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Two topics in financial mathematics : Forward utility and consumption functions & Hedging with variance swaps in infinite dimensions
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-10)
Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their ...
Comparison of multimarker logistic regression models, with application to a genomewide scan of schizophrenia.
(2010-09-09)
Abstract Background Genome-wide association studies (GWAS) are a widely used study design for detecting genetic causes of complex diseases. Current studies provide good coverage of common causal SNPs, but not rare ones. A ...
Graphical representations of Ising and Potts models: stochastic geometry of the quantum Ising model and the space-time Potts model
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsStatistical LaboratoryGonville & Caius College, 2010-02-09)
Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic
properties as ...
On eigenvectors for semisimple elements in actions of algebraic groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-02-09)
Let $G$ be a simple simply connected algebraic group defined over an algebraically closed field $K$ and $V$ an irreducible module defined over $K$ on which $G$ acts. Let $E$ denote the set of vectors in $V$ which are ...
Models of genus one curves
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-03-16)
In this thesis we give insight into the minimisation problem of genus one curves defined by equations other than Weierstrass equations. We are interested in genus one curves given as double covers of P1, plane cubics, or ...
Maximum likelihood estimation of a multivariate log-concave density
(University of Cambridge, 2010-01-12)
Density estimation is a fundamental statistical problem. Many methods are either
sensitive to model misspecification (parametric models) or difficult to calibrate, especially
for multivariate data (nonparametric smoothing ...
Iwasawa theory for modular forms at supersingular primes
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-07-06)
Let f=\sum a_nq^n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q. In ...
Cliques in graphs
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-10-12)
The main focus of this thesis is to evaluate $k_r(n,\delta)$, the minimal number of $r$-cliques in graphs with $n$ vertices and minimum degree~$\delta$. A fundamental result in Graph Theory states that a triangle-free graph ...
Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2010-07-06)
Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], ...