First SIAM Regional Math in Industry Workshop at WPI

How do interactions between university and industry begin? What forms do those interactions take? What do the participants get out of them? What sorts of problems are considered? What kinds of mathematics are used?

To a faculty member, the act of beginning an industrial interaction may seem the hardest step. Fortunately, the ways of taking that first step are so varied it seems there must be a comfortable direction for everyone.

Ferdinand Hendriks of IBM and Thomas Witelski of MIT began their joint work on the thin-film fluid dynamics of IBM's Tango class of hard disk read-write heads after Hendriks' presentation at one of RPI's annual Workshops on Mathematical Problems in Industry.

Paul Kornfeld of Morgan Stanley and Neil Chriss, now Director of the Mathematics in Finance Masters Program at the Courant Institute and a Vice President at Goldman Sachs & Company, were brought together when Kornfeld was a master's student in financial mathematics at the University of Chicago and Chriss was with Morgan Stanley. Kornfeld and another student were hired on a project basis to build a Matlab Toolkit for predicting market volatility. Besides its utility to Morgan Stanley, the project was designed to assess the students' suitability for permanent employment.

Chriss judged the program "very successful". The students and Morgan Stanley learned about one another, and the students were well prepared to find jobs. Chriss explained, "Recruiters are results-oriented. They want to hear more about things accomplished than things studied."

Richard Braun of the University of Delaware developed his connections with Steven Snow, a chemist at Dow Corning, because he intentionally sought industrial contacts at a fluid mechanics meeting. In about two years of work, he has developed models that bracket most of the data developed by Dow to characterize drainage of the thin films that form in foams. The next step is explaining intermediate regimes by adding more physical effects to the models.

Steve Shreve of Carnegie Mellon and Joseph Langsam of Morgan Stanley have cooperated in developing the computational finance master's and Ph.D. programs at CMU. After describing some of the mathematical needs of the finance industry, Langsam explained the nature of his firm's links with university faculty: consulting is "not a wide-spread way to build relationships" because his firm only hires a very few "senior faculty members from prestigious universities. But we use all the free research we can get---we read journals, review for journals, and so on. We use valuable work when we find it."

Arthur Heinricher of WPI and Richard Welch of Premier Insurance met at a church social. Heinricher said that their first meeting ultimately led to a string of worthwhile projects for undergraduate mathematics majors because "Dick's eyes didn't glaze over when I said I was a mathematician." Welch explained that one of his large corporate problems, maximizing revenue in a state-run auto insurance pool for bad drivers, yielded many student projects that "gave a fresh look at old problems I couldn't study internally" as well as offering him "interaction with knowledgeable university faculty."

Welch added, "The exposure to the students also enhances recruiting potential. The ability to solve an open-ended problem is rare, and it's hard to see in an interview. In the WPI projects, we can watch the students at work on real problems with incomplete or compromised data."

Natalia Sternberg of Clark University also met her collaborator, the experimental physicist Valery Godyak of OSRAM Sylvania, at a party. She said, "In 1987, even before interdisciplinary work was so fashionable, I was promoted from 'wife of a best friend' to mathematician." Her joint work has greatly improved the understanding of industrial plasma processing, and it is now enshrined in the Godyak-Sternberg models. "The collaboration also changed my life as a teacher," she reported. "I learned how to talk to people who don't understand mathematics. I now know what students need, and my once mediocre course evaluations have sky-rocketed."

Folkert Tangerman of SUNY Stony Brook and Mike Brazao of Storage Computer are cooperating in the construction of a PC-based supercomputer at Stony Brook. The symbiosis seems perfect: Stony Brook's Applied Mathematics Department acquires a relatively low cost parallel computer to support its modeling work and Storage Computer has a test bed for its proprietary Storage Allocation Network.

Pre- and post-doctoral thesis connections also facilitate industrial interactions. Ani Velo, a doctoral student at WPI, attacked a problem of ripple instabilities in film manufacturing at Kodak to complete a required extramural project in applied mathematics. Anna Gilbert is developing wavelet models of computer network traffic at Lucent Technologies with the support of an NSF post-doctoral appointment. Lucy Kimball of Bentley College is collaborating with the Brattle Group, a utility consulting firm, on economic dispatch problems in the electric power industry, a contact that arose out of her doctoral thesis work at WPI.

The workshop's three keynote speakers provided an overview of the variety of problems faced by industrial mathematicians, a theme that was continued in the banquet address.

William Pulleyblank offered vignettes of a few of the long-term problems being studied by his one hundred colleagues in mathematical sciences at the IBM T. J. Watson Research Center. Those problems include risk in financial models, especially rare and unpredictable events like bank failures; strategic risk management for casualty insurers; stochastic load forecasting in order to price electricity contracts; and improved web searching ("What if AltaVista had twenty four hours for a search? How could its results be improved?")

Taking a broader view of mathematics in industry, Pulleyblank paraphra sed his predecessor, Shmuel Winograd, "The strength of the mathematical sciences is that they are pervasive in many applications. The challenge is that they are only a part of each application."

Peter Castro of Kodak encouraged academic mathematicians interested in industrial problems to think in terms of impact on the bottom line and in terms of technology transfer, even if they are reluctant to face the reality of regarding mathematics as "technology".

Reinforcing Pulleyblank's theme of mathematicians building credibility in industry, Castro suggested solving small problems first. His example of that first problem was designing a mechanism path in a copier in order to minimize wear; the engineering design team ultimately settled for the output of just a few iterations of the mathematicians' optimization process, a choice that was mathematically suboptimal but a big improvement over the engineers' own initial design.

Castro described other more complex problems in modeling the manufacturing and processing of color film. He also posed and answered a common question, "What kind of mathematics is useful? Every kind, but at Kodak partial differential equations are useful more often than topology."

Nikan Firoozye of Lehman Brothers reviewed some of the challenges of pricing options and derivatives using stochastic calculus. He also noted the rising barriers facing mathematicians who seek to enter the financial industry. "Mathematicians need greater expertise, intuition, and flexibility" he said, "but such broader knowledge does mean increased demand (in the employment market)."

For her banquet address, Margaret Wright drew on her current experience at Lucent Technologies and on her earlier work at Stanford University to identify important qualities of mathematicians in industry.

She cited work on the problem of optimal power flow in an electric network as a setting in which crucial differences in terminology were only revealed when the mathematicians persisted in asking questions to the point of becoming "pesky." Despite the risk of such an accusation, she asserted, "Mathematicians must come in with a fresh viewpoint."

Other examples, including recalibrating the Stanford Linear Accelerator, protocols for testing the robustness of communications networks, and designing indoor wireless communication systems, all illustrated the full range of work habits she believes important:

"Ask thoughtful questions; be persistent; be flexible; be firm; be rigorous; aim for the best; be visionary. And," she concluded, "be active in SIAM!"

The most concrete manifestation of an organization's interest in mathematics is its decision to hire a mathematician. A panel organized by Bill Browning of Applied Mathematics reviewed the primary steps in this critical process. Panelists were Peter Castro, Cleve Moler of MathWorks, Ernie Mintel of Pratt & Whitney, and Alfredo Bequillard of Lehman Brothers.

Castro argued that applicants "need attitude, a desire to solve real world problems, to get information that wasn't available before." Castro also looks for a "team player" because of the "continuous communication" involved in industrial mathematics.

Mintel hires mostly B.S. and M.S. graduates who can support the simulation and geometric design needed to achieve Pratt & Whitney's corporate goal of "virtual overnight simulation of engine design to evaluate proposed engines before we cut metal."

Moler echoed Castro's call for teamwork and communication skills in potential employees. Among MathWorks' five hundred employees are approximately forty Ph.D's, "most in engineering with strong math backgrounds. We hire relatively few with degrees in math," Moler continued, "because math graduates don't know much about software." MathWorks hires B.S. graduates for entry-level positions such as technical support via telephone or email. Those new hires usually have some knowledge of Matlab or of Simulink, another MathWorks product.

As desirable mathematical background, Moler listed ordinary differential equations, linear algebra, numerical analysis, and probability and statistics. This mathematics should be linked to applications in such areas as controls, signal processing, image processing, or financial engineering, a connection that might come through courses in either engineering or physics. Emphasizing the need for knowledge of software, Moler said, "I would rather see an applicant who knew about make (the Unix command) instead of group theory, RCS (Revision Control System) instead of topology, html and Java instead of Besov spaces."

Bequillard outlined the two halves of the investment industry business, the sell side and the buy side. On the former, the mathematician's ultimate job is incorporating stochastic models of market behavior into computer programs that will price financial products, given the necessary parameter values. Advanced mathematics is useful, for example, in covering all angles when trying to resolve "why a model does not match the market."

He explained that Lehman hires through several approaches: associates programs in which Ph.D.'s and MBA's rotate through different parts of the organization until they find a good fit, summer hires, and permanent hires through contacts at conferences.

A typical interview with Lehman Brothers will have two stages. In the first, a trader might ask for a brief description of how to hedge a particular product. In the second and longer phase, Bequillard explained that "other scientist and engineers ask questions based on the applicant's paper work to see if the individual is still as impressive in person."

Browning's firm of twelve employees--- about half physicists and half mathematicians, one-third of them hired as new bachelor's graduates---applies mathematics to submarine and search problems. He described the working environment as "fast-paced, confidential, team-oriented, having an external focus, involving close supervision (If you are working by yourself, you aren't working on an important problem!), and requiring significant client interaction.

"Mathematical preparation must include a solid foundation in mathematics with applications-oriented courses in areas like probability and statistics, optimization, and numerical analysis. We also expect study in a field that uses mathematics---physics engineering, and so on---as well as computational skills, typically using C or C++ and various kinds of applications software."

Browning hires throughout the year. A typical interview visit lasts one to three days, and a hiring decision follows within a few weeks.

Much of the discussion following the panelists' presentations emphasized the importance of students acquiring industrial work experience through co-op employment, summer experience, or industrial project work. Mintel said that such experience "is a big discriminator among applicants." Browning added, "We look for talent and interest. Co-op shows you know what the environment is like." None of the panelists could describe more than limited opportunities for faculty consulting.

In Glimm's view, the broad Stony Brook program is "basic research that happens to have a partner," on-campus or off. "On one hand", he says, "industrial mathematics isn't different. It's numerical analysis, scientific computing, modeling, statistics, combinatorics, and so on. On the other, it's very different because of the necessity of using relevant mathematics, because of the attitudes required, and because of the interactions with users."

Since it offers industrial work to its students at all levels---B.S, M.S., and Ph.D.---Bogdan Vernescu described WPI's program as "vertically integrated industrial mathematics." Typically, students work as teams of two or three on the B.S. project but as individuals on the M.S. thesis and on the required doctoral applied mathematics project. With few exceptions, the WPI projects enjoy the financial support of their sponsors, a sign of industry's strong commitment to them.

On the first day of a five-day summer workshop, the industrial representatives---usually five or six of them---present their problems. Groups of five to ten workshop participants spend the next three days working toward a solution of the particular problem they chose. The group solutions are presented on the final day.

In addition to the slider bearing disk-drive head analysis that continued to occupy Hendriks and Witelski long after the workshop ended, participants have studied the dynamics of catalytic converters in automobile exhaust systems, clearing clogged filters via gas injection, and Ohmic heating of two-phase flows (soup!), among many other problems posed by the thirty companies and labs that have contributed over the years. Schwendeman said, "The best workshop problems involve basic physical modeling with relatively low numerics. We have to decline problems whose descriptions begin, 'My big code doesn't work.'"

Schwendeman admits that the hard part of being an organizer is developing the industrial contacts. In his experience, leads generated by Rensselaer's University Relations Office or other parts of its administration seldom panned out. Informal connections through colleagues, ex-students, friends, and so on were more fruitful.

Monk emphasized that a department's success in organizing an industrial program depends on commitment: "You need three or four dedicated faculty like Rich Braun and Pam Cook." In order to support its untenured colleagues who became involved in this program, the Delaware mathematics faculty specifically revised its departmental tenure and promotion language to recognize the value of work with industry.

The range of industrial problems, university programs, and personal experiences recounted during the workshop is persuasive evidence that there is no single prescription for successful interaction between academic mathematicians and industry. The individuals and organizations involved need to borrow and create the approaches that are best for their own circumstances.