Science, Technology and Engineering

Title: Multiscale Simulation of Biochemical Systems.

Speaker: Linda Petzold, University of California Santa Barbara

Time & date: 2pm Friday 22nd July 2008.

Venue: SEMS meeting room 221, Physical Sciences 1, La Trobe University, Bundoora Campus.

Abstract: In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA). Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multiscale nature of the underlying problem: (1) the presence of multiple timescales (both fast and slow reactions); and (2) the need to include in the simulation both chemical species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation. We will describe several recently developed techniques for multiscale simulation of biochemical systems, and outline some of the future challenges

 

Title: Real C*-algebras and their K-theory.

Speaker: Jeff Boersema, Seattle University

Time & date: 2pm Friday 19 June 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus.

Abstract: We will give a general overview of real and complex C*-algebras and their K-theory. This will include a discussion of a major classification theorem for a class of simple complex C*-algebras and a survey of recent results which may lead toward a similar result for real C*-algebras. Along the way, we will see several examples.

 

Title: The number of islands on a rectangular sea.

Speaker: Csaba Szabo, Eotvos Lorand University, Budapest

Time & date: 2pm Friday 13th June 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus.

Abstract: The talk is intended for a general mathamatical audience.
Let a rectangle of size m × n be divided into mn many unit squares. For every square of this rectangular grid a positive real number is given, its height. We think of this grid as an island in the sea. The height is constant on each square. Now, a rectangle R on our grid is called an island if the height of each cell of R is greater than the heights of the squares adjacent to R. That is iff there is a possible water level such that the rectangle is an island of the sea in the usual sense. We look for the maximum number of rectangular islands.

 

 

Title: Pi day.

Speaker: Prof Jonathan Borwein, Canada Research Chair,
Dalhousie University

Time & date: 4pm Friday 14 March 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus. Transmited from the AGR at University of Newcastle

Abstract: In N.America, the month is written first, followed by the day: hence Mar, 14 is 3,14.

 

Title: Digital atlases and difference forms.

Speaker: Prof Elizabeth Mansfield, Institute of Mathematics, Statistics and Actuarial Science, The University of Kent, UK.

Time & date: 1:45 pm Friday 14 March 2008.

Venue: Seminar Hall. Michael J Osborne Centre - Institute for Advanced Study

Abstract: When integrating a differential equation numerically, it can be important for the solution method to
reflect the geometric properties of the original model, and there is an increasingly sophisticated
subject of geometric integration concentrating mostly on local properties of the equation. This talk
concerns ways of ensuring that finite difference schemes accurately mirror global properties. To
this end, lattice varieties are introduced on which finite difference schemes and other difference
systems may be defined. There is no assumption of continuity, or that either the variety or the
difference systems have a continuum limit; our theory is more general than that of cubical
complexes, and the proofs require a different foundation. We show the global structure of a
lattice variety can be determined from its digital atlas is joint work with Peter Hydon, University of Surrey.

 

 

 

 

 

Title: Variance stabilisation approach to meta-analysis: combining the evidence.

Speaker: Elena Kulinskaya, Director of Statistical Advisory Service, Imperial College, London

Time & date: 11am Wednesday 26 November 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus

Abstract: Read the abstract of the seminar (64KB PDF)

 

Title: Bayesian Methods in Software Testing and Capability Maturity Model.

Speaker: Salilesh Mukhopadhyay, Feasible Solution Inc, USA

Time & date: 2pm Friday 4 July 2008.

Venue:Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus

Abstract: Most of the time the testing phase of the application does not allow an end-to-end testing with all the interfaces up and running in QA environment. To remedy the situation the common practice is to have coverage analysis with appropriate risk mitigation in Finacial (large) applications mainly. However the testing scenarios of E-Commerce, Business to Business Models, Electronic Raw Material Acquisition, Auction Engines are not at all different. The present paper provides a statistical analysis of the scenarios and calculates the associated risk for each phase of testing cycle like, Unit, System Integration Testing, End-to-End Testing, UAT.

The purpose of the present paper is to provide an outline of Bayesian Methods (Prior and Posterior analysis) in Software testing with special emphasize on Capability Maturity Model. Different types of testing scenarios will be analysed for each phase of testing like Unit testing, System Integration Testing, End-to-End Testing, User Acceptance Testing and post production maintenance Testing. Manual and Automated testing will be discussed in details for stable QA environment. Finally the benefits of using quantitative analysis to mitigate the associated risk in each phase will be discussed in details.

 

Title: The Coverage Probability of Confidence Intervals in 2r factorial Experiments after Preliminary Hypothesis Testing.

Speaker: Khageswor Giri, Department of Mathematics and Statistics, La Trobe University

Time & date: 2pm Friday 23 May 2008.

Venue:Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus

Abstract: We consider a 2r factorial experiment with at least two replicates. Our aim is to find a confidence interval for θ, a specified linear combination of regression parameters. We suppose that preliminary hypothesis tests are carried out sequentially beginning with the rth order interaction. After these preliminary hypothesis tests, a confidence interval for θ with nominal coverage 1-α is constructed under the assumption that the selected model is given to us a priori. We call this the naïve 1-α confidence interval for θ. We describe a new efficient Monte Carlo method, which employs conditioning for variance reduction, for estimating the minimum coverage probability of the naive confidence interval. The application of this method is demonstrated in the context of a 23 factorial experiment with 2 replicates and a particular contrast θ of interest. The naive confidence interval, with nominal coverage probability 0.95, has minimum coverage probability that is, to a good approximation, 0.464. This shows that the naive confidence interval is completely inadequate.

 

Title: Variance stabilizing the risk difference to obtain confidence intervals for effects and effect sizes.

Speaker: Associate Professor, Dr Robert Staudte,
Department of Mathematics and Statistics, La Trobe University

Time & date: 2pm Friday 16 May 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus

Abstract: I will be discussing the study of dimension reduction of high dimensional data for binomial response variable data sets when the number of individuals sampled is less than the number of measurement variables. The application of principle component analysis as a prestep to Sliced Inverse Regression and Sliced Average Variance Estimation will be presented. In this setting in order to produce an efficient algorithm, an approximation technique using first and second order perturbations is suggested as a one step eigen-analysis in the cross-validation step of the classification of the binomial response variable data sets.

 

Title: On Survival Equivalence Function.

Speaker: Mitra Jazayeri,
Department of Mathematics and Statistics, La Trobe University

Time & date: 2pm Friday 9 May 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus

Abstract: The usual estimator of the risk difference is variance stabilized, conditionally on an estimated weighted average of the unknown risks. This leads to conditional confidence intervals for the standardized risk difference, and hence for a correlation effect size. In addition, it leads to confidence intervals for the risk difference itself, with more accurate unconditional coverage than those obtained by standard asymptotic methods, as shown by simulations studies.

Methods for combining the results of several studies are presented, and illustrated on nine independent randomized clinical trials of the effect of diuretics on pre-eclampsia.

 

Title: On Survival Equivalence Function.

Speaker: Prof. T.K.Pogany,
University of Rijeka, Croatia

Time & date: 2pm Friday 29 February 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus

Abstract: The reliability of composite systems is improved by decreasing the argument of the associated survival function in the case of general positive i.i.d. random life components connected in series (paralell). The gamma-Weibull distribution has been recently introduced by Leipnik and Pearce. The density function, the probability distribution function and the characteristic function are of is expressed in terms of the confluent Fox-Wright generalization of the hypergeometric function, and its incomplete variant. The composite series (paralell) systems reliability is presented taking for the case study system components having gamma-Weibull life distribution.

 

 

 

Title: Parameter Estimation and Bias Correction for Diffusion Processes

Speaker: Prof. Song Xi Chen,
Department of Statistics, Iowa State University

Time & date: 2pm Friday 7 March 2008.

Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Bundoora Campus

Abstract: This lecture considers parameter estimation for continuous-time diffusion processes which are commonly used to model  dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter as observed in many empirical studies, we develop expansions for the bias and variance of parameter estimators for two mostly employed interest rate processes. A parametric bootstrap procedure is proposed to correct  bias in parameter estimation of general diffusion processes with a theoretical justification. Simulation studies confirm the theoretical findings and show that the bootstrap proposal can effectively reduce both the bias and the mean square error of parameter estimates for both univariate and multivariate processes.  The advantages of using more accurate parameter estimators when calculating various option prices in finance are demonstrated by an empirical study on a Fed fund rate data.

 

 

Title: Decomposable Polyhedra

Speaker: Dr David Yost, School of Information Technology and Mathematical Sciences, University of Ballarat

Time & date: 2pm Friday 7 March 2008.

Venue: 12 noon, Friday 29 February 2008, in Room B2.15, La Trobe University, Bendigo Campus

Abstract: We use graph theoretic methods to solve a problem in combinatorial geometry, namely we complete the classification, in terms of Minkowski decomposability, of the 260 types of polyhedra with 15 or fewer edges. That is, for each such polyhedron P, we can say whether or not it can be expressed as a sum of two polyhedra which are not similar to P. The novelty of our approach is the use of 4-cycles which are not faces, in the graph of the polyhedron.