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Modelling non-linear exposure-disease relationships in a large individual participant meta-analysis allowing for the effects of exposure measurement error
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsMRC Biostatistics Unit, 2012-10-09)
This thesis was motivated by data from the Emerging Risk Factors Collaboration (ERFC), a
large individual participant data (IPD) meta-analysis of risk factors for coronary heart disease(CHD). Cardiovascular disease is the ...
Statistical issues in Mendelian randomization: use of genetic instrumental variables for assessing causal associations
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsMRC Biostatistics Unit, 2012-03-06)
Mendelian randomization is an epidemiological method for using genetic variation
to estimate the causal effect of the change in a modifiable phenotype on
an outcome from observational data. A genetic variant satisfying ...
Unipotent elements in algebraic groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2012-01-10)
This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and
nilpotent elements ...
Collaborating queues: large service network and a limit order book
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsEmmanuel CollegeStatistics Laboratory, 2012-10-09)
We analyse the steady-state behaviour of two different models with collaborating queues: that is, models in which "customers" can be served by many types of "servers", and "servers" can process many types of "customers".
The ...
Hyper and structural Markov laws for graphical models
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2012-03-06)
My thesis focuses on the parameterisation and estimation of graphical models, based on the concept of hyper and meta Markov properties. These state that the parameters should exhibit conditional independencies, similar to ...
Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2012-07-03)
I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild
de Sitter spacetimes.
In the first part of this thesis two decay results are proven for general finite energy solutions to the linear ...
The Fukaya category, exotic forms and exotic autoequivalences
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2012-04-10)
A symplectic manifold is a smooth manifold M together with a choice of a
closed non-degenerate two-form. Recent years have seen the importance of associating
an A∞-category to M, called its Fukaya category, in helping ...
A Counter Example to Cercignani’s Conjecture for the d Dimensional Kac Model
(SpringerJournal of Statistical Physics, 2012-08-21)
Kac’s d dimensional model gives a linear, many particle, binary collision model from which, under suitable conditions, the celebrated Boltzmann equation, in its spatially homogeneous form, arise as a mean field limit. The ...
Sharp trace inequalities for fractional Laplacians
(American Mathematical SocietyProceedings of the American Mathematical Society, 2012-04-05)
The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on Rⁿ and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb’s ...
Algebraic boundaries of Hilbert's SOS cones
(Cambridge University PressCompositio Mathematica, 2012-10-15)
We study the geometry underlying the difference between nonnegative
polynomials and sums of squares. The hypersurfaces that discriminate
these two cones for ternary sextics and quaternary quartics are shown
to be ...