Many problems in the applications of mathematics can be reduced to the computation of a multi-dimensional integral. Of these, there exist integrals that cannot be evaluated precisely with perhaps the most common reason being the non-existence of an antiderivative of the function. Numerical methods are therefore required to approximate these calculations, while striving for a small approximation error to the actual value of the integral. The Monte Carlo integration method is one of these numerical methods which approximates an integral as the average of the integrand evaluated at a randomly selected set of points. In contrast, there also exists the quasi-Monte Carlo integration method which approximates the integral by averaging integrand values at points which are deterministic in nature, not random. Questions therefore arise from asking what properties this set of deterministic points should possess to ensure best approximation to the exact integral value. The remarkable 'Koksma- Hlawka inequality' states that the error between the approximated value by QMC methods and the exact integral value can be bounded by a product of two independent factors. Both factors can be investigated separately, however I am interested in the term which quantifies how well a sequence is distributed, namely the discrepancy of a sequence. This ensures the link between quasi-Monte Carlo methods and uniform distribution. In particular, the method desires sequences of low discrepancy to reduce the error. The theory of uniform distribution in the classical setting is concerned with the irregularity of the distribution of sequences of real numbers in the d-dimensional unit cube. This, along with theoretical abstract concepts and results for general spaces are very well understood. For example, there exists a wealth of results which have been generalised from the classical setting to compact Hausdorff spaces. However, even though there are explicit constructions for low discrepancy sequences in the classical setting such as the Halton sequence, there are no concrete constructions of uniformly distributed sequences over compact groups. Hence, currently one cannot approximate integrals defined over such abstract spaces via quasi-Monte Carlo methods. Therefore, my goal during this course of study is to extend the quasi-Monte Carlo method to a more abstract setting. Specifically, I plan to develop constructions of uniformly distributed sequences in compact groups such as the orthogonal group which is the group of all (distance-preserving) transformations of Euclidean space. I will arrive at specific examples to computationally implement in quasi-Monte Carlo methods to approximate numerical integrals defined over these groups. In addition, I will need to form a concept of discrepancy since it is not yet clear what this should be in the abstract sense. This will be used to analyse the error values between the approximation and exact integral value.

To develop the next generation product packaging system designed for intravenous drug delivery systems. The proposed product is a high performance, environmentally friendly drug container with the capability to extend the product shelf life of pharmaceutical products, reduce waste and improve manufacturing efficiency.

War is the ultimate human-induced crisis that has devastating widespread and long-term consequences for the environment (Arias, et al., 2020). From the thousands of unexploded munitions that litter the fields and forests of Ukraine, to the slaughter of rare mountain gorillas in Eastern Congo and the toxic legacy of oil fires in Syria, armed conflict leaves a permanent scar on the landscape and biodiversity of affected states. Climate change is also a growing factor in exacerbating conflict, with the International Committee of the Red Cross (ICRC) identifying that of the 25 countries deemed most vulnerable to climate change, 14 are mired in conflict (ICRC, 2020). The relationship between periods of conflict and environmental harm is multidimensional and complex, and can be broken down into four relational statements: First, the environment may be a cause of conflict. While often interacting with other social, economic and political dynamics (Schwartz and Sigh, 1999), competition over high-value extractive resources can initiate new conflicts or revitalise pre-existing conflicts (Verdeja, 2012). Second, the environment is a means to perpetuate and sustain conflict, with natural resources playing a role in financing armed conflict (Gómez-Betancur, 2020). Third, the environment may fall victim to collateral damage during the course of a conflict, or warring parties may intentionally destroy it to further their objectives. Finally, environmental harm is a barrier to lasting peace, hindering post-conflict recovery by removing potential platforms for cooperation and depleting the resources available for social reconstruction (UNEP, 2007). Despite these links, the environment-conflict nexus has been under-explored and under-theorised within transitional justice (Clark, 2016; Klinsky and Brankovich, 2019). Indeed, the prevalent anthropocentrism of transitional justice scholarship has meant that environmental harms are left unaddressed (Evans, 2022). This is particularly problematic given that transitional justice is a field defined by questions of how to respond to mass violence in divided societies. Yet, without properly acknowledging and responding to environmental harm, victims of such harm are left in the dark.

Each fellowship will last up to 18 months to cover: - A 3-month inception phase for set up activity - a 12-month placement with the host organization - an impact phase lasting up to 3 months Fellows will co-design projects and activities with their host and produce analysis to inform grovernment decision-making across a range of policy priorities. Fellows will also engage across the host organisation, building effective working relationships and supporting wider knowledge exchange with researchers. This will be supported through their embedded role within the host organisation, including line management support.

The goal of this project is development of a novel therapeutic, called COMP-Ang1, to promote vascular normalization and neuroprotection to treat diabetic retinal ischemia