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CIAM Seminars 2005

Wednesday 30 November 2005
Speaker: Dr Daniel Zachary, American University of Sharjah, UAE
Title: Convex optimization and global climate modeling

Abstract:
We show how oracle-based optimization can be used effectively for the calibration of an intermediate complexity climate model. In a fully developed example, we estimate the 12 principal transport and mixing parameters of the C-GOLDSTEIN climate model by using an oracle-based optimization tool, Proximal-ACCPM. The oracle is a procedure that finds, for each query point, a value for the goodness-of-fit function and an evaluation of its gradient with respect to the parameters to be estimated. The difficulty in the model calibration problem stems from the need to undertake costly calculations for each simulation and also from the fact that the error function used to assess the goodness-of-fit is not convex with respect to the calibration parameters. However, Proximal-ACCPM is able to find good candidates for parameter calibration approximations in spite of this non-convexity. The method converges to a 'best fit' estimate over ten times faster than a comparable test using the ensemble Kalman filter. The approach is simple to implement and potentially useful in calibrating computationally demanding models based on temporal integration (simulation), for which functional derivative information is not readily available.

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Wednesday 16 November 2005
Speaker: Dr Vyacheslav Abramov, Centre for Modelling Stochastic Systems, Monash University
Title: Loss queuing systems: An introduction, asymptotic results and applications

Abstract:
Interest to loss queuing systems is associated with their application to telecommunication systems. In this report we discuss some interesting properties of loss queuing systems, asymptotic behaviour of the loss probability and its application to analysis of performance measures and redundancy of real telecommunication systems. The report is based on the original results obtained during the last years.

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Monday 14 November 2005
Speakers: Ms Alice Bednarz, Ms Mimi Duong, Ms Louise Morton, Ms Han Vu
School of Mathematics and Statistics, University of South Australia
Title: Optimisation of Materials Handling at Olympic Dam

Abstract:
Olympic Dam is the largest underground mine in Australia recovering more than 9 million tonnes of ore per year. Material is mined from up to 35 stopes each month and transported to one or more of 14 fixed orepasses using boggers and trucks. Ore from the mining levels is passed through the orepasses to the lowest level of the mine where an automated rail system collects and transports the ore to an underground rock crusher. The crushed material is hoisted to the surface via the Clark Shaft. The Clinic team has modelled this system with the goal of maximising the tonnage extracted from the mine. The model incorporates delays caused by vehicular interference and the current production limit imposed by the Clark Crusher. The team used a well-known commercial software package (GAMS) and a purpose built linear program to formulate and solve the problem for each shift. The program determines the optimal fleet allocation and best orepass for each stope and finds the number of times each orepass must be emptied by the trains. Initial results indicate that optimal resource allocation and enhanced crushing capacity could significantly increase production.

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Thursday 8 September 2005
Speaker: Professor Elena Litsin, Department of Mathematics, Ben-Gurion University, Israel
Title: Stabilization of Linear Differential Systems via Hybrid Feedback Controls

Abstract:
We study so-called "hybrid feedback stabilizers" for an arbitrarily general system of linear differential equations. We prove that under assumptions of controllability and observability there exists a hybrid feedback output control which makes the system asymptotically stable. The control is designed by making use of a discrete automaton implanted into the system's dynamics. In general, the automaton has infinitely many locations, but it gives rise to an "uniform" (in some sense) feedback control. The approach we propose goes back to the classical feedback control technique combined with some ideas used in the stability theory for equations with time-delay.

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Wednesday 24 August 2005
Speaker: Professor Alfredo Iusem, Institute for Pure and Applied Mathematics (IMPA); Rio de Janeiro, Brazil
Title: How Pointed Is A Cone?

Abstract:
We present the notion of pointedness for closed and convex cones in the Euclidean space. A cone is said to be pointed when it contains no lines. We introduce several options for quantifying the degree of pointedness of a cone, and discuss the relations between them and their respective properties.

Bio:
Professor Alfredo Iusem was awarded a BSc in Mathematics at the University of Buenos Aires in 1971. In 1981 he obtained a PhD degree in Operations Research at Stanford University. His supervisor w as G. Dantzig. Since 1981 he is a full Researcher at the Institute for Pure and Applied Mathematics (IMPA); Rio de Janeiro, Brazil. He worked on different subjects within the field of continuous optimization, including projection algorithms for image reconstruction, iterative methods for linear complementarity problems, nonquadratic variants of the proximal point method, extensions of the proximal point method to Banach spaces, enlargements of monotone operators, algorithms for vector-valued optimization, algorithms for equilibrium problems, etc. He is a member of the Brazilian Academy of Sciences.

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Tuesday 26 July 2005
Speaker: Professor Floske Spieksma, University of Leiden, The Netherlands
Title: Lyapunov function criteria for stability and optimal control of stochastic networks

Abstract:
We consider stochastic networks that can be modelled by a discrete time Markov chain on a countable state space. Say, it has transition matrix P. A method often used for deriving conditions for the stability of such a system is to check the existence of a Lyapunov function f. That is, the network is stable (ergodic) if there exists a non-negative function f, a finite set of states A, and positive constants c,d, such that \sum_xP_{xy}f(y)\leq f(x)-c+d{\bf 1}_{x\in A}. Roughly speaking, this function dominates the expected return time to the set $A$ for each initial state.
If this function is Lipschitz and jumps are bounded, then one can apply an exponential transformation to Lyapunov function f. This has many useful consequences: first of all, the stochastic network is exponentially stable, that is, the marginal distributions converge to the stationary distribution exponentially quickly. Suppose that there are costs per unit time associated with operating the network. Then also the expected marginal costs converge at an exponential rate to the long run average cost, provided the costs are say polynomial in the state variable.
We will also discuss consequences of having a Lipschitz Lyapunov function, in the presence of control. Further, we will address the difficult problem of computing the rate of convergence to stationarity. There are a number of examples of internet traffic models, where quadratic Lyapunov functions are used for showing stability. These are not Lipschitz. If the expected return times to a selected state are Lipschitz in the state variable, a Lipschitz function must exist. We will give some examples where this the case indeed, and we will discuss how to construct it.

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Tuesday 14 June 2005
Speakers: Third year Mathematics Clinic students
Title: Optimisation of Materials Handling at Olympic Dam

Abstract:
Olympic Dam is the largest underground mine in Australia recovering more than 9 million tonnes of ore per year. Material is mined from up to 35 stopes each month and transported to one of 14 fixed ore passes using loaders and trucks. Ore is passed from the mining levels to the lowest level of the mine via the ore passes. An automated rail system then collects and transports the ore to an underground rock crusher. The crushed material is then hoisted to the surface via the Clark Shaft. WMC have asked the Clinic team to investigate how best to distribute the mined material to the ore passes and schedule the trains in order to improve the material handling system and maximize the tonnage through the crusher.

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Wednesday 25 May 2005
Speaker: Professor Art Benjamin, Harvey Mudd College, Claremont, California
Title: The Art of Mental Calculation

A very well received public presentation by the world leader in Rapid Mental Calculation - Professor Art Benjamin, was held on the 25th May at the General Purpose Building at the Mawson Lakes campus. Guests for the evening were amazed at Professor Benjamin's ability and humour.

Biography:
Arthur Benjamin is a Professor of Mathematics at Harvey Mudd College in Claremont, California, having received his PhD in Mathematical Sciences from Johns Hopkins University in 1989.
He is co-author of three books and has taught children and adults the secrets of rapid mental calculation.
In 2000, the Mathematical Association of America awarded him the Haimo Prize for Distinguished College Teaching. Arthur Benjamin is also a professional magician, and frequently performs at the Magic Castle in Hollywood.; He has demonstrated and explained his calculating talents to audiences all over the world.

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Friday 8 April 2005
Speakers: Jerzy K. Filus & Lidia Z. Filus
Title: New n-Variate Probability Densities as Models for Systems Reliability and Maintenance Applications

Abstract:
A new natural extension of the class of Rn à Rn affine transformations to the class of so named “pseudoaffines” is constructed. The pseudoaffine transformations are then applied to sets of n independent normal, Weibullian or gamma random variables.  As result one obtains nice and analytically easily treatable n-variate “pseudonormal”, “pseudoWeibullian” or “pseudogamma” joint pdfs respectively.
The so obtained new pdfs turn out to be natural generalizations of the original distributions as some essential properties of the originals are preserved. Reliability and maintenance applications are to be discussed.  It is expected that, in some cases, choice of a multivariate pseudonormal model, in place of the normal ones, may increase significantly the accuracy in sense of better fit to data in a given modeling process.

Biography:
Jerzy K. Filus received his M.S. degree in Mathematics from the University of Warsaw, Poland in 1972 and Ph.D. from the Systems Research Institute of the Polish Academy of Sciences in 1979. Recently he is an Adjunct faculty in the Dept. of Mathematics and Computer Sciences at Oakton Community College, Des Plaines, IL.
His research interests have mainly been focused on applied probability problems with emphases on reliability modeling, multivariate probability distributions and their extensions towards stochastic processes.

Lidia Z. Filus received her M.S (1971) and Ph.D. (1979) degrees in Mathematics from the University of Warsaw, Poland. Recently she is a Professor of Mathematics at Northeastern Illinois University, Chicago, IL.
Her research interests have been in many areas of operations research, in particular
fixed points algorithms and their applications, most recently in stochastic models in operations research.

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Thursday 7 April 2005
Speaker: Associate Professor Isao Yamada, Department of Communications and Integrated Systems, Tokyo Institute of Technology
Title: Hybrid Steepest Descent Method and Adaptive Projected Sub gradient Method -Their Unified View and Signal Processing Applications.

Abstract:
In this talk, we introduce recently developed mathematical techniques: the hybrid steepest descent method and the adaptive projected sub gradient method}, and their rich applications to broad range of signal and image processing problems.  The hybrid steepest descent method can minimize smooth convex functions over the fixed point set of certain quasi-nonexpansive mappings in a real Hilbert space, and therefore it is applicable to broad range of convexly constrained nonlinear inverse problems as well as convex optimization problems defined over the level set of nonsmooth convex functions.
The adaptive projected sub gradient method can minimize asymptotically certain sequence of nonnegative convex functions over a closed convex set in a real Hilbert space, and therefore it can handle a time-varying version of nonsmooth-nonnegative convex optimization problems, where the convex objective itself keeps changing in the whole process. The adaptive projected sub gradient method can serve as a unified guiding principle of a wide range of et-theoretic adaptive filtering schemes for nonstationary random processes.

Biography:
Isao YAMADA was born in Tokyo, Japan, on September 26, 1962. He received the B.E. degree in computer science in 1985 from University of Tsukuba, Ibaraki, Japan, and the M.E. and Ph.D. degrees in Electrical and Electronic Engineering from Tokyo Institute of Technology, Tokyo, Japan, in 1987 and 1990, respectively. In 1990, he joined the Department of Electrical and Electronic Engineering at Tokyo Institute of Technology, as a research associate, and became an associate professor there in 1994. Currently, he is an associate professor in the Department of Communications and Integrated Systems at Tokyo Institute of Technology.

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Thursday 17 March 2005
Speaker: Professor Richard Huggins, Centre for Mathematics and Its Applications, Australian National University
Title: Semiparametric estimation of animal abundance using capture-recapture data from open populations.

Abstract:
A semiparametric partially linear model for the size of an open population is proposed and inference is conducted using weighted martingale estimating equations. This extends a previous nonparametric approach to modelling capture-recapture data for open populations with frequent capture occasions. Analytic expressions for the large sample variances are derived and these are confirmed in a simulation study. The method is illustrated on monthly penguin banding data collected over 6 years.

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