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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Randomized iterative methods for linear systems: momentum, inexactness and gossip
(The University of Edinburgh, 2019-11-28)In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem ... -
Moduli space of supersymmetric black holes in five dimensions
(The University of Edinburgh, 2019-11-28)This thesis presents a classification of all asymptotically at, supersymmetric and biaxisymmetric (i.e. possessing a U(1)2-symmetry) soliton and black hole solutions to five-dimensional minimal supergravity. In particular, ... -
Mutation frequencies in a birth-death branching process
(The University of Edinburgh, 2019-08-20)A growing population of cells accumulates genetic mutations. We study stochastic models of this process. Cells divide and die as a branching process, and a cell's genetic information is a sequence of nucleotides which ... -
Cancer recurrence times and early detection from branching process models
(The University of Edinburgh, 2019-11-28)Cancer is among the leading causes of death worldwide. While primary tumors are often treated effectively, they can spawn secondary cancers called metastases which dramatically decrease chances of survival. In order to ... -
Stochastic dispersive PDEs with additive space-time white noise
(The University of Edinburgh, 2019-11-28)In this thesis, we will discuss the Cauchy problem for some nonlinear dispersive PDEs with additive space-time white noise forcing. We will focus on two different models: the stochastic nonlinear beam equation (SNLB) ... -
Quantitative propagation of chaos of McKean-Vlasov equations via the master equation
(The University of Edinburgh, 2019-11-28)McKean-Vlasov stochastic differential equations (MVSDEs) are ubiquitous in kinetic theory and in controlled games with a large number of players. They have been intensively studied since McKean, as they pave a way to ... -
Stochastic PDEs beyond standard monotonicity: well posedness and regularity of solutions
(The University of Edinburgh, 2019-11-28)Nonlinear stochastic partial differential equations (SPDEs) are used to model wide variety of phenomena in physics, engineering, finance and economics. In many such models the equations exhibit super-linear growth. In ... -
Tilting theory of contraction algebras
(The University of Edinburgh, 2019-07-01)This thesis focuses on a class of finite dimensional symmetric algebras arising in geometry, known as contraction algebras. The main results presented here combine to give a complete description of the derived equivalence ... -
Applications of the blow-up technique in singularly perturbed chemical kinetics
(The University of Edinburgh, 2019-07-01)This thesis addresses the geometric analysis of traveling front propagation in singularly perturbed dynamical systems. The study of front propagation in reaction-diffusion systems has received a significant amount of ... -
Basis preconditioning in interior point methods
(The University of Edinburgh, 2019-07-01)Solving normal equations AAᵀx = b, where A is an m x n matrix, is a common task in numerical optimization. For the efficient use of iterative methods, this thesis studies the class of preconditioners of the form BBᵀ , where ... -
Properties and advances of probabilistic and statistical algorithms with applications in finance
(The University of Edinburgh, 2019-07-01)This thesis is concerned with the construction and enhancement of algorithms involving probability and statistics. The main motivation for these are problems that appear in finance and more generally in applied science. ... -
Automated theory formation in pure mathematics
(The University of Edinburgh, 2001)The automation of specific mathematical tasks such as theorem proving and algebraic manipulation have been much researched. However, there have only been a few isolated attempts to automate the whole theory formation ... -
The development of statistical theory in Britain, 1865-1925: a historical and sociological perspective
(The University of Edinburgh, 1978)This thesis discusses the development of statistical theory in Britain in the period 1865 to 1925, and attempts to account for this development as an institutional and an intellectual phenomenon. Close connections are ... -
Analytical properties of certain probability distributions
(The University of Edinburgh, 1938)This research has been carried out on Dr Aitken's suggestion. The first chapter is largely a recapitulation of known results which I have learnt from Dr Aitken, here arranged for convenience of reference later in the thesis. -
Allied subsets of topological groups and linear spaces
(The University of Edinburgh, 1967)1, Basic theory, 4 || 2. Allied sets in linear spaces, 17 || 3. Cauchy nets and completeness, 29 || 4, Subgroups and subspaces. 39 || 5. Locally compact subsets of topological linear spaces. 46 || 6. ... -
The estimation of statistical coefficients from samples
(The University of Edinburgh, 1944)Statistics, it has been said, is the reduction of data. This definition fails, however, to bring out one of the most important and interesting aspects of modern statistical theory - the making of estimates. Let us consider ... -
Contributions to the theory of statistical estimation and other topics
(The University of Edinburgh, 1959)A • 1 On the Efficiency of the Method of Moments and Neyman's Type A Distribution. • 2 Maximum Likelihood and the Efficiency of the Method of Moments. • 3 Efficiency of the Method of Moments and the Gram- Charlier Type ... -
Curve-fitting according to the method of A. Ekke and R. Schmidt
(The University of Edinburgh, 1940)When fitting a curve to. a given set of data , it is usual , having chosen the curve-type which will best suit the data, to take as abscissae for the plotted points of the curve the observations themselves ,.. and then ... -
Contributions to the theory of groups
(The University of Edinburgh, 1975)A 1. The influence on a finite group of its proper abnormal structure. J. London Math. Soc. 40 (1965). 348-61; MR30#4838. • B 2. Abnormal depth and hypereccentric length in finite soluble groups, Math. Z. 90 (1965). ... -
The basic theorems of analysis of variance with special reference to field experiments
(The University of Edinburgh, 1947)The statistical procedure of analysis of variance was invented by R.A. Fisher during his stay as statistician at Rothamsted Experimental Station. His first, more or less tentative, discussion of the theory was set forth ...
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