MSI Weekly Bulletin - Week starting Monday 5 March, 2007

A wireless ad hoc network consists of mobile nodes that are equipped with energy-limited batteries. As mobile nodes are battery-operated, an important issue in such a network is to minimize the total power consumption for each operation. Multicast is one of fundamental operations in any modern telecommunication network including wireless ad hoc networks. Given a multicast request consisting of a source node and a set of destination nodes, the problem is to build a minimum-energy multicast tree for the request such that the total transmission power consumption in the tree is minimized. Since the problem in a symmetric wireless ad hoc network is NP-complete, we instead devise an approximation algorithm with provable approximation guarantee. The approximation of the solution delivered by the proposed algorithm is within a constant factor of the best-possible approximation achievable unless P=NP. We also report the extended work from this including online multicasting and all-to-all multicasting in ad hoc networks. BIO: http://cs.anu.edu.au/~Weifa.Liang/

In this talk on results obtained in collaboration with B Go{\l}dys (UNSW) I will speak about an important notion related to mathematical theory of turbulence, i.e. of a stationary regimes (or solutions). It is unknown whether such regimes exists for deterministic Navier-Stokes equations but a lot of research has been done assuming that the so called "Kraichnan theory of fully developed turbulence" holds for the NSEs. I will describe recent attempts to justify this assumptions for NSEs driven by a random force.