Mathematics, School of
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Bayesian analysis of jointly heavytailed data
(The University of Edinburgh, 20221129)This thesis develops novel Bayesian methodologies for statistical modelling of heavytailed data. Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability ... 
Size and shape of things: magnitude, diversity, homology
(The University of Edinburgh, 20221129)This thesis has to do with magnitude: a numerical invariant of enriched categories which, when specialized to examples such as posets, groupoids or metric spaces, turns out to encompass a variety of sizerelated quantities ... 
Pretrained solution methods for unit commitment
(The University of Edinburgh, 20221116)This thesis aims to improve the solution methods for the unit commitment problem, a shortterm planning problem in the energy industry. In particular, we focus on DantzigWolfe decomposition with a column generation ... 
On the dynamics of measure flows and multiagent and meanfield financial games
(The University of Edinburgh, 20221124)This thesis comprises two different collection of results. We present several ItôWentzell formulae on Wiener spaces for realvalued functional random field of Itô type that depends on measure flows. We distinguish the ... 
Optimal coordination of multiple pricemaker electricity storage units for price arbitrage
(The University of Edinburgh, 20221011)Decarbonization of the electricity supply via the integration of renewable generation poses significant challenges for electric power systems, but also creates new market opportunities. Electric energy storage can take ... 
Stability, Hilbert scheme and PT moduli of genus four curves and failure of the MMP/Wallcrossing correspondence
(The University of Edinburgh, 20221124)Inspired by concepts in string theory, the notion of stability conditions on triangulated categories was introduced by Bridgeland in 2002. Its impact across mathematics includes the solutions of classical problems in ... 
Change detection in spatiotemporal SAR data for deforestation monitoring
(The University of Edinburgh, 20220822)Forests play a vital role in the wellbeing of our planet. Large and small scale deforestation across the globe is threatening the stability of our climate, forest biodiversity, and therefore the preservation of fragile ... 
Preconditioned iterative methods for optimal control problems with timedependent PDEs as constraints
(The University of Edinburgh, 20220627)In this work, we study fast and robust solvers for optimal control problems with Partial Differential Equations (PDEs) as constraints. Speci cally, we devise preconditioned iterative methods for timedependent PDEconstrained ... 
Bayesian analysis of nonstationary extremes
(The University of Edinburgh, 20220627)Extreme value theory (EVT) provides theoretical foundation to assess the probability of rare and extreme events. This thesis provides novel Bayesian semiparametric models for capturing the behaviour of extreme events and ... 
Role of structure in oscillatory integral estimates
(The University of Edinburgh, 20220622)Although oscillatory integrals intrinsically depend only on measuretheoretic properties of the phase and amplitude functions, in practice most techniques for deriving estimates invoke structural information either implicitly ... 
Stochastic dynamics and partitioned algorithms for model parameterization in deep learning
(The University of Edinburgh, 20220616)In this thesis, we study model parameterization for deep learning applications. Part of the mathematical foundation for this work lies in stochastic differential equations and their constrained counterparts. We will study ... 
Local and global analysis of geometric partial differential equations and their application to curvature flow problems
(The University of Edinburgh, 20220615)“An analytical approach to many problems in geometry leads to the study of partial differential equations.” (A. V. Pogorelov, Foreword to The Minkowski Multidimensional Problem) This thesis concerns itself with three ... 
Uncertainty quantification in seismic interferometry
(The University of Edinburgh, 20220613)It is a wellestablished principle that crosscorrelating wavefield observations at different receiver locations yields new responses that, under certain conditions, provide a useful estimate of the Green's function between ... 
Multijoints and multilinear duality
(The University of Edinburgh, 20220525)The joints problem is related to geometric questions at the heart of harmonic analysis. In three dimensions, a joint is a point of intersection of three lines that do not lie within a common plane. Given a collection of ... 
Quantum symmetric pairs in topological field theory
(The University of Edinburgh, 20191128)[No Deposit Agreement] 
Factorisation homology and skein categories of surfaces
(The University of Edinburgh, 20191128)[No Deposit Agreement] 
Fano varieties: positivity, Kstability and more
(The University of Edinburgh, 20220411)This thesis is about Fano varieties and their properties. We will determine the Kstability of certain singular del Pezzo surfaces and smooth Fano 3folds, the existence of cylinders in singular del Pezzo surfaces, and ... 
Iterative methods for solving stochastic optimal control problems
(The University of Edinburgh, 20220404)Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Therefore, most of the time, they have to be solved numerically. In this ... 
Regularized interior point methods for convex programming
(The University of Edinburgh, 20220323)Interior point methods (IPMs) constitute one of the most important classes of optimization methods, due to their unparalleled robustness, as well as their generality. It is well known that a very large class of convex ... 
Bayesian methods for biomarker evaluation and disease diagnosis
(The University of Edinburgh, 20220322)Accurate diagnosis of disease is of fundamental importance in medical research and clinical practice. For such reason, the role that diagnostic testing and screening play is undeniable. The major goal of a diagnostic ...