MSI Weekly Bulletin - Week starting Monday 7 May, 2007

This talk considers privacy of personal or otherwise sensitive data used in statistical analysis and data mining and focuses on a scenario where only range queries are allowed. We present an overview of the area, propose new protection methods based on combination of noise addition and query restriction and present new results regarding data base usability. BIO: http://www.newcastle.edu.au/school/elec-eng-comp-sci/our_staff/profiles/brankovic_ljiljana.html

Last week, I explained what the ring of Witt vectors with entries in another, given ring is. In this talk, I'll explain how to geometrize this construction. More precisely, I'll explain how we can glue together rings of Witt vectors to produce, instead of the Witt rings of a given ring, the "Witt space" of a given (algebraically defined) space. For example, we can then define the Witt space of n-dimensional projective space defined over the ring of integers. However, I'll probably begin with some non-geometric complements to last week's talk.

The introduction of bilinear functions to IFS theory has made feasible the construction of certain interesting fractal homeomorphisms, whose smoothness may be analysed in detail. This talk will introduce some key concepts of IFS theory and fractal transformations used in the construction of two superIFSs consisting of IFSs of bilinear transformations. The attractor of each of these two superIFSs consists of a a set of graphs of fractal interpolation functions which forms a tiling. A proof of the existence of a homeomorphic fractal transformation between the two tiled regions will also be given.

A standard way to generate probability measures supported on fractal sets is to regard them as limiting probability distributions for processes obtained from random iterations of functions. It is typically not possible to generate natural random fractals like e.g. Brownian motion in a similar way due to the complexity of these objects. This has restricted applications in fractal modeling. In joint work with Michael Barnsley and John Hutchinson we introduced V-variable fractals as a way of resolving this. Random V-variable fractals can be generated quickly as "points" along trajectories of a fractal-valued random iteration process. Simultaneously they can be used to approximate "standard" random fractals.