# Past Seminars

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The Mechanics of Nanoscale Devices

*Speaker:* John Elie Sader

*Institution:* The University of Melbourne (Maths & Stats)

*Date:* Fri 12 Sep 2008

*Time:* 3:15 pm

*Location:* Theatre 1, ICT Bldg (Rm:205-Flr:2, 111 Barry Street, Carlton)*Abstract:* Nanomechanical sensors are often used to measure environmental changes
with extreme sensitivity. Controlling the effects of surfaces and fluid
dissipation presents significant challenges to achieving the ultimate
sensitivity in these devices. In this talk, I will give an overview of
theoretical/experimental work we are undertaking to explore the underlying
physical processes in these systems. The talk will be general and aimed at
introducing some recent developments in the field of nanomechanical
sensors.

Approximating an epidemic process by a branching process

*Speaker:* A. D. Barbour

*Institution:* University of Zuerich

*Date:* Fri 29 Aug 2008

*Time:* 1:15 pm

*Location:* Russell Love Theatre, Richard Berry Bldg*Abstract:* The growth of an epidemic process is often effectively approximated in its early stages by that of an associated branching process, an observation
first formalized by Whittle (1955). The same ideas frequently form the basis for describing the local structure of random graphs, including
those exhibiting `small world' or power law behaviour. In this talk, we discuss ways of formalizing the approximation, by using stochastic coupling
methods.

A (Gentle) Introduction to Regular Variation and Applications

*Speaker:* Daniel Tokarev

*Institution:* MASCOS, University of Melbourne

*Date:* Wed 20 Aug 2008

*Time:* 3:15 pm

*Location:* Chemical & Biomolecular Engineering Theatre, Room G20, Chemical*Abstract:* Regular Variation theory, introduced by J. Karamata, is concerned with
relating asymptotic behaviour of (real) functions and operators, such as
Laplace transform, convolution and n-fold functional iterate. It has
become an important tool in Probability, Analysis and other fields, and
has greatly simplified and clarified much theory, such as in theorems of
Abelian and Tauberian type and results on maxima and sums of independent
and identically distributed random variables. This talk is intended to
introduce the concept of regular variation and some fundamental results
and applications in Probability.

Diffusion Approximation for a Heavily Loaded Multi-User Wireless Communication System with Cooperation

*Speaker:* Professor Ruth Williams

*Institution:* University of California, San Diego

*Date:* Fri 1 Aug 2008

*Time:* 3:15 pm

*Location:* Theatre 1, ground floor of the ICT Building, 111 Barry St, The University of Melbourne*Abstract:* We consider a model for a cellular wireless communication system in which data is transmitted to multiple users over a common channel. For information theoretic reasons, the rate of transmission over this channel can be enhanced by cooperation. Assuming a fixed channel and that the average arrival rate of data for each user is known, we consider a simple scheduling policy which exploits cooperation and which has been shown to be throughput-optimal under Markovian assumptions. As a measure of performance under this policy, we establish a heavy traffic diffusion approximation for the workload process. This diffusion process is a semimartingale reflecting Brownian motion (SRBM) living in the positive orthant of N-dimensional space (where N is the number of users). Nominally, this SRBM has one direction of reflection associated with each of the 2^{N}-1 boundary faces. However, we show that in fact only those
directions associated with the (N-1)-dimensional boundary faces matter in the heavy traffic limit. Based on joint work with Sumit Bhardwaj.

The pivot algorithm for self-avoiding walks

*Speaker:* Nathan Clisby

*Institution:* MASCOS, The University of Melbourne

*Date:* Fri 9 May 2008

*Time:* 3:15 am

*Location:* Theatre 1, ground floor of the ICT Building, 111 Barry St, The University of Melbourne*Abstract:* The self-avoiding walk (SAW) is an important model in statistical mechanics, as it is a standard model in the study of critical phenomena (phase transitions) and in addition it accurately characterises the excluded volume effect of real polymers (long chain molecules).

The pivot algorithm is a technique with a long history, and is an extremely powerful tool in the study of SAWs. For a number of important quantities (e.g. critical exponents) it is by far the most efficient known method of calculation. It works via a Markov chain where successive SAWs are generated by attempting to 'pivot' part of the walk by rotating or reflecting the walk around a randomly selected pivot point. I will explain how to implement the pivot algorithm and why it is so effective, and then describe my current research: by incorporating additional geometric information while running the Markov chain it is possible to dramatically improve the speed of the algorithm.

First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes

*Speaker:* Andrew Downes

*Institution:* MASCOS, The University of Melbourne

*Date:* Fri 18 Apr 2008

*Time:* 3:15 pm

*Location:* Theatre 1, ICT Building, 111 Barry St, Carlton*Abstract:* We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one.

In doing so we establish the existence of the first-passage time density and provide an upper bound for this function. In the case of processes with diffusion interval equal to **R** this is extended to a lower bound, as well as bounds for the first crossing time of a lower boundary. These results are illustrated by numerical examples.

Modelling Carbon Emissions Reduction from the Australian Electricity Sector

*Speaker:* Ilya Pavlyukevich

*Institution:* Humboldt Universität zu Berlin

*Date:* Sat 29 Mar 2008

*Time:* 3:15 pm

*Location:* Theatre 3, ICT Bldg, 111 Barry Street, Carlton*Abstract:* We consider a one-dimensional dynamical system driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a stable symmetric non-Gaussian L'evy process whose scale parameter decreases as a power function of time. It turns out that the limiting behaviour of the perturbed dynamical system is different for slow and fast decrease rates of the noise intensity. As opposed to the well-studied Gaussian case, the limiting probability is not concentrated in the global minimum of U.

Finally, we discuss simulated annealing of jump processes with a non-constant stability index and consider applications to non-local random search and stochastic optimisation.

Modelling Carbon Emissions Reduction from the Australian Electricity Sector

*Speaker:* Deb Chattopadhyay

*Institution:* CRA International

*Date:* Fri 29 Feb 2008

*Time:* 3:15 pm

*Location:* Theatre 3, ICT Bldg, 111 Barry Street, Carlton*Abstract:* Carbon emissions reduction has been a central part of public policy debates in recent years. Yet, there has been relatively little effort to explore the cost implications for alternative greenhouse gas (GHG) policies such as a mandatory introduction of renewable energy vis-à-vis an emissions trading scheme. We will first review the background GHG policy issues and choices within the electricity sector.

This study uses a set of mathematical programming models to analyse the optimal choice of technology and quantitatively address the implications for alternative GHG policies. There are two core models. The first model characterises the interaction among the players in the Australian National Electricity Market (NEM) as a non-cooperative Cournot game to determine
the profit maximising generation strategy for the generators. This model is solved iteratively with a stochastic LP that mimics the centralised production scheduling performed by the electricity market operator. The Cournot game is formulated as a mixed complementarity problem (MCP) and is solved to obtain the equilibrium generation strategy for each generator
over a number of years. The stochastic LP solves for the long-term investment and production schedule for all electricity generators in the system. An overview of these models will be provided.

Finally, a case study that CRA International had undertaken for the National Generators Forum in 2006/07 using these models, will be presented. Australia generates over 80% of its electricity from coal. Therefore, Australia faces a daunting task to substantially cut down its sectoral carbon emissions in the long term to achieve a 50% reduction from the 2000 emissions by 2050. The key study outcomes include the potentially very significant role that baseload low emission technologies such as nuclear and carbon capture and storage, need to play to achieve such a
deep cut. It also highlights the ineffectiveness and sub-optimal nature of some of the other policies that rely solely on renewables to achieve the target.

Incentive-based control of ad hoc networks: a performance study

*Speaker:* A.E. Krzesinski

*Institution:* University of Stellenbosch, South Africa

*Date:* Tue 18 Dec 2007

*Time:* 11:00 am

*Location:* Old Geology Theatre 1, Parkville*Abstract:* Ad hoc networks are self-configuring networks of mobile nodes,connected by wireless links. If a destination node is beyond the transmission range of an origin node, then the nodes must cooperate to provide a multi-hop route. Any node can act as a sender, receiver or transit node. It is clear that it is in a node's interest to be a sender or receiver, but it is less clear what the value is of forwarding traffic on behalf of other nodes. The nodes should therefore be given incentives to act as transit nodes, because otherwise the network would fail to function. A way to do so is by introducing (for each node) a credit balance, where nodes use credits to pay for the costs of sending their own traffic, and earn credits by forwarding traffic from other nodes.

In this talk we focus on the situation where each node can move to improve its utility (expressed in terms of either credit balance or throughput). Here radio interference plays a pivotal role, as it defines an interesting trade-off: nodes may prefer to be close together in order to reduce the energy needed to transmit data, but on the other hand proximity increases interference, and has therefore a negative effect on connectivity. Simulation experiments
reveal that the positions of the nodes converge to (non-trivial) optimal operating points.

Modeling price dynamics of emission allowances

*Speaker:* Juri Hinz

*Institution:* National University of Singapore

*Date:* Tue 11 Dec 2007

*Time:* 11:00 am

*Location:* Old Geology Theatre 1, Parkville*Abstract:* The climate rescue is on the top of the agendas today. To protect the environment, emission trading schemes are considered as one of the most promising tools. In a system of such type, a central authority allocates credits among emission sources and sets a penalty which must be paid per unit of pollutant which is not covered by credits at the end the period. This regulatory framework introduces a market for emission allowances and creates a need for risk management by appropriate emission-related financial contracts. In this talk we apply methodologies from stochastic analysis to address logical principles underlying price formation of tradable pollution certificates. Based on tools from optimal control theory, we characterize the equilibrium allowance prices and show the existence of the proposed price dynamics. Further, we illustrate the computational tractability of the resulting models. In the context of the least squares Monte Carlo method, we utilize fixed point arguments to derive appropriate numerical schemes, which are illustrated by examples.

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