Over 800 people attended the 2005 annual meeting of the Society for Industrial and Applied Mathematics (SIAM) in New Orleans, July 11-15. Hurricane Dennis had little effect on New Orleans, but it did affect other areas in the southeastern U.S., and caused some people to change their travel plans. Below are descriptions of some of the events that took place at the meeting.
Simulation-Based Medicine: Predicting Outcomes of Cardiovascular Interventions, Charles A. Taylor, Stanford University
Cardiovascular disease is the leading cause of death in industrialized nations and is predicted to be the leading cause of death in developing nations by 2010. Yet there are few tools to predict outcomes of techniques such as bypass surgery or angioplasty. Taylor spoke about modeling blood flow and the challenges associated with creating good models of blood flow. There is a great deal of data collected from a patient, so that eventually that data could be used to form pre-operative models, plan a medical intervention, and then simulate the effects of the intervention.
New "Dimensions" in Genome Annotation, Bernhard Palsson, University of California, San Diego
The sequencing of the human genome is one-dimensional in nature, even though it was a monumental task. Palsson explained other dimensions involved in our genome and those of other organisms. Most of the talk dealt with problems in two dimensions, essentially reconstructing biological networks using graphs and matrices. In this case, the topological properties of the networks are not as important as their functional states. To illustrate this point, Palsson used the analogy of a city's road map: Its topological properties are the same at 4 a.m. and 4 p.m., yet the behavior of the transportation system at the two times is likely to be very different. In regard to other dimensions, Palsson said that genomes are curled-up three-dimensional structures, and as they change in time their study incorporates four dimensions.
Past President's Address: How Mathematical Modeling and Analysis Impacts Our Lives, Mac Hyman, Los Alamos National Laboratory
In this address, former SIAM president Mac Hyman gave several examples of applications of mathematics to weather, biology, design, hardware, and software. Hurricanes were on the minds of many attendees and Hyman stated that evacuating a mile of coastline in the U.S. costs $1 million a day. Better weather and climate models would lead to better forecasting and more effective evacuations. Hyman also noted how math has been used to build models of power grids for phased-in resumption of service after a hurricane. He pointed out how a model was very successful restoring power after Hurricane Jeanne in 2004. Hyman is involved in the TRANSIMS model which uses vast amounts of data gathered from residents of Portland, Oregon to model movement in a city. One of the many uses of TRANSIMS is modeling the spread of disease in a city. Researchers found that individuals changing their habits (such as electing to say inside) during an outbreak is one of the most effective ways of controlling an epidemic. Previous outbreak models had to assume that individual behavior remained unchanged during an outbreak. Hyman finished his address with a description of the changes in computer hardware over the years and said that if other goods' costs had decreased as much as the cost of computing power, then it would now be feasible to heat our homes with peanut butter.
The John von Neumann Lecture: Geometry and Computational Dynamics, Jerrold E. Marsden, California Institute of Technology
Marsden began his lecture with two observations: His von Neumann number is 3 (his Erdős number is 4) and while a graduate student at Princeton, he tutored the son of Oskar Morgenstern, who was von Neumann's collaborator on game theory. The majority of the lecture concerned Lagrangian Coherent Structures (LCS) which act like separatrices, separating particles with different dynamical behavior. In one particular example involving pollution released in Monterey Bay, the LCS were determined to be more significant than tides in how the pollution flowed in the bay. One future direction is to apply LCS to three dimensions, so that a phenomenon like upwelling could be modeled. Other future applications of LCS are to the cardiovascular system and to the atmosphere. (Image of Monterey Bay courtesy of Jerrold E. Marsden.)
Draping, Wrinkling and Crumpling: Geometry and Physics, L. Mahadevan, Harvard University
Mahadevan gave a high-energy lecture, first noting how wrinkles form when a material drapes because the material is trying to hang perfectly vertically, but can't. He then showed wrinkling at different scales, from those in mountains to wrinkles in a gel with widths of 10-7m. Mahadevan demonstrated how wrinkles form in Saran Wrap, noting the conflict between stretching and bending. Many of the calculations used Gaussian curvature. Crumpling is much harder to model. Mahadevan concluded his talk with a verse (with apologies to Jonathan Swift):
Big crumples fold into little crumples
That store energy in bending
And little crumples have lesser crumples
And so on to stretching.
Gilbert Strang, who introduced Mahadevan, noted that he had never liked Saran Wrap and always thought that it was his fault that Saran Wrap wrinkled, but now he knew it was Gauss's fault.
Numerical Solution of Nonlinear Eigenvalue Problems: How Numerical Linear Algebra Can Make a Difference, Volker Mehrmann, Technische Universitaet Berlin
Railroad tracks are "excited" by high-speed trains so it is important to model the tracks' behavior in order to find if high-speed travel is safe. Unfortunately, the equations in the model can be intractable. One company's model was virtually useless since the accuracy of the approximation for associated eigenvalues was not correct even to one digit. Mehrmann used the structure of the equations in the model and particular linearizations to get eigenvalue approximations good to five digits. With this method, the company, which had been unable to do the required calculations, could now proceed with its program. Mehrmann's solution was so good that the company's CEO remarked, "Next time, I'm asking a mathematician first."
Control of Advanced Automotive Engines, Mrdjan Jankovic, Ford Motor Company
Jankovic explained that in modern cars, computers control the engine, transmission, brakes, traction, and deployment of air bags. Technology has enabled lower emissions--by maintaining proper air/fuel ratios--and optimized performance and fuel economy--through the addition of new devices. Gathering data to improve performance in an operating car is not feasible in all situations because some calculations can't be done fast enough for control devices to adapt, but Jankovic did show how a method he used makes sampling more efficient.
Prizes and Awards Luncheon
SIAM President Martin Golubitsky hosted this luncheon and handed out the following prizes and awards:
Cancer Modeling: Classical to Contemporary, Trachette L. Jackson, University of Michigan
Jackson described the stages a normal cell goes through to become cancerous. Models are used in each stage, but so far there is no model for the entire process. She then gave a historical look at models that have been used in modeling tumor growth. Originally models assumed that tumors had radial symmetry, which is true in lab-grown tumors, but not necessarily true of those in the body. Later models allowed for more diverse shapes but could not take into account that tumor cells are heterogeneous (nearby cells can be as different as third cousins are). Current models account for tumor cell heterogeneity and for the connections between cells and blood, which may help to explain how cells change from benign to cancerous. (Image of vascular tumor growth courtesy of Trachette L. Jackson.)
The 2006 SIAM annual meeting will be in Boston, July 10-14. A description of the 2004 SIAM annual meeting with links to descriptions of previous SIAM annual meetings is also available.