonly take on the form of competition via the host’s immune system and have been shown to cause complex dynamical behaviours and population structuring. It has also recently emerged that natural stochasticities in time and space can have profound effects on the epidemiology on such multi-strain systems, yet their effect on pathogen evolution has not yet been addressed. The aim of this project is to investigate the effects of immunological competition in combination with natural variations in disease transmission on the evolutionary dynamics of multi-strain pathogens.

Optimization and Control of arrays of Wave Energy Converters – Markus Mueller

Sustainable energy from the sea and the oceans is still a rather underdeveloped sector of the renewable energy mix. To make wave energy more economically viable it is essential for single energy extracting devices, such as hydroelectric turbine buoys or surface waves following devices, to be deployed in arrays to share the expensive infrastructure (in particular for off shore energy generation). This project aims to develop novel mathematics to understand and control the hydro-dynamical interactions of devices to maximise power output and minimise risk to the technology in a potentially hazardous wave environment. This will include predictive and distributed control and optimization strategies and requires the consideration of mechanical interactions as well as the communication between devices in the array on different levels: from nearest neighbours to clustered to global interactions, control and optimization.

Funnel predictive control – Markus Mueller

Funnel control is a highly advanced nonlinear control strategy that overcomes identification of systems and hence is applicable to highly uncertain linear, nonlinear, time-varying, infinite dimensional, and many more classes of systems. Funnel control can achieve robust transient and asymptotic tracking of a pre-scribed system's output behaviour. – In model predictive control a change in the dependent variables of the modelled system caused by changes in the independent variables is predicted for a given finite prediction horizon. The control is updated iteratively according to the optimal predicted behaviour. – This project aims to integrate these both concepts: a funnel predictive control will adaptively find the optimal control even when system parameters are subject to uncertainty. The optimization will only rely on structural properties of the system and will also be able to cope with external disturbances only assuming general pre-specified bounds on the disturbances. A funnel predictive strategy will find its application in control and optimization of highly uncertain systems with uncertain disturbances, for example in the field of renewable energy technologies, in particular wave energy.

Control systems for integrated renewable energy/technology – Markus Mueller, Stuart Townley

Solar power needs sunny weather, wind and wave power need windy weather, bio-crops rely on sun and plentiful water supply, hydro-electric power needs reservoirs to be filled to capacity. But sunlight quality and precipitation rates are asynchronous. Consumption timescales rarely match those of energy generation. So how can we better manage these intermittent technologies without over-reliance of expensive batteries? The answer may lie in the use and development of tools and techniques from modern control systems theory. This project will explore the dynamical interplay between various renewable energy sources and the corresponding renewable technologies and develop robust management strategies to maximize power outputs from integrated systems that combine solar/wind/wave in reliable and sustainable co-generation of power and other products (clean water, food).

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