Science, Technology and Engineering

Department of Mathematics and Statistics, Bendigo

Mathematics Seminars 2006

Below is a list of seminars presented during 2006 in the Seminar Program of the Department of Mathematics and Statistics at La Trobe University's campus in Bendigo, Victoria.

Barry Jessup

Does symmetry punch holes in space?, by Professor Barry Jessup (University of Ottawa)

Scheduled: 12 noon, Friday 4 August 2006, in Room B2.15

Abstract: Symmetry in a problem effectively reduces its dimension, making it easier to solve. An important question is then: "How much symmetry can the manifold M of configurations of a system support?"

The toral rank of M is the largest integer r such that a compact abelian symmetry group of dimension r acts freely on M, and is difficult to determine in general. Estimates are therefore useful, and in 1968 Steve Halperin conjectured (based on very little evidence, as he likes to admit) that the toral rank of a closed manifold is at most log (base 2) of the total number of "holes" in M.

We will survey this stubborn conjecture, which remains open in general. After being a bit more precise about how we shall count "holes", if we have time, we will focus on the case when M "comes from" a nilpotent Lie algebra L (e.g. the Heisenberg lie algebra), where the toral rank of M is known to be the dimension of the centre of L.

The principal tools we will use are those of rational homotopy, whose success essentially relies on systematically ignoring small groups, an approach the speaker does not support in every situation.

Terry Mills

Emergency Maths, by Professor Terry Mills (La Trobe University, Bendigo)

Scheduled: 12 noon, Friday 7 July 2006, in Room B2.15

Abstract: Most of us have had to visit the emergency department of a hospital either as a patient, or accompanying a patient. The emergency departments are well known for long waits and short fuses while the staff try valiantly to meet the patients' needs.

In this seminar, I will describe ways in which mathematics can be used to describe various aspects of the emergency department of a hospital.

James McEwan

Egyptian Mathematics, by James McEwan (Bendigo Senior Secondary College)

Scheduled: 11.30 am, Friday 23 June 2006, in Room B1.29

Abstract: As part of the CSIRO Student Research Scheme, James McEwan has been working in the Department of Mathematics and Statistics. In this presentation, James will discuss his work on the history of Egyptian mathematics.

Robert Gray

Extracting discrete information from a continuous world: Quantization, Compression, and Classification, by Professor Robert M. Gray (Stanford University) – Professor Gray is a 2006 Distinguished Lecturer of the IEEE Signal Processing Society

Scheduled: 12 noon, Wednesday 22 March 2006, in Room B1.29

Abstract: Scientists and engineers often seek to measure, communicate, store, process, reproduce, or analyze signals encountered in the real world. Most such signals are inherently continuous or analog in nature, yet increasingly the means for communicating, storing, and manipulating such information are discrete or digital. Generally something is lost when continuous information is converted into discrete approximations, so a natural goal is to preserve as much of the original information as possible. This is the general problem of quantization, a technique that historically has cropped up in a variety of branches of signal processing, taxonomy, physics, mathematics, and statistics as well as playing a key role as the interface between a continuous world and digital processing. Quantization traditionally has been used to model analog to digital conversion, Shannon source coding, and data compression. Viewed generally, quantization also models the extraction of information from signals, including statistical classification, clustering methods, and machine learning. This talk will describe the fundamentals of quantization along with examples and recent research topics in theory and application.

Rachael Hamilton-Keene

Modelling Patient Satisfaction, by Rachael Hamilton-Keene (ICE-EM Vacation Scholar 2006)

Scheduled: 11.00 am, Wednesday 15 February 2006, in Room B2.15

Abstract: This presentation is the result of a 6-week research project carried out as an ICE-EM summer scholar. The project involved modelling hospital inpatient satisfaction at Bendigo Health. Patient satisfaction is an important measure of health care provider performance because preliminary research has linked it to better health outcomes, and because patients are paying customers. Patient satisfaction at Bendigo Health has been assessed over several years with patient satisfaction surveys. Binary logistic regression analysis was used to determine the key drivers of patient satisfaction. Discussed will be the process of data clean-up, binary logistic regression itself, and the results of the analysis.