Forthcoming and recent seminars
Below are details of forthcoming and recent (since 2009) 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, Christopher Lenard.
Mary Martin and Robert Champion
Methods to map and model patient flow in the emergency department at Bendigo Health, by Mary Martin (Department of Computer Science and Computer Engineering, La Trobe University, Bendigo) and Robert Champion (Department of Mathematics and Statistics, La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 7 October 2011, in Room B2.15
Abstract: Unified Modelling Language (UML) models of the patient journey in a regional Australian emergency department (ED) were used to develop an accurate, complete representation of ED processes and drive the collection of comprehensive quantitative and qualitative service delivery and patient treatment data as an evidence base for hospital service planning. The focus was to identify bottle-necks that contribute to over-crowding. Data was collected entirely independently of the routine hospital data collection system. The greatest source of delay in patient flow was the waiting time from a bed request to exit from the ED for hospital admission. It represented 61% of the time that these patients occupied ED cubicles. The physical layout of the triage area was identified as counterproductive to efficient triaging, and the results of investigations were often observed to be available for some time before clinical staff became aware. The use of independent primary data to construct UML models of the patient journey was effective in identifying sources of delay in patient flow, and aspects of ED activity that could be improved. The findings contributed to recent department re-design and informed an initiative to develop a business intelligence system for predicting impending occurrence of access block.
Ruth Williams
Queueing up for enzymatic processing: correlations through coupled degradation, by Professor Ruth Williams (Department of Mathematics, University of California, San Diego)
Scheduled: 1pm, Wednesday 24 August 2011, in Room AS1 3.03 [This seminar is presented jointly with the Seminar Program of the Faculty of Science, Technology and Engineering at Bendigo.]
Abstract: A major challenge for systems biology is to deduce the molecular interactions that underlie correlations observed between concentrations of different intracellular molecules. Although direct explanations such as coupled transcription or direct protein-protein interactions are often considered, potential indirect sources of coupling have received much less attention. Here we show how correlations can arise generically from a posttranslational coupling mechanism involving the processing of multiple protein species by a limited number of copies of a common enzyme. By observing a connection between a stochastic model and a multiclass queue, we obtain a closed form expression for the steady-state distribution of the numbers of molecules of each protein species. From analytic expressions for the moments and correlations associated with this distribution, we observe a striking phenomenon that we call correlation resonance: for small dilution rate, correlations peak near the balance-point where the total rate of influx of proteins into the system is equal to the maximum processing capacity of the enzymes. The talk will describe the theoretical developments and the results of related experiments, and is based on joint work with Natalie Cookson, Tal Danino, Jeff Hasty, Will Mather, Octavio Mondragon-Palomino and Lev Tsimring.
Terry Mills
Edge-connectivity in graphs, by Emeritus Professor Terry Mills (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 13 May 2011, in Room B2.15
Abstract: The level of connectedness is an important concept in assessing the strength of a network or graph. "Edge-connectivity" is a particular measure of the level of connectedness. The focus of this seminar will be the edge-connectivity of Cartesian products of graphs. I will define the relevant concepts from graph theory, draw diagrams, prove some standard results, and consider these ideas in the context of Cartesian products. This work is part of a collaborative project being conducted with Lakoa Fitina (Divine Word University, Papua New Guinea) and Christopher Lenard.
Jennifer Coopersmith
What is Energy?, by Dr Jennifer Coopersmith (Honorary Research Associate, Department of Civil Engineering and Physical Sciences, La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 25 March 2011, in Room B2.15
Abstract: In this seminar, Jennifer will talk partly about how 'energy' came into physics and partly about current problems connected with 'energy'.
Dr Jennifer Coopersmith is the author of Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein which was published by Oxford University Press in 2010. The book seeks to explain the concept of energy, at a semi-popular level, by examining the history of its emergence in physics. It is aimed at historians and philosophers of science as well as at physicists and other scientists.
Terry Mills
Connectivity in Graphs, by Emeritus Professor Terry Mills (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 5 March 2010, in Room B2.15
Abstract: A graph is "connected" if you can travel from any vertex to any other vertex by a sequence of edges in the graph. We can measure the degree of connectedness by a number which is called the "connectivity" of the graph. Connectivity is a fundamental notion in graph theory. This seminar will focus on connectivity of Cartesian products of graphs. I will define the key concepts from graph theory, draw lots of diagrams, prove some standard results, and then discuss how these ideas can be applied to Cartesian products. This work is part of a collaborative project being conducted with Lakoa Fitina (Divine Word University, Papua New Guinea) and Christopher Lenard.
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.