Past Seminars

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Alternative view of asymptotic expansions and the Stokes’ phenomenon
Ed Smith
La Trobe University
Start time: 3:15 pm
Date: Friday 13 October 2006
Location: Theatre 2, Ground Floor, 111 Barry Street, Carlton.

The traditional view of asymptotic expansions, due to Stokes, is to use only the series out to its term of least magnitude. This is called “superasymptotics”. Stokes also noted that solutions to second order linear differential equations had expansions which were linear combinations of expansions of two standard solutions of the equation, but that the coefficients were discontinuous across Stokes lines, behaviour known as Stokes phenomenon. Later (140 years) Berry and others used Borel summation of the (divergent) post superasymptotic series to derive expansions of solutions of differential equations which gave smooth variation of the multipliers according to a generic error function of scaled argument. In this seminar, I will consider asymptotic expansions of Laplace type integrals which are solutions of second order differential equations. They may be expanded in convergent series which embed the traditional asymptotic expansions. When the superasymptotic expansion (a finite series) is subtracted from this convergent expansion, a convergent series representation for the remainder is obtained. Stokes phenomenon then results from terms in this reminder series close to the cut off in the superasymptotic expansion, on both sides of the cut off. Stokes phenomenon is derived without resorting to divergent series

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Generalized Cross-Entropy Methods
Dirk Kroese
The University of Queensland
Start time: 3:15 pm
Date: Tuesday 26 September 2006
Location: Theatre 3, 1st Floor, 111 Barry Street, Carlton.

The Cross-Entropy (CE) and Minimum Cross-Entropy (MCE) methods are well-known Monte Carlo techniques for rare-event probability estimation and optimization. The principal distance measure used in both cases is the Kullback-Leibler cross-entropy. In this talk we investigate how the CE and MCE can be extended and generalized to include more general cross-entropy distances. We formulate a generalized cross-entropy framework which subsumes both CE and MCE, and show how in particular the chi square distance yields a viable alternative to Kullback-Leibler distance. The theory is illustrated with various examples in rare-event simulation and optimization. (Joint work with Zdravko Botev and Thomas Taimre).

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Seeing Polymers in a New Light
Professor Andrew B. Holmes, ARC Federation and VESKI Fellow
Bio21 Institute and CSIRO Molecular and Health Technologies, University of Melbourne
Start time: 3:15 pm
Date: Friday 15 September 2006
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

Polymers (plastics) are materials that have dominated our lives in the latter half of the twentieth century. They are generally perceived as lightweight potential replacements for much heavier structural materials such as wood and metals. Most plastics consist of materials witha distribution of chain lengths and structural variation which means that we have to measure their average properties rather than a specific property of just one molecule. This variability has the advantage of allowing the properties to be "tuned" to various applications. Most of us associate the electrical properties of plastics with their ability to act as good insulators. However, in the 1970's a group of chemists and physicists showed that certain (conjugated) polymers could behave as conductors, with conductivities reaching levels as high as that of metallic copper. Along with that development came the realisation that conjugated polymers could also be used as semiconductors to complement and even replace in some cases the electronic properties of silicon and related materials. This lecture will illustrate some of the general properties of polymers and will describe how conjugated polymers can be used as sources of light (LEDs), as transistors and as solar cells.

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How Many Needles are in a Haystack, or how to Solve #P-Complete Counting Problems Fast
Reuven Rubinstein
Faculty of Industrial Engineering and Management, Technion
Start time: 3:15 pm
Date: Friday 8 September 2006
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

We present a new generic randomized algorithm for approximating quite general #P-complete counting problems, like the number of Hamiltonian cycles in a graph, the permanent, and the number of self-avoiding walks of certain length. To do so we cast the underlying counting problem into an associate rare-event probability estimation one, and then apply the cross-entropy (CE) method for updating the parameters of the importance sampling (IS) distribution. We use importance sampling to speed up the simulation process and, thus to produce a low variance estimate of the desired counting quantity. We establish convergence and speed of convergence of our algorithm for some particular #P-complete counting problems and present supportive numerical results, which strongly suggest that the presented algorithm has polynomial complexity in the size of the network. For more details see our homepage www.cemethod.org and for wikipedia - the cross-entropy method

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Diagnosing mental diseases with discriminant analysis
Yao-ban Chan
The University of Melbourne
Start time: 3:15 pm
Date: Friday 1 September 2006
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

The Mental Health Research Institute of Victoria has been using a technique called electrophoresis to analyse the proteomic structure of brains with mental diseases, in particular schizophrenia and bipolar disorder. In this talk, I shall explain how we use various statistical methods on these electrophoresis scans to diagnose these patients. In particular, we concentrate on a classification technique called Fisher's linear discriminant analysis, and some of its extensions and variants.

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