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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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                <text>Metastable Dynamics of Interacting Particle Systems</text>
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                <text>Tim Gunaydin&#13;
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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>resource allocation algorithms, algorithm optimisation, optimisation, paralellisation, hpc, servers, convex optimisation, computer science, maths, performance</text>
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                <text>Aadya Mudgil</text>
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                <text>Arpan Mukhopadhyay</text>
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                <text>Computer Science </text>
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                <text>On Optimal Resource Allocation Algorithms for Paralellisable Jobs</text>
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                <text>2024</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>diffusion models, geometric Brownian motion, stochastic processes, financial modelling, stock price analysis, multiscale modelling, rough path signatures, Ornstein-Uhlenbeck, Brownian motion, timescales, volatility</text>
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                <text>Aabid Anas, Anastasia Papavasiliou, Pablo Ramses Alonso Martín</text>
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                <text>Statistics </text>
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                <text>Financial Modelling, Diffusion Processes, Stock Price Behaviour, Stochastic Methods, Rough Path Theory</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>Physics, Astrophysics, Supernovae, Thermonuclear, White Dwarf, </text>
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                <text>Thomas Bebbington</text>
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                <text>Dr Mark Magee</text>
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                <text>Physics</text>
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                <text>A Census of Thermonuclear Explosion Scenarios</text>
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                <text>2024</text>
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