# Past Seminars

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Attribution of Responsibility for Climate Change: The Mathematics Behind the Brazilian Proposal

*Speaker:* Professor Ian Enting

*Institution:* MASCOS, The University of Melbourne / CSIRO

*Date:* Fri 2 Mar 2007

*Time:* 3:15 pm

*Location:* Theatre 3, 1st Floor, 111 Barry Street, Carlton.*Abstract:* During the negotiations that led to the Kyoto Protocol, Brazil proposed that targets for emission reductions should be set in proportion to the extent that each nation was responsible for global warming. This was perceived as technically complex and was referred to the Subsidiary Body for Scientific and Technical Advice (SBSTA), under the UN FCCC (Framework Convention on Climate Change).
This talk covers the basis on which such attribution can be made, in terms of the causal sequence from emissions to warming. It then reviews the sensitivity relations to show how a single function can help collapse much of the complexity of the analysis. This is expressed as an adjoint sensitivity or Frechet derivative. Practical means of calculating such sensitivities are outlined, using automatic differentiation based on operator overloading.
Finally, some initial attribution results are presented.

Untangling polymer systems: Structure prediction in polymer networks with quenched disorder

*Speaker:* Dr Abigail Klopper

*Institution:* Max Planck Institute for the Physics of Complex Systems

*Date:* Wed 13 Dec 2006

*Time:* 11:00 am

*Location:* Room 213, Dept. of Mathematics and Statistics, The University of Melbourne*Abstract:* Highly concentrated liquids comprising long polymeric chains can undergo processes of cross-linking and entanglement, giving rise to intriguing macroscopic properties. The key ingredient is connective quenched disorder, which freezes the topology of the liquid in the form of a polymer network. The translational invariance in the system is spontaneously broken and the phase space is divided into disjoint ergodic regions.
Such behaviour is well-known from a large class of systems exhibiting the so-called glassy phase, characterised by randomness and slow dynamics. This opens the door to an extensive analytic formalism for structure prediction in cross-linked polymer systems. By constructing a theoretical framework which makes use of simulation data, one can draw from these techniques without resorting to microscopic detail and otherwise unphysical assumptions. In the study presented, the spin-glass replica formalism is applied to data from molecular dynamics simulations of ideal non-interacting cross-linked polymer systems in order to describe neutron scattering measurements in interacting systems.

From series expansions to exact solutions

*Speaker:* Dr Iwan Jensen

*Institution:* MASCOS, The University of Melbourne

*Date:* Mon 27 Nov 2006

*Time:* 3:15 pm

*Location:* Theatre 1, Ground Floor, 111 Barry Street, Carlton*Abstract:* Recently we have been able to find numerically the exact solutions for a number of lattice polygon models. In all cases we start by calculating an
exact series expansion for the problem at hand and we then proceed to find the exact solution. In the simplest cases this is done via an
educated guess of the form of the solution leaving only some
polynomials to be determined. In more complicated cases we find solutions in the form of high order linear ODEs. In one particular instance we are able to find a closed form solution to a problem involving a 4th order ODE.
In this talk I will briefly outline why we study these problems, how we calculate the series and find the exact solutions and discuss what we have learned.
This is joint work (in part) with Tony Guttmann and Christoph Richard.

Multifractal Analysis : the wavelet leaders contribution

*Speaker:* Patrice Abry

*Institution:* CNRS, Laboratoire de Physique, Ecole Normale Supérieure de Lyon

*Date:* Fri 24 Nov 2006

*Time:* 3:15 pm

*Location:* Theatre 2, Ground Floor, 111 Barry Street, Carlton.*Abstract:* The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, in order to yield the entire and correct spectrum of Hölder singularities. The properties of this new multifractal formalism and of the alternative weak scaling exponent multifractal formalism are investigated. Examples based on known synthetic multifractal processes illustrate its numerical implementation and abilities. The benefits of the use of wavelet leaders is also illustrated on actual empirical data coming from hydrodynamics turbulence experiments.
(Joint work with S. Jaffard, Dept. of Mathematics, Université Paris XII, Creteil France)

Some hidden Markov models I have known

*Speaker:* Professor Terry Speed

*Institution:* University of California, Berkeley and Walter & Eliza Hall Institute of Medical Research, Melbourne

*Date:* Fri 17 Nov 2006

*Time:* 3:15 pm

*Location:* Theatre 2, Ground Floor, 111 Barry Street, Carlton.*Abstract:* Hidden Markov models emerged in the late 1960s in the literature of probability and statistics. They were introduced into genetics in the mid-1980s, and shortly after that into biomolecular sequence analysis, now part of what is known as bioinformatics. Their range of applications in that field is now very wide. In this talk I'll describe some examples, including a few with which I have been associated.

Self-avoiding walk enumeration via the lace expansion

*Speaker:* Dr Nathan Clisby

*Institution:* MASCOS, The University of Melbourne

*Date:* Fri 20 Oct 2006

*Time:* 3:15 pm

*Location:* Theatre 2, Ground Floor, 111 Barry Street, Carlton.*Abstract:* We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion. Combined with another algorithmic improvement which we call the two step method, we have been able to
significantly extend the series for the simple cubic lattice from 26 to 30 terms, and dramatically extend series for hypercubic lattices with dimensions greater than three.

Alternative view of asymptotic expansions and the Stokes’ phenomenon

*Speaker:* Ed Smith

*Institution:* La Trobe University

*Date:* Fri 13 Oct 2006

*Time:* 3:15 pm

*Location:* Theatre 2, Ground Floor, 111 Barry Street, Carlton.*Abstract:* 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

Generalized Cross-Entropy Methods

*Speaker:* Dirk Kroese

*Institution:* The University of Queensland

*Date:* Tue 26 Sep 2006

*Time:* 3:15 pm

*Location:* Theatre 3, 1st Floor, 111 Barry Street, Carlton.*Abstract:* 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).

Seeing Polymers in a New Light

*Speaker:* Professor Andrew B. Holmes, ARC Federation and VESKI Fellow

*Institution:* Bio21 Institute and CSIRO Molecular and Health Technologies, University of Melbourne

*Date:* Fri 15 Sep 2006

*Time:* 3:15 pm

*Location:* Theatre 1, Ground Floor, 111 Barry Street, Carlton*Abstract:* 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.

How Many Needles are in a Haystack, or how to Solve #P-Complete Counting Problems Fast

*Speaker:* Reuven Rubinstein

*Institution:* Faculty of Industrial Engineering and Management, Technion

*Date:* Fri 8 Sep 2006

*Time:* 3:15 pm

*Location:* Theatre 1, Ground Floor, 111 Barry Street, Carlton*Abstract:* 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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