Bi-algebras, generalised geometry and T-duality

A study of sigma models whose target space is a group G that admits a compatible Poisson structure is presented. The natural action of O(D,D;Z) on the generalised tangent bundle TG+T*G and a generalisation of the Courant bracket that appears are reviewed. This background provides a concrete example where the generalised geometry and doubled geometry descriptions are both well understood. Connections between the two formalisms are discussed and the world-sheet theory from Hamiltonian and Lagrangian perspectives is investigated. The comparisons between the approaches given by generalised geometry and doubled geometry suggest possible ways of generalising the analysis beyond the known examples.Comment: 43 page

Semi-Supervised Kernel PCA

We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher discriminant analysis. The second, LSKPCA is a hybrid of least squares regression and kernel PCA. The final LR-KPCA is an iteratively reweighted version of the previous which achieves a sigmoid loss function on the labeled points. We provide a theoretical risk bound as well as illustrative experiments on real and toy data sets

Analyzing dropout rates of B.Sc students

Survival analysis is a useful statistical technique for analyzing failure time data. It overcomes the limitations of cross-sectional analysis and convention regression analysis. This study proposes three statistical models that analyze the failure time when university students withdraw from B.Sc courses. The sample comprises all the 91 students who commenced their four-year studies with the Faculty of Science in 2002. The first approach uses the Kaplan-Meier product limit method for estimating the survival functions under non-informative censoring. The second approach uses the Cox regression model, which involves the assumption of proportional hazard functions. The third approach uses a parametric model to estimate the hazard function using an appropriate distribution. The aim of the study is to fit survival models that predict the probabilities of retention and dropout of B.Sc students within each study area using the facilities of SPSS and STATA.peer-reviewe