Mathematical Sciences - Masters by Research Theses
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Item Dynamics of adaptive recurrent neural networks(University College Cork, 2023) Fox, David; Amann, Andreas; Keane, Andrew; University College CorkIn 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.Item Statistical applications in health and social research(University College Cork, 2022) Kenny, Alan; O'Sullivan, Kathleen (Catherine); Conway, Damian; Wolsztynski, EricThe 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.Item Empirical analysis of relative impact of COVID-19 on sectoral stock returns in China(University College Cork, 2021-01-05) Chang, Keying; Huang, JianSince 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.Item A close knit complex network: statistical examination of board interlocks and their impact on financial results(University College Cork, 2021) Dave, Kirtivardhan Parantap; Roy, SupratikBoard of directors are at the pinnacle of the corporate world, in any company they form the highest decision making authority. A position on the board of a company is one of immense privilege and power. Thus, making any individual who occupies such a position privy to information about the company which most people would not have. Even the shareholders who are the owners of the company are not privy to this information. In this study I look at complex networks formed by board interlocks in the United Kingdom. When one director sits on the board of two companies, it creates a board interlock, where he acts as a link between the two companies. The main aim of the study is to look at the relationship between the features of these networks and their impact on the financial results of public limited companies in the United Kingdom. The first part of this study looks at these corporate networks and how they have evolved over the past three decades. Using varied network analysis features, the board interlock network was studied from two different perspectives. First, as a dual mode network or a people to company network. In this kind of network edges are formed between a board member and the company on whose board she sits. Second, as a single mode network where common board members between two companies form an edge between those companies. We find that the corporate network has become denser over the years, exhibiting small world properties. Companies that did not share board members with any other company have nearly halved over the course of the three decades. There have been quite a few studies that have looked at the impact of network features on financial results from various academic perspectives be it financial, sociological, management, and more recently network analysis. I have used four different centrality measures and proposed a ranking based model. Which unlike any other existing study also goes deeper by incorporating different community sizes into the regression model. This allowed me to check whether network features of better connected companies or companies that are a part of larger communities are stronger predictors of financial performance. This study shows an upward trend with the regression fit improving over time.Item Rate-induced tipping in a moving habitat(University College Cork, 2021-03) MacCárthaigh, Ruaidhrí; Wieczorek, Sebastian; Hasan, CrisAs our planet's surface warms, its ecosystems are shifting to cooler and more suitable climates to survive [1]. This issue raises some important research questions. How successfully can life on earth adapt to these changes? How fast can populations be pushed to migrate before they fail to adapt and collapse to extinction? This thesis addresses the problem of species adapting to shifting habitats, using the framework of ``critical transitions'' or ``tipping points''. Specifically, it explores the persistence of a single species in a fast-moving habitat, and how the nature of its population growth affects its adaptability. The spatiotemporal evolution of the species concerned is described by partial differential equations (PDEs) in the form of nonlinear one-dimensional reaction-diffusion equations and reaction-convection-diffusion equations. Two distinct growth models are constructed and the moving habitat is incorporated into each model with the addition of a continuous non-autonomous term. The first model is a quadratic monostable model of logistic growth limited by the carrying capacity of the habitat, similar to models used in previously published work on the topic of species in a moving habitat [2,3,4]. The second model is made cubic and bistable by incorporating an additional limitation to population growth at low population densities, known as the Allee effect. The spatial distribution of the populations are computed as standing wave solutions in the static habitat and travelling pulse solutions in the moving habitat, drifting at a constant habitat speed. A critical habitat speed is found for both the monostable and bistable models, above which no physical travelling pulse solution exists, meaning that the population within the habitat dies out. In the monostable Logistic Model, a transcritical bifurcation occurs between its travelling pulse solution and its zero (extinction) solution, which gives rate-induced tipping that can be reversed with a clear indication of an eventual local extinction as this critical speed is approached. In contrast, in the bistable Allee Model a saddle-node bifurcation of travelling pulses occurs, which produces an rate-induced tipping point, which typically cannot be reversed in nature, at which the population in the habitat abruptly collapses to extirpation, without any clear indication of the imminent collapse. This provides a stark ecological insight into how the increasing rate of climate change may give little to no advanced warning of extinction for some species that are observed to have an Allee effect and other complex features influencing their population dynamics.