This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.

Recent Submissions

  • Design of reliable aerospace system architecture 

    Schäfer, Lukas Matthias (The University of Edinburgh, 2018-11-29)
    Reliability and redundancy of safety-critical 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 high-dimensional data: application to genomic data 

    Mestres, Adrià Caballé (The University of Edinburgh, 2018-07-02)
    This thesis provides novel methodology for statistical analysis of paired high-dimensional 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 

    Cabezas García, José Xavier (The University of Edinburgh, 2018-07-02)
    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 

    Csiba, Dominik (The University of Edinburgh, 2018-07-02)
    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 

    Tope, Bryan Keith (The University of Edinburgh, 2018-07-02)
    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 

    Sachs, Matthias Ernst (The University of Edinburgh, 2018-07-02)
    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 

    Avery, Thomas Charles (The University of Edinburgh, 2017-11-30)
    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 

    Zhang, Xiling (The University of Edinburgh, 2017-11-30)
    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 

    Wallace, Ian Patrick (The University of Edinburgh, 2017-11-30)
    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 non-convex non linear problems, ...
  • Entanglement entropy of locally perturbed thermal systems 

    Štikonas, Andrius (The University of Edinburgh, 2017-11-30)
    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 Ryu-Takayanagi (RT) and Hubeny-Rangaman ...
  • Birational geometry of Fano fibrations 

    Krylov, Igor (The University of Edinburgh, 2017-07-10)
    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 

    De Oliveira Silva, Rafael (The University of Edinburgh, 2017-07-10)
    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 multi-parameter multipliers 

    Bakas, Odysseas (The University of Edinburgh, 2017-11-30)
    This thesis is motivated by the problem of understanding the endpoint mapping properties of higher-dimensional Marcinkiewicz multipliers. The one-dimensional case was definitively characterised by Tao and Wright. In ...
  • Aspects of the constructive omega rule within automated deduction 

    Baker, Siani (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 

    Baker, Bevan Braithwaite (The University of Edinburgh, 1923)
  • Construction of orthogonal representations of the symmetric group 

    Anderson, Hamish G. (The University of Edinburgh, 1949)
  • Optoelectronic simulation of nonhomogeneous solar cells 

    Anderson, Tom Harper (The University of Edinburgh, 2016-11-29)
    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 

    Bahl, Raj Kumari (The University of Edinburgh, 2017-11-30)
    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 

    White, Noah Alexander Matthias (The University of Edinburgh, 2016-11-29)
    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 

    Vitturi, Marco (The University of Edinburgh, 2017-07-10)
    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, ...

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