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              <text>Terabotics is the unification of terahertz light and surgical robots to advance the detection of conditions in vivo. Terahertz medical imaging is useful for characterising skin conditions due to its ability to measure skin hydration as skin lesions, such as tumours, are known to affect the hydration of the skin. In the project, I tested different types of imaging and determined methods in order to calculate their resolution.</text>
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              <text>This research explores the potential of Maglev technology as a sustainable transportation solution, with a focus on its alignment with SDG 11 (Sustainable Cities and Communities) and SDG 13 (Climate Action). Using the Shanghai Maglev as a case study, the paper highlights the system’s energy efficiency, reduced carbon emissions, and low noise pollution, which contribute to environmental sustainability. The electromagnetic suspension (EMS) and electrodynamic suspension (EDS) systems eliminate friction, resulting in significant energy savings compared to conventional rail systems. While the technology presents considerable benefits, including low operational and maintenance costs, its widespread adoption faces challenges due to high infrastructure costs and the complexity of integrating it with existing transit networks. Despite these hurdles, Maglev has the potential to be powered by renewable energy, further reducing its environmental impact. This paper argues that Maglev technology, with its longterm sustainability benefits, represents a viable alternative for future urban and intercity transportation, particularly in areas where traditional transit systems are insufficient to meet growing sustainability targets.</text>
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              <text> Extreme Type Ia supernovae present challenges for our understanding of thermonuclear explosion physics. A census of Type Ia supernova theoretical models for various parameter spaces was conducted. This enabled a comparative analysis of the diversity and overlap between distinct explosion scenarios and observed data. With the assistance of my supervisor, Dr Mark Magee, I was able to conclude the physical properties driving this overlap.  </text>
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              <text>This study explores the validity of using the diffusion assumption to model stock prices across various timescales. The diffusion model, based on Geometric Brownian Motion, is commonly applied in financial markets but may not adequately capture price dynamics at finer timescales. By simulating paths and examining rough path signatures, we aim to determine the optimal timescale at which the diffusion approximation effectively models stock price movements.</text>
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              <text>Unprecedented demands are being placed on compute resources due to HPC jobs such as next-gen machine learning. Distributed systems rely on resource provisioning algorithms to parallelise these jobs across many nodes; however, traditional algorithms are unlikely to perform- an inefficient and costly waste of power and time. This research aims to design the optimal algorithm for parallelisable tasks, under a real-world workload, and validate theoretical expectations with the results from system simulations.</text>
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                <text>On Optimal Resource Allocation Algorithms for Paralellisable Jobs</text>
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              <text>We consider a stochastic Ising model evolving according to Glauber dynamics on a complete graph $\G$ with two clusters $\G_1$,$\G_2$. We analyse the metastability of the model and its dependence on the interaction coefficient $J^*$ between vertices $v\in G_1$, $w \in \G_2$. We also investigate the change to dynamics when a positive magnetic field with strength $h$ is introduced. In our study of the metastability we focus on the expected hitting time $\mathbb{E}[\tau^m_s]$. In \cite{Manzo}, the authors show that in the absence of deep cycles, provided we have good control on the typical paths from a $\X_m$, it is possible to derive asymptotic results concerning this value. In addition to asymptotic behaviour, we analyse the dynamics in the $n\to \infty$ limit via large deviation theory. Thus we provide weak convergence results for the Gibbs measure for under the mean-field assumption and identify changes to the dynamics below and above critical temperatures. </text>
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              <text>Markov Processes, Interacting Particle Systems, Large Deviation Theory</text>
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                <text>Dr Paul Chleboun</text>
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