Mathematics, School of
Our research groups cover a broad range of Mathematics, Statistics and Operational Research. Please visit the School of Mathematics home pages for more information.
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Heuristic methods for solving two discrete optimization problems
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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 ... -
Optoelectronic simulation of nonhomogeneous solar cells
(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
(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
(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
(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, ... -
Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter
(The University of Edinburgh, 2016-11-29)We are interested in rigorous asymptotic results pertaining to three different differential equations which lie in the Heun class (see [1] §31). The Heun class contains those ordinary linear second-order differential ... -
Categories and distributively generated near-rings
(The University of Edinburgh, 1979) -
Indirect reference in German mathematical discourse
(The University of Edinburgh, 1987) -
Rapid mixing through decomposition and induction
(The University of Edinburgh, 2004) -
Weight functions on the torus and the approximation property in banach spaces
(The University of Edinburgh, 1978)
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