Past Seminars

Some Properties of Principal Components Analysis for Functional Data

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Speaker: Mr Mohammad Hosseini-Nasab
Institution: Australian National University
Date: Thu 1 Dec 2005
Time: 2:15 pm
Location: Theatre 2, Old Geology Building, The University of Melbourne

Abstract: Functional data analysis is intrinsically infinite-dimensional; functional principal component analysis, or PCA, reduces dimension to a finite level, and points to the most significant components of the data. However, while this technique is often discussed, its properties are not as well understood as they might be. In this talk, it is shown how the properties of functional PCA can be elucidated through stochastic expansions and related results. The approach quantifies the errors that arise through statistical approximation, in successive terms of orders $n^{-1/2}, n^{-1}, n^{-3/2}$,..., where $n$ denotes sample size. The expansions show how spacings among eigenvalues impact on statistical performance. The results can be used to explore properties of existing methods, and also to suggest new techniques. In particular, we suggest bootstrap methods for constructing simultaneous confidence regions for an infinite number of eigenvalues, and also for individual eigenvalues and eigenvectors.

Random Sequential Packing: An Overview of Recent Results

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Speaker: Professor Joseph E. Yukich
Institution: Lehigh University, Pennsylvania
Date: Fri 4 Nov 2005
Time: 3:15 pm
Location: Theatre 2, Ground Floor, ICT Building (111 Barry St, Carlton)

Abstract: Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with either finite or infinite input. We show how to prove a law of large numbers and central limit theorem for the number of packed balls in the thermodynamic limit. We prove analogous results for numerous related applied models, including cooperative sequential adsorption, ballistic deposition, and spatial birth-growth models.

Mathematical and CFD modelling of a motor powered by latent heat of condensation

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Speaker: Dr Noel Barton
Institution: Sunoba Renewable Energy Systems
Date: Thu 29 Sep 2005
Time: 11:00 am
Location: Theatre 1, Old Geology Building, The University of Melbourne

Abstract: The Bernoulli Effect for a compressible gas shows there will be a drop in pressure, temperature and density when the gas speed increases isentropically in the narrowing section of a duct. For saturated moist air, the temperature drop can lead to rapid condensation of microscopic water droplets and release of latent heat. If the droplets are collected and thereby prevented from re-evaporation, we find that when the flow has slowed down isentropically at the duct outlet, the pressure of the energised flow will be - in theory - greater than the inlet pressure. Surplus pressure can be used to drive a turbine for electrical or mechanical power. The lecture will present mathematical models for the proposed motor. The models will include a one-dimensional cross-sectionally averaged thermodynamic model to predict theoretical power output and efficiency, diffusion models for droplet growth and latent heat release, and estimates for dimensions of the device. In theory, the motor will deliver power (electrical or mechanical) and chilled distilled water as co-products. In the real world, feasibility of the motor is far from certain; triumph of utility over futility will require brilliant engineering to overcome numerous practical difficulties, as well as inspired design based on extensive Computational Fluid Dynamics simulations. The lecture will finish with a description of CFD work in progress.

Integer programming at work / A combined model for online scheduling with stochastic information

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Speaker: Dr Thorsten Koch and Ms Nicole Megow
Institution: MATHEON, Berlin
Date: Fri 16 Sep 2005
Time: 1:05 pm
Location: Room 213, Richard Berry Building, The University of Melbourne

Abstract: This seminar is presented in conjunction with ORSUM, and will comprise two 1/2-hour talks.

Tracking and Sensor Fusion for Australian Wide Area Surveillance

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Speaker: Dr Neil Gordon
Institution: Defence Science and Technology Organisation (DSTO)
Date: Thu 8 Sep 2005
Time: 1:15 pm
Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne

Abstract: Australia's geographic location and extensive coastline make wide area surveillance a key component of national defence. There are a multitude of sensors available to provide surveillance information and to make best use of these assets effective tracking and sensor fusion algorithms are vital. The role of these algorithms is to provide an unambiguous and accurate picture of objects moving within Australia's geographic region. In this talk we shall describe research being done within the Tracking and Sensor Fusion group at the Defence Science and Technology Organisation (DSTO) to extend and develop Australia's surveillance capabilities. The talk is organized in two parts. First we review the tracking and sensor fusion problem in the context of Australian defence and describe some of the particular applications we have been involved in. We will then consider several outstanding technical problems related to data and information fusion in distributed sensor networks and multi-sensor tracking and identification algorithms. The intention is to hopefully identify opportunities for collaborative research.

Magnetic Resonance Imaging: Designing Optimal SSFP Pulse--Sequences for Tissue Quantification

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Speaker: Dr Renata Sotirov
Institution: Department of Mathematics and Statistics, The University of Melbourne
Date: Fri 26 Aug 2005
Time: 3:15 pm
Location: Theatre 2, Ground Floor, ICT Building (111 Barry St, Carlton)

Abstract: Are you interested to find out how Magnetic Resonance Imaging works? Do you want to see the inside of the human body? What does math have to do with that? In this seminar we address the above mentioned issues and much more. We formulate an optimization problem for deriving the design variables that are used in MRI. Our non-convex, nonlinear, semidefinite optimization problem compute the steady-state free precision (SSFP) pulse-sequence variables by minimizing the error in the reconstructed tissue densities. For solving the problem, we develop a sequential, semidefinite, trust-region algorithm. Using obtained design variables, we are able to separate tissue types which could not be separated up to date. Our approach is applicable for quantification of arbitrary number of tissues.

Data Network Models of Burstiness

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Speaker: Professor Sidney Resnick
Institution: School of Operations Research and Industrial Engineering, Cornell University, USA
Date: Fri 12 Aug 2005
Time: 3:15 pm
Location: Theatre 2, Ground Floor, ICT Building (111 Barry St, Carlton)

Abstract: We review characteristics of data traffic which we term stylized facts: burstiness, long range dependence, heavy tails, bursty behavior determined by high bandwidth users, dependence determined by users without high transmission rates. We propose an infinite source Poisson input model which accounts for traffic in adjacent time slots. This model has the ability to account for many of the stylized facts.

The lilypond model: existence, uniqueness and absence of percolation

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Speaker: Professor Gunter Last
Institution: University of Karlsruhe, Germany
Date: Fri 29 Jul 2005
Time: 3:15 pm
Location: Theatre 2, Ground Floor, ICT Building, 111 Barry St, The University of Melbourne

Abstract: The lilypond system model based on a locally finite subset of the Euclidean space R^n is defined as follows. At time 0 every point of the locally finite subset starts growing with unit speed in all directions to form a system of balls in which any particular ball ceases its growth at the instant that it collides with another ball. A stochastic version of this model has been introduced by Haggstrom and Meester (1996) in the context of percolation and by Daley, Stoyan and Stoyan (1999) in the context of hard-sphere models with maximal non-overlapping spheres. In the first part of the talk we will present recent results obtained jointly with Matthias Heveling (Karlsruhe) showing that the lilypond model is uniquely defined for any locally finite subset. Actually we will show that these results apply in the far more general setting, where the locally finite subset is a subset of some pseudo-metric space. We will also discuss an algorithm approximating the system with at least linearly decreasing error. In the second part of the talk we will consider a stochastic lilypond model based on a stationary point process N. We present analytic conditions on N implying the absence of percolation in this model. Examples are Cox, Poisson cluster and Gibbs processes satisfying certain exponential moment conditions. This part of the talk is based on joint work with Daryl Daley (Canberra).

Mathematics: The Enabling Tool for Industrial Innovation

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Speaker: Prof Arvind Gupta
Institution: MITACS, Canada
Date: Mon 18 Jul 2005
Time: 4:30 pm
Location: Theatre 2, Ground Floor, ICT Building (111 Barry St, Carlton)

Abstract: In Canada we have witnessed an explosion of industrial interest in using advanced mathematical techniques for solving industrial problems. The Mathematics of Information Technology and Complex Systems (MITACS) network acts as a focal point for academic-industry interaction. There have been a number of notable successes within the network that have directly lead to industrial innovations. In this talk I will choose projects from three MITACS themes: A project on haplotyping from the Biomedical theme, on Facility Location Problems from the Information Processing theme, and on Seismic Imaging from the Environment theme. In each case I will explain the role of mathematics and its impact on the partner organization.

Some applied problems of Markov Processes

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Speaker: Prof G. Tsitsiashvili
Institution: Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia
Date: Fri 8 Jul 2005
Time: 3:15 pm
Location: Theatre 2, Ground Floor, ICT Building, 111 Barry St, The University of Melbourne

Abstract: Various applications of Markov Processes will be considered, including multiserver queueing systems with competing servers, queueing networks with prohibitions, optimization of customer handling in an open queueing network, and diffusion on an interval with reflecting edges. The main idea is to combine probability theory with algebra, geometry and graph theory methods to solve some applied probability problems.