In recent years, Sparse Principal Component Analysis has emerged as an extremely popular dimension reduction technique for highdimensional data. The theoretical challenge, in the simplest case, is to estimate the leading ...

We study generalized additive models, with shape restrictions (e.g. monotonicity, convexity and concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a non-parametric ...

We explore transversals of finite index subgroups of finitely generated groups. We show that when H is a subgroup of a rank n group G and H has index at least n in G then we can construct a left transversal for H which ...

In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both ...

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of ...

Positron Emission Tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are ...

We show that the motive of the Hilbert scheme of length-n subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, ...

We study F-saturation games, first introduced by Füredi, Reimer and Seress [4] in 1991, and named as such by West [5]. The main question is to determine the length of the game whilst avoiding various classes of graph, ...

In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay ...

In his 2011 work, Maas has shown that the law of any time-reversible continuoustime Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. ...

We give results on when a finitely generated torsion free group does or does not embed in SL(2, C). For instance if we glue two copies of the figure 8 knot along its torus boundary then the fundamental group of the resulting ...

We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called ‘Taylor–Wiles hypothesis’. We apply this to the problem ...

In the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central ...

Mandarin Chinese is characterized by being a tonal language; the pitch (or F0) of its utterances carries considerable linguistic information. However, speech samples from different individuals are subject to changes in ...

We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, ...

We study the problem of variation of Frobenius eigenvalues on the cohomology of families of local systems of algebraic curves over finite fields.

We show that if a closed orientable 2k-manifold K, k > 2, with Euler characteristic χ(K) ≠ -2 admits an exact Lagrangian immersion into C2k with one transverse double point and no other self intersections, then K is ...

This thesis presents methods for the inference of system state and the learning of model structure for a number of hidden-state time series models, within a Bayesian probabilistic framework. Motivating examples are taken ...

The use of trading stops is a common practice in financial markets for a variety of reasons: it reduces the frequency of trading and thereby transaction costs; it provides a simple way to control losses on a given trade, ...