#1  Date:

September 30, 2005 

Speaker:

Jonathan Barzilai, Dept. of Industrial Engineering, Dalhousie University, Barzilai@dal.ca

Title:

Problems with von Neumann's Theory: Modelling Empirical Systems and the Reconstruction of the Mathematical Foundations of the Social Sciences

Abstract:

The applicability of addition and multiplication to utility scales was  not proved (nor was it claimed -- it was taken for granted) by von  Neumann and Morgenstern. These operations are not applicable to utility

scales or to any scales that are based on the models of the classical  theory of measurement.

The mathematical basis for measurement in the physical and non-physical  sciences has been studied since 1887 and is conceptually difficult.  This problem is of theoretical and practical importance: among other  things, subjective measurement underpins utility theory, the theory of  games, decision theory, mathematical psychology and other applied fields.  Major problems in the classical theory have been unsolved until now. These include the "scale-type" problem which deals with issues  concerning the classification of measurement scales and the problem of  applicability of mathematical operations to scales. This state of  affairs indicates that there are fundamental errors of measurement in the social sciences and this, indeed, is the case.

A new theory of measurement which addresses these problems and has

far-reaching implications will be presented.

Speaker

Bio:

Jonathan Barzilai holds B.Sc., M.Sc. and D.Sc. degrees in Applied Mathematics from the Technion, Israel Institute of Technology. His research interests include measurement theory, decision analysis, and numerical optimization. He has held positions at the University of Texas at Austin (Mathematics), York University (Business), Dalhousie (Business), the Technical University of Nova Scotia (Computer Science) and currently Dalhousie University (Industrial Engineering).

Dr. Barzilai has published major papers on measurement and decision theory and has developed a methodology, Preference Function Modelling, for measurement, evaluation, and decision making by a single decision maker or a group as well as software implementing this methodology

#2  Date:

October 14, 2005

Speaker:

Eldon Gunn, Dept. of Industrial Engineering,

                      Dalhousie University, eldon.gunn@dal.ca

Title:

Radial Basis Functions in Approximate Dynamic Programming

Abstract:

 "Approximate dynamic programming" (also known as neuro DP and/or reinforcement learning). holds out the potential for tackling problems usually considered too big for traditional dynamic programming approaches.  There are a many interesting issues issues in approximate DP.  The one we focus on for this talk is the necessity of approximating the cost-to go functions over either a continuum or a very large finite set of states because we  can only afford to directly evaluate the function over a relatively sparse mesh.  Radial basis functions poses a potentially interesting solution to this problem but come with their own set of problems.  We will show some applications from forest management and from the economic  lot scheduling problems.  Anyone who knows more about radial basis functions than the speaker is particularly welcome at this talk.

Speaker Bio:

Eldon Gunn holds a B Sc (HonMath) from Mount Allison, an MA (Math) from Dalhousie and a Ph.D. (Industrial Engineering) from University of Toronto. His research interests include mathematical programming, production planning and control and forest management, not necessarily in that order. He has been a member of the Department of Industrial Engineering since 1980.  Prior to that he was at the Nova Scotia Research Foundation from 1971-1978. Among his current research interests is the field known variously as reinforcement learning theory, neuro dynamic programming and approximate dynamic programming

#3  Date:

October 28, 2005

Speaker:

Jonathan M. Borwein, FRSC, Canada Research Chair in IT, Faculty of Computer Science, E-mail: jborwein@cs.dal.ca

Title:

Computational Mathematical Lists and Challenges

Abstract:

This lecture will look at `lists and challenges' in mathematics.
 
I shall discuss three lists--- and mention others. One is a set of \emph{Ten Symbolic Computational Mathematics Problems} including
$$\int_0^\inty\cs(2x)\prod_{n=1}^\infty\cos\left(\fracxn\right)\,dx \stackrel{?}{=}\frac{\pi}{8},$$ by Bailey, Borwein, Kapoor and Weisstein, to appear in the MAA Monthly. I invite you to try this integral before the talk! Our problem set was stimulated by Nick Trefethen's recent and more numerical \emph{SIAM 100 Digit, 100 Dollar Challenge} which I shall also survey.

Speaker

Bio:

Jonathan M. Borwein was Shrum Professor of Science (1993-2003) and a Canada Research Chair in Information Technology (2001-08) at Simon Fraser University, and was founding Director of the Centre for Experimental and Constructive Mathematics. In 2004, he (re-)joined the Faculty of Computer Science at Dalhousie as a Research Chair in Distributed and Collaborative Research, cross-appointed in Mathematics, while preserving an adjunct appointment at Simon Fraser.

He was born in St Andrews in 1951, and received his DPhil from Oxford in 1974, as a Rhodes Scholar. Prior to joining SFU in 1993, he worked at Dalhousie (1974-91), Carnegie-Mellon (1980-82) and Waterloo (1991-93). He has received various awards including the Chauvenet Prize (93), Fellowship in the Royal Society of Canada (94), Fellowship in the American Association for the Advancement of Science (02), an honorary degree from Limoges (99), and foreign membership in the Bulgarian Academy of Sciences (03).

Dr. Borwein is a past President of the Canadian Mathematical Society (2000-02) and past Chair of (the National Science Library) NRC-CISTI's Advisory Board. He chairs the International Math Unions committee on electronic information and communications (2002-2006). His interests span pure (analysis), applied (optimization), computational (numerical and computational analysis) mathematics, and high performance computing. He has authored ten books (most recently two on Experimental Mathematics(www.expmath.info) and over 250 journal articles, and is co-founder (1994) of a software company, MathResources (www.mathresources.com), producing interactive CD and Web tools for school and university mathematics.

#4  Date:

November 18, 2005

Speaker:

Roman Smirnov,  Department of Mathematics & Statistics, Dalhousie

Title:

Applicable differential geometry: differential invariants and image recognition

Abstract:

In recent years various techniques that have their roots in classical differential geometry have strongly contributed to the development of new approaches to image recognition whose applications range from medicine and consumer environments to defense and security.

I will review the main ideas behind the approach to object recognition via geometric invariance that can be traced back to Felix Klein (1849-1925) and Elie Cartan (1869-1951).

Speaker

Bio:

Roman graduated in 1992 from Kiev National University (Ukraine) with a BSc  degree in Mathematics and in 1996 he graduated from Queen's with a PhD. In 1998-2001 worked as an NSERC PDF and Research Assistant Professor at University of Waterloo (Appl. Math. Department) and in 2001-03 was working in Germany (University of Paderborn) as an Alexander von Humboldt Foundation Research Fellow.  In 2003 Roman joined the Department  of Mathematics & Statistics here at Dalhousie. His main research interests relate to applicable differential geometry.

#5  Date:

December 2, 2005

Speaker:

Andrew Eberhard, RMIT University. Melbourne, Australia.

Title:

A Convex Analysis Approach to Limits of Performance in Control

Abstract:

When designing a controller, practising engineers currently iterate a design process that involves the development of an approximate model, an experimental design, simulations of the controller and an "experimental rig".  This is a costly process in human effort and resources and can be repeated many times before a successful controller has been designed. Any measure that can be used to eliminate unproductive avenues and avoid such a waste of human effort is of interest to practitioners of controller design. Fundamental Limits of Performance is a methodology that concentrates on the comparison of "raw" measures of system performance to judge whether a given nominal plant can achieve a desired performance objective, before any effort has been expended in designing a controller.  Traditionally, such methods have revolved around a simulation approach. The Holy Grail of this area is the development of formula to make calculations of such comparisons "on the back of a scrap piece of paper".
 
This talk discusses a promising approach to the development of such formula. We present a framework based on conjugate functionals which systematically gives dual formulations for a wide class of problems occurring in feedback control system design. Application is made to problems concerning the time-domain shaping of response to a fixed input for the standard discrete-time one-parameter feedback configuration.  We apply Fenchel duality to obtain dual optimization problems that facilitate derivations of exact formula for simple, low dimensional problems. Surprisingly, some general theorems can be derived to obtain the equivalent performances from related problems whose plants are of arbitrarily higher dimension. These are obtained from the lower dimensional problem by adding non-minimum phase zeros and/or unstable poles in a structured manner.
 

Speaker:

Andrew Eberhard has an  degree with honours in computing and mathematics and a PhD in Applied Mathematics from Adelaide University, graduating in 1984.  He briefly held a positions at the Adelaide University and the University of SA before taking up a position in the mathematics department at RMIT (Royal Melbourne Institute of Technology) in the eighties. Currently he is an Associate Professor in the school of Mathematical and Geospatial sciences.
His research interests revolve around the applications of convex, nonsmooth and variational analysis within the areas of optimization, control theory and PDE theory.

Date:

January 13, 2006

Speaker:

Josh MacArthur

Title:

Abstract: