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              <text>Named after Diophantus of Alexandria, Diophantine approximation is a field in number theory that studies how well real numbers can be approximated by rational numbers. In 1984 Mahler presented eight problems in transcendental number theory and Diophantine approximation. One of these problems posed the questions, ‘how well can irrationals in the middle third Cantor set be approximated by rationals in the middle third Cantor set?’ and ‘how well can irrationals in the middle third Cantor set be approximated by rationals not in the middle third Cantor set?’. This problem serves as the inspiration for this paper. The middle third Cantor set can be described as a missing digit set of base 3, which motivates our study of missing digit sets. In this paper, we will address the following related question, `How well can irrationals in a missing digit set be approximated by rationals with polynomial denominators?' and prove some related results. To achieve this, we will be closely looking at Khintchine's theorem, particularly the convergence case and aim to prove a Khintchine-like convergence theorem for missing digit sets with large bases and rationals with polynomial denominators.</text>
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              <text>This project is supervised by Han Yu in Warwick Mathematics Institute. The main aim of this project is to explore the Khinchine's theorem on \mathbb(R)^n, and further restrict to a non-degenerate manifold \mathcal{M} with Gaussian curvature on \mathbb{R}^n, with relative measure on \mathcal{M}. For simplicity we just prove the result over [0,1]^n.</text>
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              <text>Epilepsy is one of the most common neurodegenerative diseases, characterised by electrical imbalances in neurons yielding seizure activity. Around 600 people with epilepsy in the UK die every year from sudden unexpected death in epilepsy (SUDEP). A major cause of SUDEP, seizure-induced cardiorespiratory autonomic dysfunction, is known, however exact neuronal and microglial inflammatory mechanisms governing this impairment have not been characterised. Microglia, the resident multifunctional immune cells of the central nervous system were shown to surround cardiorespiratory neurons and to exhibit both pro- and anti-epileptic functions, supporting their modulatory role in the breathing phenotype characteristic of epilepsy. Cardiorespiratory dysfunction was previously suggested to arise resulting from propagating neuronal hyperexcitability into the brainstem and the consequent microglia-induced neuroinflammation. Based on this phenotype we hypothesize that seizure-induced microglial activation changes from being initially beneficial against seizures in acute epilepsy, to detrimental by progressively decreasing the threshold for seizures in chronic epilepsy, to ultimately fatal by compromising the activity of cardiorespiratory autonomic neurons in the brainstem. Cardiorespiratory function was examined in awake, freely moving epileptic and sham-treated mice in response to different levels of CO2 levels. Microglia activity rescued the breathing phenotype in acute but worsened it in chronic epilepsy. These findings suggest microglia may remodel cardiorespiratory neuronal circuits in epilepsy potentially leading to SUDEP. This research suggests directions for novel treatments for epilepsy that appropriately modify microglia activity.</text>
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              <text>Compassion has been an increasingly studied topic within psychology, found to have psychological and wellbeing benefits (Neff, 2015; Macbeth &amp; Gumley, 2012) as well as on motivation for healthcare professionals (Kotera et al., 2021). Thus, this study aimed to understand whether the reported benefits of compassion on motivation and mental health applied to undergraduate Psychology students, in comparison to undergraduate Business students. Participants were given the self-compassion scale, as well as the compassion for others scale (Pommier et al., 2019; Raes et al., 2011), as well as the PHQ-9 (Koneke et al., 2001) and the GAD-7 (Spitzer et al., 2006), as well as their degree choice and career aspirations. Scores on the PHQ (depression), as well as compassion for others, significantly differed by degree choice, with depression scores being higher for business students, but not career choice. This lends support for the ‘wounded healer’ hypothesis as to motivation for studying psychology, potentially having implications at university and in the workplace. </text>
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              <text>O2 , pH and CO2 are useful indicators of health conditions in human body. Common methods used involve taking body fluids from the patients with needle and syringe which is not only invasive but also time consuming. Furthermore, traditional sensors for O2, CO2 and pH are big and therefore difficult to take in-vivo measurements. Their miniaturized forms also have drawbacks such as fragility and difficult to operate1. The Warwick Electrochemistry and Interfaces group has produced electrodes that have conductive diamond (sp3) form of carbon and non-diamond (sp2) carbon to make sure they are all sensitive to O2 CO2 and pH. 3D printed macro electrodes with the same pH sensitive surface group have also been studied due to their increased affordability and access to the 3D printing technology2. The 3D printed electrodes have been assessed and proved to have high quality in measuring O2,CO2 and pH. Some preliminary experiments have been carried out and future work is ongoing.</text>
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