Past Seminars

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Data Network Models of Burstiness
Professor Sidney Resnick
School of Operations Research and Industrial Engineering, Cornell University, USA
Start time: 3:15 pm
Date: Friday 12 August 2005
Location: Theatre 2, Ground Floor, ICT Building (111 Barry St, Carlton)

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.

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The lilypond model: existence, uniqueness and absence of percolation
Professor Gunter Last
University of Karlsruhe, Germany
Start time: 3:15 pm
Date: Friday 29 July 2005
Location: Theatre 2, Ground Floor, ICT Building, 111 Barry St, The University of Melbourne

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).

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Mathematics: The Enabling Tool for Industrial Innovation
Prof Arvind Gupta
MITACS, Canada
Start time: 4:30 pm
Date: Monday 18 July 2005
Location: Theatre 2, Ground Floor, ICT Building (111 Barry St, Carlton)

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.

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Some applied problems of Markov Processes
Prof G. Tsitsiashvili
Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia
Start time: 3:15 pm
Date: Friday 8 July 2005
Location: Theatre 2, Ground Floor, ICT Building, 111 Barry St, The University of Melbourne

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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Magnets, Criticality and Collective Intelligence
Dr Julianne Halley
School of Biological Sciences, Monash University
Start time: 3:15 pm
Date: Saturday 18 June 2005
Location: Theatre 1, Old Geology Building, The University of Melbourne

There is abundant evidence that natural selection is a dominant force in evolution, but a growing number of researchers suggest that it acts in concert with self-organization. From the smallest to largest scales, self-organization can be found in most (if not all) levels of biology, and parallels the ubiquity of self-organization in the non-biological world. In this seminar, a brief overview of the history of the study of self-organization in general and self-organized criticality in particular will be provided. I then discuss groups of feeding Argentine ants, showing how self-organization to an almost critical state enables a group to collectively balance foraging efficiency with the need to avoid excessive mortality. A new type of self-organized criticality, which I call rapid self-organized criticality, will also be introduced.

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