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Profile of David W. McLaughlin
When applied mathematician David W. McLaughlin arrived as a freshman at Creighton University (Omaha, NE), his guidance counselor greeted him with a curious statement. “I assume you are going to try to get a Ph.D.,” the counselor told the young McLaughlin, whom he had just met. The remark was surprising to McLaughlin, because he had grown up in smalltown Iowa in the 1950s, where graduate college degrees were not common. “I was so taken aback. That really changed my perspective, as strange as that might sound,” says McLaughlin, who took the assumption to heart and went on to earn a doctorate in physics. “I have no idea why he said that, but it was effective.”
Today, McLaughlin is a professor of Mathematics and Neural Science at New York University (NYU), as well as the university's provost. Elected to the National Academy of Sciences in 2002, McLaughlin has spent his career developing mathematical models of complex and chaotic systems, with applications from laser beams to the behavior of the visual cortex. His Inaugural Article, published in a recent issue of PNAS (1), describes a model of neurons in a single layer of the primary visual cortex, which is of sufficient lateral extent to describe certain preattentive optical illusions.
Starting from First Principles
Before toying with mathematical equations in college, McLaughlin played sports—baseball, basketball, football, and track—and performed music in high school. His father sold gas to farmers in Woodbine, his hometown of 1,300 people in western Iowa. A college degree earned by an uncle was the only higher education in his immediate family. McLaughlin's parents supported their son's intellectual development, however, and McLaughlin always assumed that college would be part of his life. He chose to attend Creighton University, where he met his wife, Ruth Aubuchon, an artist and mother to their four children.
At Creighton, McLaughlin played the trumpet in the school orchestra but dropped his athletic activities in favor of a double major in physics and mathematics. The intellectual atmosphere of the university resonated with McLaughlin's inclinations, and he discovered a love and talent for science while there. He soon set a course for graduate school. The physics program at Indiana University (Bloomington) had a mathematical emphasis that appealed to McLaughlin, and he applied to the doctoral program there. In 1966, he graduated summa cum laude from Creighton and moved to Indiana University for graduate school.
At Indiana, McLaughlin studied theoretical physics with Larry Schulman, a rising mathematical physicist not much older than his students. Schulman's work focused on path integrals, a function–space integration method useful for representing solutions of the Schrödinger equation. The Schrödinger equation, the fundamental equation of quantum mechanics, describes how the wave function of a physical system evolves over time. Schulman's and McLaughlin's approach applied asymptotic methods to function–space integrals (2, 3). This approach required a rigor and clarity that appealed to McLaughlin. “I liked being able to derive things from first principles in a very logically selfconsistent way,” he says.
A Glimpse of Intensity
McLaughlin received his doctorate in physics in 1971 and moved to NYU as an assistant professor in mathematics. He was recruited by Joseph Keller, a member of the National Academy of Sciences and one of the leading applied mathematicians worldwide. Keller was interested in asymptotic methods of the sort studied by McLaughlin and Schulman. This interest was fortunate, McLaughlin says, because few jobs were available in physics at the time, and many of McLaughlin's graduateschool colleagues were forced to leave physics and sometimes even science altogether. Keller's interest allowed McLaughlin to continue the research pursuits he had begun in graduate school (4).
At NYU, Keller's large group of young applied mathematicians taught at the Heights campus (Bronx, NY) and pursued research in the Courant Institute at the Washington Square campus in New York. They enjoyed a passionate collaborative environment, McLaughlin says, and were guided by Keller's deep intelligence, personality, and leadership. “Joining that group and seeing the level of intensity that could be brought to research in applied mathematics on problems that were important for science—it completely changed my view of research,” McLaughlin says.
In 1972, however, NYU announced the sale of its Heights campus, and the researchers in Keller's group dispersed to other positions nationwide. “We are still close friends and colleagues today,” says McLaughlin, “and almost without exception, each continues to work intensively in applied mathematics.” McLaughlin accepted an assistant professor position in mathematics at Iowa State University (Ames) in 1972. After 2 years, he accepted an associate professor position at the University of Arizona (Tucson), which was building an applied mathematics group. McLaughlin was attracted to the university's nonlinear optics center and its substantial theoretical component.
Multidisciplinary Goals
McLaughlin remained at the University of Arizona for 15 years. He served as chairman of the applied mathematics program and also as codirector of the Arizona Air Force Office of Scientific Research (AFOSR) Center of Math Sciences. During this time, McLaughlin helped expand interdisciplinary research in applied mathematics. “Today, mathematics and computational science can really play a major role toward the solution of many of the problems in science,” he says, “and so I firmly believe that young people who are skilled in mathematics should have the opportunity to work on not only mathematical problems, but also on problems at the forefront of science.”
After leaving Arizona in 1989, McLaughlin joined Princeton University (Princeton, NJ) as a professor of mathematics. In his 5 years at Princeton, McLaughlin spent the last 2 years as the director of the applied and computational mathematics program. He then returned to NYU in 1994 to serve as director of the Courant Institute, where he had started his career 24 years previously.
At Courant, McLaughlin focused on faculty recruitment in a variety of fields, especially in mathematics, applied mathematics, computational science, and computer science. He was also involved in helping the faculty form new interdisciplinary programs, which included atmosphere ocean studies, financial mathematics, multimedia technology, and computational biology.
In 2002, McLaughlin was appointed as provost of NYU, a position he currently occupies. “By far the most interesting part of the provost job is that you interact with scholars from across the university. You get a glimpse of scholars and their work in the humanities, in law, in public policy, in medicine, in the business world, in the arts, in the sciences, and in the social sciences,” he says.
Collective, Coherent, and Chaotic
Throughout most of McLaughlin's career, his work has been largely collaborative as an applied mathematician working with scientists. “Whatever successes my work has enjoyed have been due in large part to these collaborations,” he says. From his earliest research days, McLaughlin's interests have revolved around mathematical models of complex systems. He has been especially interested in nonlinear dispersive waves, which occur in physical and natural systems where wave dissipation is weak (5), such as in nonlinear optics.
McLaughlin is intrigued by the mathematical properties of solutions to these equations, especially in how the collective behavior of a system's individual components can be seen in properties of the solutions. His work has centered on how individual elements can collectively produce coherent behavior (6, 7), chaotic behavior (8⇓–10), and dispersive wave turbulence (11, 12). “My work in nonlinear waves, which I worked on from 1972 until 2000, is one place where that interplay of the collective, the coherent, and the chaotic was realized in a very beautiful and crisp way,” he says.
When McLaughlin first became interested in nonlinear waves, the field was rapidly changing. “Whether you were using numerical experiments or different forms of mathematical analysis, the mathematical technology that was becoming available to us at that time was unveiling rich, striking properties of these nonlinear wave equations,” he says. “It was a very, very exciting time when one could extract from the equations such a clear description of their qualitative behaviors. There was a lot of excitement as these new properties were being discovered and understood.”
For roughly the first two decades of his career as an applied mathematician, McLaughlin collaborated mostly with physicists and other physical scientists. At Courant, however, he began working in the field of neuroscience. McLaughlin teamed with Robert Shapley, a visual neuroscientist at NYU's Center for Neural Science, to form a working group of researchers focused on the interface between mathematics and neuroscience. Gradually McLaughlin moved his application area from the physical sciences to visual neuroscience, where most of his research work is done today.
Parallel Advances
The field of neuroscience holds many examples of large systems with complex behavior. McLaughlin studies how information is processed by the visual cortex, where many neurons work together collectively. “It's becoming more and more clear that there are coherent aspects to the system's response, and there are chaotic, noisy, fluctuating aspects to the system's response. The two are fundamentally coupled,” he says.
“The most interesting part of the provost job is that you interact with scholars from across the university.”
McLaughlin's PNAS Inaugural Article focuses on the primary visual cortex, the “front end” of the visual system and the first area along the brain's visual pathway in which significant cortical processing occurs (1, 13⇓–15). “It's very much a frontend study, but it's a study where you have to understand the biology of the cortical system in order to model it,” he says.
McLaughlin's visual neuroscience research has benefited from advances in technology. For example, in the experimental arena, advances in optical imaging with special voltagesensitive dyes (16, 17) can allow for high spatial and temporal resolution of cortical responses in cats and monkeys. This high resolution allows researchers a “collective glimpse” of how the front end of the visual system responds to visual stimulation. “Instead of looking at the response of individual neurons, neuroscientists actually look at the finescale temporal response of several millimeters of cortical area, which was not possible 15 years ago,” he says.
McLaughlin's work also relies on technological advances in computational algorithms. “Those advances have enabled us to model, quite realistically, the same several millimeters of cortical area that the optical imaging can access,” he says. “What is so exciting about our recent work in cortical modeling is that it's relevant to the most recent experimental observations in optical imaging. You have the ability to compare the outputs of the model with the outputs of these optical imaging methods in a very natural way.” In biology, technological advances often lead to striking experimental observations, McLaughlin points out, and “the same is true about software algorithms. It's technological advances in the software algorithms that often lead to striking theoretical discoveries. This parallel between the technology and the science, the fact that there is a technology on the theoretical side as well as a technology on the experimental side, is a point that this particular Inaugural Article really illustrates,” he says.
These cortical systems are large and complex, McLaughlin says, containing both excitatory and inhibitory neurons and with temporal fluctuations rather than a steady signal dominating the neural response. Recurrent interactions between neurons accentuate their collective behavior and change how neurons behave collectively versus individually (18). In his Inaugural Article, McLaughlin and his colleagues David Cai and Aaditya Rangan use new computational algorithms to represent the dynamic behavior of the complex cortical system in response to visual stimuli. This stimulation results in a striking optical illusion, the “linemotion illusion,” in which certain static stimuli are perceived as moving. Although these features all exist on the front end and for single layers of neurons, interactions between layers of neurons and between regions of neurons also exist, adding further complexity to the overall visual system.
McLaughlin wants next to incorporate such additional neural layers into the model, exemplifying yet again his careerlong application of mathematics to the study of highly complex systems. This future research focus illustrates his unabated interdisciplinary drive for scientific understanding. From smalltown Iowa to bigcity New York, McLaughlin has remained dedicated to his research, and his passion for multidisciplinary study continues to contribute knowledge to diverse corners of the scientific world.
Footnotes

This is a Profile of a recently elected member of the National Academy of Sciences to accompany the member's Inaugural Article on page 18793 in issue 52 of volume 102.
 © 2006 by The National Academy of Sciences of the USA
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