July 17, 2024

The Fields Institute
Industrial Mathematics Seminar Series

Thursday, October 15, 1998
5:00 - 7:30 p.m.
Room 230, The Fields Institute


5:00 - 6:00 p.m.
"Mathematical Successes and Challenges on the Network Edge"
André Van Schyndel, Network Edge Technology Laboratories, Northern Telecom (Nortel)

6:30 - 7:30 p.m.
"Inverse Problems: Formulation and Solution"
Henning Rasmussen, Department of Applied Mathematics, University of Western Ontario


"Mathematical Successes and Challenges on the Network Edge"
André Van Schyndel

The "Network Edge" labs at Nortel translate the bits and bytes of network communication into the real world of eyes, ears, touch, and all human cognition. A successful construction of this interface needs expertise in psychology, human factors, industrial design and ergonomics as well as mathematics and physics. One crucial realization of our team has been the value of the experts in universities and other centers of expertise (like the Fields Institute) for fresh input into the myriad of design opportunities afforded by today's technology. In this industrial seminar, I would like to present a few of our many challenges where mathematics has played a key role in both understanding the problems and producing novel solutions. I would also like to present a few of the many potential products where we have yet to solve the mathematics needed for successful implementation. I have chosen some current unsolved mathematics involving inverse boundary value problems (where we know the differential equation but need to find the boundary values which will produce solutions with particular characteristics) and generalized Fourier series (where we need to identify integral transforms amenable to modern digital signal processing which produce optimal inverses in the presence of noise). We consider ourselves very fortunate to have the opportunity to discuss these ideas with such a distinguished audience of students, professors, experts and onlookers that the Fields Institute has the unique capability of attracting; especially my co-presenter Professor Henning Rasmussen, a recognized expert in mathematics related to these challenges.

"Inverse Problems: Formulation and Solution"
Henning Rasmussen

Many engineering problems can be modeled by one or more differential equations and associated boundary and initial conditions; the difficult part is to ensure that the model contains enough detail that it represents the engineering problem accurately enough but is simple enough that it can be solved. Usually the solution procedure results in a computer program since very few mathematical models of practical problems can be solved analytically.

However, there exists a large class of very important engineering problems in which some of the very important details of the physical situation are not known but must be deduced from measurements. As an example one can mention the non-destructive testing of welding seams. In this case it is not known if the weld forms a continuous seal between two metal pieces, and in fact this is the information which is required. The mathematical models of such problem contain parameters that during the modeling process are unknown but which must be determined, usually in an iterative manner by comparing the output of the model to measured data.

In order to illustrate the process by which such problems can be treated I will discuss the modeling and development of computational programs for two inverse problems. The first one consists of estimating the extent of a metallic ore body without any additional drilling while in the second one we will show how electromagnetic waves might be useful in the monitoring of the treatment of leukemia.


André Van Schyndel is Senior Staff Scientist in Nortel's Network Edge Technology laboratories in Ottawa. His primary duties include both creating and bringing in new ideas and technologies to interface communication networks to their human users. He has a Ph.D. in solid state physics and acoustics from the University of British Columbia, but has a reputation for being interested in everything. Dr. Van Schyndel has recently been involved with Fields Institute initiatives to encourage students with an aptitude in mathematics and science to explore their creativity and perhaps pursue related careers.

Henning Rasmussen is a professor in the Department of Applied Mathematics at the University of Western Ontario and past-President of the Canadian Applied Mathematics Society. After receiving his Ph.D. in Applied Mathematics from the University of Queensland, Australia, he held postdoctoral positions at Monash University and Southampton University and taught at Technical University of Denmark. His research interests include numerical methods, free boundary problems, fluid mechanics and industrial mathematics. An active researcher, Henning Rasmussen has 80 papers published in refereed journals.


The Industrial Mathematics Seminar is offered to any interested participant -- no reservation is necessary.