Honours Talks - 16 Oct 2018
Who: Ellen Molloy and Joel Zimmerman
When: 12pm Tuesday 16 October
Methods of Aligning Shapes
A time-series such as the plot of a continuous output over time, or the outline of an object can both be seen as curves. Performing statistical analysis of these curves is problematic because they are not inherently aligned - a set of object outlines can be in different places in an image, and a time-series of growth patterns of humans look similar once the age at which growth starts is standardised. Otherwise, pointwise comparisons such as the mean average over time hide the pattern in the data. In this report we investigate some different techniques that can be used to compare variation between curves. We begin by looking at techniques to remove the linear variation coming from rotation, translation, and scaling. We then move on to consider different parametrisations of the curves which allow us to analyse the non-linear variation between the curves. These techniques can be used either before or after aligning the curves, and we compare both cases.
Constructing Groupoid C*-algebras Through Steinberg Algebras.
Groupoid C*-algebras generalise a number of different types of C*-algebras, including group C*-algebras, transformation group C*-algebras, and C*-algebras of equivalence relations. We show that given an ample groupoid one can construct a C*-algebra from the Steinberg algebra of the groupoid. Further, we show that if the groupoid is both ample and second-countable then this is the full C*-algebra associated to the groupoid.