Past Seminars

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Multilevel clustering of extremes
Dr S.Yu.Novak
Middlesex University, UK
Start time: 3:15 pm
Date: Friday 13 July 2007
Location: Room 213, Richard Berry Building, Department of Mathematics and Statistics, The University of Melbourne

A sample element is considered “extreme’’ if it exceeds a certain level. Various quantities of interest in Extreme Value Theory can be expressed in terms of the number of such exceedances. For example, the distribution of the sample maximum is closely related to that of the number of such exceedances. This topic is of interest to insurers as an insurance company may be interested in a number of claims varying between certain levels. The empirical point process of exceedances (EPPE) takes into account heights as well as locations of extremes. EPPE’s play a central role in Extreme Value theory. We describe the class of limit laws for EPPE’s, and present necessary and sufficient conditions for the weak convergence of an EPPE to a given element of that class.

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On the connections between chaos theory and statistical mechanics
Henk van Beijeren
Institute for Theoretical Physics, Utrecht University
Start time: 3:15 pm
Date: Thursday 7 June 2007
Location: Russell Love Theatre, Richard Berry Building, Department of Mathematics and Statistics, The University of Melbourne

The past years have seen a surge of activity on the connections between chaos theory and statistical mechanics. Among the connections known I want to mention: 1) the Gaussian thermostat formalism, developed by Hoover, Evans et al. Here the irreversible entropy production in a stationary non-equilibrium system is related to the sum of all of its Lyapunov exponents. 2) the escape-rate formalism of Gaspard and and Nicolis, in which transport coefficients determining the rate of escape of systems from phase space through an open boundary are related tot the Kolmogorov-Sinai entropy and the sum of all positive Lyapunov exponents on a small subset of phase space. 3) Ruelle's thermodynamic formalism, in which chaotic as well as transport properties can be obtained from a single dynamical partition function. This is even more ambitious, but for the majority of many-particle systems calculation of the dynamical partition function is a very hard task. Here I will briefly introduce dynamical systems and discuss their characteristic properties. I will show how quantities like Lyapunov exponents, Kolmogorov-Sinai entropies and topological pressures may be calculated for a dilute Lorentz gas (disordered billiard), which is a system with fixed scatterers on random positions, with which a point particle makes elastic collisions. Comparisons of the results with computer simulation results show a very good agreement. For a dilute hard sphere gas in equilibrium both the KS entropy (equal to the sum of all positive Lyapunov exponents) and the largest Lyapunov exponent can be calculated analytically to leading orders in the density. Again, comparisons to computer simulations show good agreement. The smallest positive Lyapunov exponents for these systems show very interesting collective behavior, which can also be explained through kinetic theory calculations. Finally I wil discuss some outstanding open problems.

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COSNet/MASCOS Seminar - Heat Conduction in Nonlinear Systems
Professor Bambi Hu
Department of Physics, Hong Kong Baptist University, and Department of Physics, University of Houston
Start time: 3:15 pm
Date: Friday 20 April 2007
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

Heat conduction is an old yet important problem. Since Fourier introduced the law bearing his name two hundred years ago, a first-principle derivation of this law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions, and the necessary and sufficient conditions for its validity are still far from clear. In this talk I'll review recent works done on this subject. I'll also report our latest work on asymmetric heat conduction. The study of heat conduction is not only of theoretical interest but also of practical interest. It'll shed light on the thermal properties of carbon nanotubes. The study of electric current has led to the invention of electric diodes and transistors. The study of heat conduction may also lead to the invention of thermal diodes and transistors in the future.

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Adjoint based Optimization Methods
Andreas Griewank
Humboldt Universitaet zu Berlin and DFG Research Center Matheon
Start time: 3:15 pm
Date: Thursday 19 April 2007
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

As recently confirmed by an NP completeness result of Uwe Naumann the evaluation of Jacobians, Hessians, and other derivative matrices is a potentially costly computational task. In contrast, not only tangents representing Jacobian-vector products but also first and second order adjoints representing vector-Jacobian and Hessian vector products, can be obtained at a cost similar to the underlying vector or scalar function. After reviewing the above results we discuss their impact on the design of optimization algorithms. I particular we present a new class of adjoint based quasi-Newton updates and a matrix-free one-shot approach to optimizing very large systems like those arising through the discretization of partial differential equations in aerodynamics and geophysics.

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Attribution of Responsibility for Climate Change: The Mathematics Behind the Brazilian Proposal
Professor Ian Enting
MASCOS, The University of Melbourne / CSIRO
Start time: 3:15 pm
Date: Friday 2 March 2007
Location: Theatre 3, 1st Floor, 111 Barry Street, Carlton.

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.

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