http://theses.ncl.ac.uk/jspui/handle/10443/89 2026-02-04T05:00:07Z http://theses.ncl.ac.uk/jspui/handle/10443/5465 Title: Magnetohydrodynamics in hot Jupiters Authors: Hindle, Alexander William Abstract: Hot Jupiters are Jupiter-like exoplanets found in close-in orbits. This subjects them to high levels of stellar irradiance and is believed to tidally-lock them to their host stars, causing extreme day-night temperature differentials which in-turn drive atmospheric dynamics. A ubiquitous feature of hydrodynamic models of hot Jupiter atmospheres is equatorial superrotation, which advects their hotspots (equatorial temperature maxima) eastwards (prograde). Observational studies generally find eastward hotspot/brightspot offsets. However, recent observations of westward hotspot/brightspot offsets suggest that this is not ubiquitous. Prior to these observations, three-dimensional magnetohydrodynamic simulations predicted that westward hotspots could result from magnetohydrodynamic effects in the hottest hot Jupiters, yet the mechanism driving such reversals is not well understood. We study the underlying physics of magnetically-driven hotspot reversals using a shallow-water magnetohydrodynamic model. This captures the leading order physics of hot Jupiter atmospheres, but with reduced mathematical complexity. The model’s hydrodynamic counterpart is well-established and has successfully been used to explain equatorial superrotation in hydrodynamic models of hot Jupiter atmospheres in terms of planetary scale equatorial wave interactions. However, until now, shallow-water magnetohydrodynamic models have not been applied to hot Jupiters. Firstly, we find that the model can indeed capture the physics of magnetically-driven hotspot reversals. We use non-linear numerical simulations to understand the dominant force balances that drive the reversals and use a linear analysis of the system’s planetary scale equatorial waves to understand the reversal mechanism in terms of wave interactions. We then use the developed theory to place physically motivated observational constraints on the magnetic field strengths of hot Jupiters exhibiting westward hotspot/brightspot offsets, finding that on the hottest of these the observations can be explained by moderate planetary magnetic field strengths. Finally, we identify candidates that are likely to exhibit magnetically-driven hotspot reversals to help guide future observational missions. Description: PhD Thesis 2021-01-01T00:00:00Z http://theses.ncl.ac.uk/jspui/handle/10443/5361 Title: Bayesian optimal design using stochastic gradient optimisation and surrogate utility functions Authors: Harbisher, Sophie Abstract: Experimental design is becoming increasingly important to many applications from genetic research to robotics. It provides a structured way of allocating resources in an e cient manner prior to an experiment being conducted. Assuming a model for the data, one approach is to introduce a utility function to quantify the worth of a design given some data and parameters. Typically experiment-speci c utility functions are di cult to elicit and hence a pragmatic choice of utility concerning the information gained about the model parameters is used. Bayesian experimental design aims to maximise the expected utility accounting for uncertainty in the model parameters and the data which could be observed. For this approach, di culties arise as the expected utility is typically intractable and computationally costly to approximate. Modern applications often seek high dimensional designs. In these settings existing algorithms such as the MCMC scheme of Müller (1999) and ACE (Overstall and Woods, 2017), require a high number of utility evaluations before they converge. For the most commonly used utility functions this becomes a computationally costly exercise. Therefore there is a need for an e cient and scalable method for nding the Bayesian optimal design. The contributions of this thesis are as follows. Firstly, stochastic gradient optimisation, a scalable method widely used in the eld of machine learning, is applied to the Bayesian experimental design problem. The second contribution is to consider a utility function based on the Fisher information matrix as a Bayesian utility function by showing it has a decision theoretic justi cation. These utilities are often available in a closed-form so are fast to compute. The nal contribution is to investigate surrogate functions for expensive utilities as an e cient way of nding promising regions of the design space. Description: PhD Thesis 2021-01-01T00:00:00Z http://theses.ncl.ac.uk/jspui/handle/10443/5320 Title: Modelling Voxel Dependent Hemodynamic Response Function Authors: Fletcher, Darren Abstract: An important challenge of contemporary neuroscience is the detection and understanding of significant brain activity using functional magnetic resonance imaging (fMRI). One of the many motivations of this research, related to the data set used in this thesis, is to investigate brain activation and connectivity patterns aimed at identifying associations between these patterns and regaining motor functionality following a stroke. Much statistical modelling has attempted to interpret noisy fMRI data and detect changes in response to activity. However due to the large data sets usually involved in fMRI modelling, here as many as 150, 000 measurements in localised spatial volumes known as voxels at each time point, many simplifying assumptions are usually made to make computation feasible. This is known to have a negative impact on detecting voxel activation. In this work we fit a space-time model to a fMRI data set using a sequential approach to allow for scalability. However, the main contribution of this work is an alternative method to detect activation in the brain. Here we take the novel approach of using topological data analysis to investigate the model residuals to detect changes in the fMRI data. In particular we analyse the spatial distribution of topological features of the residuals to provide a test for normality, and also by providing a method to analyse how the spatial distribution of such features change over time, we are able to detect changes in the data in response to activity where conventional methods cannot. A recommendation for future work is to also investigate how topological features change for different filtration levels of the field, as this may provide new insights on brain activation. Description: Ph. D. Thesis. 2020-01-01T00:00:00Z http://theses.ncl.ac.uk/jspui/handle/10443/5311 Title: Bayesian inference for linear stochastic differential equations with application to biological processes Authors: McLean, Ashleigh Taylor Abstract: Stochastic differential equations (SDEs) provide a natural framework for describing the stochasticity inherent in physical processes that evolve continuously over time. In this thesis, we consider the problem of Bayesian inference for a specific class of SDE – one in which the drift and diffusion coefficients are linear functions of the state. Although a linear SDE admits an analytical solution, the inference problem remains challenging, due to the absence of a closed form expression for the posterior density of the parameter of interest and any unobserved components. This necessitates the use of sampling-based approaches such as Markov chain Monte Carlo (MCMC) and, in cases where observed data likelihood is intractable, particle MCMC (pMCMC). When data are available on multiple experimental units, a stochastic differential equation mixed effects model (SDEMEM) can be used to further account for between-unit variation. Integrating over this additional uncertainty is computationally demanding. Motivated by two challenging biological applications arising from physiology studies of mice, the aim of this thesis is the development of efficient sampling-based inference schemes for linear SDEs. A key contribution is the development of a novel Bayesian inference scheme for SDEMEMs. Description: Ph. D. Thesis. 2020-01-01T00:00:00Z