Forthcoming and recent seminars
Below are details of forthcoming and recent seminars presented in the Seminar Program of the Department of Mathematics and Statistics at La Trobe University's campus in Bendigo, Victoria. For further information about any of the talks, please contact the seminar organizer, Terry Mills.
Andriy Olenko
Kotel'nikov-Shannon sampling procedure for deterministic and stochastic signals, by Dr Andriy Olenko (Department of Mathematics and Statistics, La Trobe University, Bundoora)
Scheduled: 12 noon, Friday 27 November 2009, in Room B2.32
Abstract: Whittaker-Kotel'nikov-Shannon sampling procedure is discussed for deterministic and stochastic signals. Truncation error analysis and convergence rate are studied. Various characterizations of uniform upper bounds in regular Whittaker-Kotel'nikov-Shannon sampling procedure are given. Sharp uniform upper bounds on aliasing error of truncated sampling cardinal series and corresponding extremals are presented. Various applications to weak Cramer class random processes and fields are shown.
Phil Broadbridge
Shannon entropy as a diagnostic tool for evolution PDEs, by Professor Phil Broadbridge (Head of School of Engineering and Mathematical Sciences, La Trobe University)
Scheduled: 12 noon, Friday 20 November 2009, in Room B1.29
Abstract: From a "constant-mass" solution to any local conservation law, one may construct a probability density and evaluate the Shannon entropy. For any second order nonlinear heat equation, necessity of heat flow from hotter regions to cooler regions is equivalent to the necessity of Shannon entropy increasing. However, for an isolated system governed by 4th order diffusion, the second law of thermodynamics does not hold in such a simple form. Even for linear fourth order "diffusion", there are strange overshoot phenomena that are no longer proscribed by the maximum principles of second order diffusion, as shown in examples from exact calculations. Despite the strange 4th order effects, we can construct a non-trivial class of fourth order quasilinear diffusion equations that increase the Shannon entropy, do not generate ripples and maintain positivity. Shannon entropy of the actual solution seems to be a simple diagnostic tool, leading to conjectures that are yet to be properly formulated.
Eder Kikianty
Integral means and orthogonality in normed spaces, by Eder Kikianty (Victoria University, Melbourne)
Scheduled: 12 noon, Friday 16 October 2009, in Room B2.15
Abstract: In inner product spaces, two vectors are said to be orthogonal when their inner product vanishes. The study of orthogonality in normed spaces deals with the extensions of this notion without necessarily having inner product construction. The purpose of this talk is to discuss some new notions of orthogonality, which are defined by utilising the integral mean of the squared norm on a segment in a normed space. These notions of orthogonality are closely related to the classical ones, namely James' and Carlsson's orthogonalities. Some characterisations of inner product spaces and strictly convex spaces follow when these orthogonalities satisfy certain properties.
Mary Martin
Mary Goes to CHERC or When IT meets Health, by Mary Martin (Department of Computer Science and Computer Engineering, La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 25 September 2009, in Room B2.15
Abstract: A unique research fellow scheme and La Trobe University's Outside Studies Program has allowed La Trobe academic Mary Martin to take a period of study leave at Bendigo Health's Collaborative Health Education and Research Centre (CHERC). From January to June 2009, Mary was located at CHERC working alongside project officers, health educators and researchers, participating or consulting in health projects and activities that included information technology components.
Mary's main activity was as a member of a research project looking at factors that affect emergency department demand and service levels, and applying modelling technologies commonly used in the software engineering discipline. New models for patient flow were constructed and research project reports presented to Bendigo Health groups (Bendigo Health Executive Board and Emergency Department staff) and the Monash School of Rural Health. The findings of research carried out in 2007 and 2008 were written up in a research paper entitled "Mapping Patient Flow in the Emergency Department: A Model Driven Approach".
The placement also provided the opportunity to apply computer science expertise to projects within CHERC leading to better understanding by both disciplines of the role of computer science in health care. A documentation and modelling activity within CHERC and involving final year IT students is an ongoing exercise and is typical of the type of activity that has potential for further applied research.
Guang-Da Hu
Runge-Kutta methods in nonlinear control systems, by Professor Guang-Da Hu (Department of Electronics and Information Engineering, University of Science and Technology Beijing, China)
Scheduled: 12 noon, Friday 14 August 2009, in Room B2.15
Abstract: The talk is concerned with Runge-Kutta methods applied to nonlinear control systems. For input-to-state stable (ISS) control systems, we present conditions for which the resulting discrete (difference) systems derived from Runge-Kutta (RK) methods are also ISS. In addition, computer implementation of nonlinear controller for nonlinear system by Runge-Kutta methods is discussed.
Terry Mills
Mathematical models in health care, by Emeritus Professor Terry Mills (La Trobe University, Bendigo and Loddon Mallee Integrated Cancer Service)
Scheduled: 12 noon, Tuesday 7 July 2009, in Room B2.09
Abstract: This seminar is a presentation of a paper by Jon Karnon (University of Adelaide), Mark Mackay (University of Adelaide), and Terry Mills. We will describe several case studies that illustrate how we have used modelling to improve the delivery of health care. The studies cover various settings in health care, utilise a variety of mathematical modelling techniques, and include descriptions of the impact of the model on the health care system. These examples illustrate the potential for applying mathematical modelling and simulation in health care.