Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 13 of 13 for “"Research Subject Categories::MATHEMATICS"”.
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Deformations of Cayley submanifolds
Cayley submanifolds of R^8 were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volume-minimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley submanifolds are 4-dimensional submanifolds which may be defined in an 8-manifold …
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Free groups and the axiom of choice
The Nielsen–Schreier theorem states that subgroups of free groups are free. As all of its proofs use the Axiom of Choice, it is natural to ask whether the theorem is equivalent to the Axiom of Choice. Other questions arise in this context, such as whether the same is true for free abelian groups, …
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Contributions in fractional diffusive limit and wave turbulence in kinetic theory
This thesis is split in two different topics. Firstly, we study anomalous transport from kinetic models. Secondly, we consider the equations coming from weak wave turbulence theory and we study them via mean-field limits of finite stochastic particle systems. $\textbf{Anomalous transport from …
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Generalised nonlinear stability of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models
In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and …
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Spectral methods and computational trade-offs in high-dimensional statistical inference
Spectral methods have become increasingly popular in designing fast algorithms for modern highdimensional datasets. This thesis looks at several problems in which spectral methods play a central role. In some cases, we also show that such procedures have essentially the best performance among all …
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The power spectrum and bispectrum of inflation and cosmic defects
Much of the recent progress in cosmology has come from studying the power spectrum of the cosmic microwave background (CMB). The latest results from the Planck satellite confirmed that the inflationary paradigm with the $\Lambda$CDM six-parameter model provides a very good description of the …
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First-order gradient regularisation methods for image restoration: reconstruction of tomographic images with thin structures and denoising piecewise affine images
The focus of this thesis is variational image restoration techniques that involve novel non-smooth first-order gradient regularisers: Total Variation (TV) regularisation in image and data space for reconstruction of thin structures from PET data and regularisers given by an infimal-convolution of …
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New PDE models for imaging problems and applications
Variational methods and Partial Differential Equations (PDEs) have been extensively employed for the mathematical formulation of a myriad of problems describing physical phenomena such as heat propagation, thermodynamic transformations and many more. In imaging, PDEs following variational …