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              <text>This paper discusses the polity of the Norman adventurer Roussel de Bailleul which existed between 1073 and 1075. It answers how the polity survived for nearly two years with the use of a 'Norman Frontier Society Model' which was similar to other Norman polities such as the Kingdom of Sicily and the Principality of Antioch. Alongside this model, primary sources are utilised to create a contextualised picture of this polity in terms of its politics, economy and society.</text>
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                <text>The Normans in Anatolia: An Analysis of the Functioning of the Polity of Roussel de Bailleul during the 1070s</text>
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                <text>Byzantine Anatolia during the 1070s, primarily the polity of Roussel de Bailleul</text>
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                <text>Aysu Dincer Hadjianastasis</text>
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              <text>This project investigates digit phenomena motivated by a question of Paul Erdős. We study the occurrence of the digit 7 in powers of 2, asking whether every sufficiently large power of 2 contains the digit 7. More generally, we consider the sequence (a·2ⁿ) for varying positive integers a and formulate the following conjecture: the set of a for which a·2ⁿ contains the digit 7 for all sufficiently large n has full natural density. In pursuit of this conjecture, we develop useful combinatorial and arithmetic estimates, together with a dynamical approach to the leading digits of these numbers.</text>
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              <text>number theory, digit occurrence, powers of two, geometric progressions, Benford's law, natural density, logarithmic density, dynamical systems, shrinking targets, irrational rotations, combinatorics, Erdős</text>
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                <text>Digit Occurrence in Geometric Progressions</text>
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                <text>Mathematics – Number Theory and Dynamical Systems</text>
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                <text>Joel Moreira</text>
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              <text>In this project, I investigate how the timing and strength of mosquito vector-control interventions can be optimised to reduce dengue transmission in Veracruz, Mexico. I develop a seasonally forced SEIR model, fitted to historical dengue case data from 2006, to assess the effectiveness of larval control and adulticide independently and in combination. I explore how changes in implementation start day, intervention duration and control strength affect the reduction in dengue cases to identify the optimal strategy. I then explore how long their effectiveness can be maintained when the intervention is delayed.</text>
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              <text>This project investigates whether time-series signals can be compressed without losing the information needed for reliable classification. Four compression methods—PAA, PLA, APCA and Fourier representations—are evaluated on the FordA and ECG5000 datasets using a shared neural-network classifier. The experiments examine classification performance, training and inference efficiency, and robustness to noise and missing values when only 50% or 25% of the original input width is retained. Signal reconstructions and PCA visualisations are also used to examine which structures remain after compression. The results show that Fourier representations provide the strongest overall trade-off, sometimes improving classification performance while reducing input width and model size, although computational speed-ups depend on the dataset and compression method.</text>
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              <text>machine learning, dimensionality reduction, signal processing, Fourier transform, neural networks, robustness</text>
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                <text>Kaitao (Kenneth) Jiang</text>
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                <text>Weiren Yu</text>
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              <text>The Ehlers-Danlos syndromes (EDS) are a group of genetic disorders characterised by joint hypermobility, stretchy skin, or fragile skin, which are not well understood and can have a disabling effect on a person’s life. These syndromes are caused by changes in the structure and function of proteins, such as collagen, which comprise the extracellular matrix (ECM). The ECM holds cells together, but not much is known about how changes in its composition and molecular dynamics contribute to the development of EDS. This study will use solid-state nuclear magnetic resonance (NMR) spectroscopy to determine the atomic structure and dynamics of ECM obtained from cell culture of fibroblasts from people with and without EDS. By carrying out quantitative comparison of NMR relaxation spectra of the two types of samples, we aim to find similarities and differences that lead to the identification of molecular signatures of specific subtypes of EDS. We envisage that this research will lead to a deeper understanding of EDS and provide insights into how it develops and operates on a molecular level. In the long term, we anticipate that our work may lead to developing better diagnosis strategies and more targeted treatments.</text>
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                <text>Using Solid-State NMR to Identify Molecular Dynamic Signatures of Extracellular Matrix Dysfunction in Ehlers-Danlos Cells </text>
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                <text>Dr. Wing Ying Chow, Christopher Dean, Abi Hesson and Dr Adil Safeer</text>
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                <text>Using Solid-State NMR on Biological Samples</text>
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              <text>Bacterial black rot disease, caused by Xanthomonas campestris pv. campestris (Xcc), is a global threat to agriculture through infection of key crops such as Brassicas. Treatment options are limited - agrochemicals, such as copper compounds and antibiotics, have limited effectiveness due to bacterial resistance, and phytotoxicity in the environment. Bacteriophages, or phages, are naturally occurring viruses that specifically target and kill pathogenic bacteria and offer a promising biocontrol alternative. Our aim is to investigate the in vitro efficacy of six phages in reducing a diverse range of Xcc populations.</text>
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              <text>Bacteriophages, Phage, Phage Therapy, Xanthomonas, Black rot disease, Brassicas </text>
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                <text>Morgan Rabiey</text>
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              <text>This project showcases the packing of circles and ellipses using conic shapes and focal conics. We derive Descartes’ equation and an equivalent of it in hyperbolic space, then go over an application within a liquid crystal and derive the cylcides of Dupin that are around a given focal conic.</text>
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              <text>Physics, Theoretical physics, Mathematics, Geometry</text>
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                <text>Focal Conics: From Number Theory to Materials Geometry</text>
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                <text>Dr. Gareth Alexander</text>
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              <text>This project is about the prime orbit theorem for shifts of finite type and my attempt to logically verify the theorem using the LEAN proof assistant.</text>
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              <text>mathematics, dynamical systems, number theory, LEAN,  proof assistant</text>
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                <text>Formalising prime orbit theorem for shifts of finite type in LEAN4</text>
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                <text>Akira Corr</text>
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                <text>Formalisation of mathematics</text>
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