Mathematical Sciences - Masters by Research Theses

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https://hdl.handle.net/10468/9978

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Modelling the tumour microenvironment and reversible and irreversible chemotherapy resistance
(University College Cork, 2024) Quinlan, Thomas; Wieczorek, Sebastian; Alkhayuon, Hassan; Mulchrone, Kieran F.; University College Cork
The tumour microenvironment (TME) comprises various cell types, including cancer cells, immune cells, and stromal cells, which all engage in complex, dynamical interactions. Understanding these interactions, particularly their role in promoting cancer growth and the emergence of drug resistance, is crucial for developing effective treatment strategies. This project constructs a comprehensive mathematical model of the TME that incorporates the effects of chemotherapy. We systematically derive a series of process-based equations to describe the tripartite interactions between cancer cells, immune cells and stromal cells within the TME, as well as their response to chemotherapy. Throughout the model development, we analyse sub-models to ensure we capture key qualitative behaviours. Finally, we conduct a qualitative study by simulating our model under various hypothetical TME scenarios and different chemotherapy dosing schedules. Our simulations demonstrate how variations in stromal activity and treatment regimens can lead to diverse patient outcomes, highlighting the need for personalised treatment strategies.
Invariant polynomials in harmonic analysis
(University College Cork, 2024) Murphy, Fergal; Spyridon, Dendrinos; Mustata, Andrei; University College Cork; La Trobe University
This thesis presents a methodology for analysing equiaffine invariant measures on surfaces, building on a modified version of a comparability lemma from a 2019 work of P. Gressman. The research focuses on simplifying the process of calculating the equiaffine invariant measure for 2-surfaces in R^n by avoiding the need for a complete set of generators for the algebra of invariant polynomials. Instead, we compute a sufficient set of invariant polynomials whose intersection characterises the set of unstable points under the SL_2(C) action. Our approach is demonstrated on specific surfaces in R^6, R^10, and R^15, where we successfully identify the relevant invariant polynomials and use them, along with the modified lemma, to derive the associated density functions. These density functions can then be used to define the equiaffine invariant measure. The results offer a practical framework for understanding affine invariants in geometric contexts and suggest possible extensions to higher-dimensional surfaces and different group actions. This work aims to provide a foundation for future studies in geometric invariant theory and harmonic analysis, exploring the interplay between algebraic geometry, invariant theory, and analysis.
Dynamics of adaptive recurrent neural networks
(University College Cork, 2023) Fox, David; Amann, Andreas; Keane, Andrew; University College Cork
In this thesis a simple, phenomenological model of a neural network with plasticity is presented in the form of a slow-fast adaptive dynamical recurrent neural network. The plasticity rule is chosen from the class of Hebbian learning rules, in which the synaptic connection between two neurons evolves continuously as a function of their correlation in the recent past. Initially an analysis of networks of two neurons is presented, which exhibit relaxation oscillations in which one neuron switches between an ’off’ state, where it takes a negative value, and an ’on’ state, where it takes a positive value, while the other neuron stays in one on/off state. Then, by means of an example with a nine neuron network, the system is shown to exhibit both stable frequency cluster synchronization and transient frequency cluster synchronization.
Statistical applications in health and social research
(University College Cork, 2022) Kenny, Alan; O'Sullivan, Kathleen (Catherine); Conway, Damian; Wolsztynski, Eric
The MSc comprised four projects based on different statistical techniques. Each project is an individual chapter in the thesis and has been written independently. The first project is based on a student-wide survey conducted by University College Cork (UCC) to examine the student experience. As this study was unique to the Irish college system, factor analysis was employed to validate the use of purpose-built scales. Reliability analysis was conducted to determine if the scales were internally consistent, and the results of factor and reliability analysis and summary results were presented. The second project focuses on 15O Positron Emission Tomography (PET) Imaging Data and its ability to quantify underlying metabolic processes, namely cerebral blood flow in an Alzheimer’s disease patient. Kinetic analysis, using a 1-compartmental model, was employed and functional parameters were estimated. The technique was validated through comparisons with a non-parametric approach. This study confirmed that there was lower blood flow in brain regions that are affected by Alzheimer’s disease. The third project is an actuarial study, which explores the process known as graduation by standard table. Using information collected from a population, a set of crude rates are deduced. These rates need to be improved using the graduation by standard table method. Our graduated rates are then tested using five statistical tests to verify they are reliable. This study confirmed that use of the graduation method could improve crude rates to make them reliable. The fourth project focuses on structural empowerment in an Irish nursing context. Our study concentrates specifically on perceptions of formal power. Univariate analysis was conducted to identify associations between demographic characteristics and perception of formal power. Multivariate regression was used to identify which combination of demographic characteristics significantly affected a respondent’s perception of formal power. Respondents’ perceptions of formal power were in line with previous studies.
Empirical analysis of relative impact of COVID-19 on sectoral stock returns in China
(University College Cork, 2021-01-05) Chang, Keying; Huang, Jian
Since it broke out in China in December 2019, Covid-19 has brought an unprecedented impact on every aspect of social, economic, and cultural life globally. The direct impact includes a fragile system of health-care, cut off supply chain and trade, and sharp decline in production, consumption, and investment activities. The impact of Covid-19 on the stock market performance has attracted lots of research interests in the literature. In this study, we explore the relative effects of Covid-19 on the sectoral performance of the stock market in China, using daily time series stock market data spanning 1 st Jan 2020 to 30th Dec. 2020. First, we employed the principal component analysis to derive a proxy for each sector based on its composite shares. Second, we carried out t-test to estimate whether there existed a difference between average returns before and after Wuhan lockdown due to the outbreak of Covid-19. Finally, we employed the event study methodology to investigate the impact of Wuhan lockdown on the sectoral performance of stock market in China The event study found that Wuhan lockdown have significant effects on the stock returns in China. The pandemic has adversely impacted sectors such as Public Transport, Logistic Attractions and Tourism, Hotel and Catering. However, Manufacturing, Information Technology, Education and Health-care industries have been resilient to Wuhan lockdown.

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