Mathematics thesis and dissertation collection
This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
Recent Submissions

Design of reliable aerospace system architecture
(The University of Edinburgh, 20181129)Reliability and redundancy of safetycritical network systems is a paramount issue in system engineering. Be it in evaluating existing network systems or solving optimization problems for designing network systems, it ... 
Statistical methods for the testing and estimation of linear dependence structures on paired highdimensional data: application to genomic data
(The University of Edinburgh, 20180702)This thesis provides novel methodology for statistical analysis of paired highdimensional genomic data, with the aimto identify gene interactions specific to each group of samples as well as the gene connections that ... 
Heuristic methods for solving two discrete optimization problems
(The University of Edinburgh, 20180702)In this thesis we study two discrete optimization problems: Traffic Light Synchronization and Location with Customers Orderings. A widely used approach to solve the synchronization of traffic lights on transport networks ... 
Data sampling strategies in stochastic algorithms for empirical risk minimization
(The University of Edinburgh, 20180702)Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data ... 
Controlling optical beams in nematic liquid crystals
(The University of Edinburgh, 20180702)A major area of research recently has been the study of nonlinear waves in liquid crystals. The availability of commercial liquid crystals and the formation of solitons at mWpower levels has meant that experimental ... 
Generalised Langevin equation: asymptotic properties and numerical analysis
(The University of Edinburgh, 20180702)In this thesis we concentrate on instances of the GLE which can be represented in a Markovian form in an extended phase space. We extend previous results on the geometric ergodicity of this class of GLEs using Lyapunov ... 
Structure and semantics
(The University of Edinburgh, 20171130)Algebraic theories describe mathematical structures that are defined in terms of operations and equations, and are extremely important throughout mathematics. Many generalisations of the classical notion of an algebraic ... 
On numerical approximations for stochastic differential equations
(The University of Edinburgh, 20171130)This thesis consists of several problems concerning numerical approximations for stochastic differential equations, and is divided into three parts. The first one is on the integrability and asymptotic stability with ... 
Improved computational approaches to classical electric energy problems
(The University of Edinburgh, 20171130)This thesis considers three separate but connected problems regarding energy networks: the load flow problem, the optimal power flow problem, and the islanding problem. All three problems are nonconvex non linear problems, ... 
Entanglement entropy of locally perturbed thermal systems
(The University of Edinburgh, 20171130)In this thesis we study the time evolution of Rényi and entanglement entropies of thermal states in Conformal Field Theory (CFT). These quantities are usually hard to compute but RyuTakayanagi (RT) and HubenyRangaman ... 
Birational geometry of Fano fibrations
(The University of Edinburgh, 20170710)An algebraic variety is called rationally connected if two generic points can be connected by a curve isomorphic to the projective line. The output of the minimal model program applied to rationally connected variety is ... 
Modelling sustainable intensification in Brazilian agriculture
(The University of Edinburgh, 20170710)At the United Nations Framework Conference on Climate Change COP15 (2009) Brazil presented ambitious commitments or Nationally Appropriate Mitigation Actions (NAMAs), to reduce greenhouse gases emissions (GHGs) mitigation ... 
Mapping properties of multiparameter multipliers
(The University of Edinburgh, 20171130)This thesis is motivated by the problem of understanding the endpoint mapping properties of higherdimensional Marcinkiewicz multipliers. The onedimensional case was definitively characterised by Tao and Wright. In ... 
Aspects of the constructive omega rule within automated deduction
(The University of Edinburgh, 1993)In general, cut elimination holds for arithmetical systems with the w rule, but not for systems with ordinary induction. Hence in the latter, there is the problem of generalisation, since arbitrary formulae can be cut ... 
Convergence of the trigonometric series of dynamics
(The University of Edinburgh, 1923) 
Construction of orthogonal representations of the symmetric group
(The University of Edinburgh, 1949) 
Optoelectronic simulation of nonhomogeneous solar cells
(The University of Edinburgh, 20161129)This thesis investigates the possibility of enhancing the efficiency of thin film solar cells by including periodic material nonhomogeneities in combination with periodically corrugated back reflectors. Two different ... 
Mortality linked derivatives and their pricing
(The University of Edinburgh, 20171130)This thesis addresses the absence of explicit pricing formulae and the complexity of proposed models (incomplete markets framework) in the area of mortality risk management requiring the application of advanced techniques ... 
Combinatorics of Gaudin systems: cactus groups and the RSK algorithm
(The University of Edinburgh, 20161129)This thesis explores connections between the Gaudin Hamiltonians in type A and the combinatorics of tableaux. The cactus group acts on standard tableaux via the Schützenberger involution. We show in this thesis that the ... 
Double Hilbert transforms along surfaces in the Heisenberg group
(The University of Edinburgh, 20170710)We provide an L² theory for the local double Hilbert transform along an analytic surface (s, t ,φ(s, t )) in the Heisenberg group H¹, that is operator f ↦ Hφ f (x) := p.v.∫∣s∣,∣t∣≤1 f (x ∙ (s, t ,φ(s, t ))¹) ds/s dt/t, ...