Past Seminars
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Some Properties of Principal Components Analysis for Functional Data
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 MelbourneAbstract: 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
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
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 MelbourneAbstract: 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
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 MelbourneAbstract: 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
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 MelbourneAbstract: 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
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
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
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 MelbourneAbstract: 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
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
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 MelbourneAbstract: 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.
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