Math study may make complex problems easier to solve Published June 29, 2006 By William J. Sharp Air Force Office of Scientific Research Public Affairs ARLINGTON, Va. -- The Air Force Office of Scientific Research here recently began funding a new research area that includes a number of studies involving computational math. The new area, formally launched at a meeting with AFOSR principal investigators at Syracuse University, Syracuse, N.Y., is entitled Information Forensics and Process Integration. The overall portfolio of projects consists of three areas of research emphasis – incomplete information and metrics; search, interactive design, and active querying; and cognitive processing. Dr. Carla Gomes, a professor in the computing and information science, applied economics and management, and computer science departments, Cornell University, N.Y., is a member of one of the many teams funded by AFOSR to employ computational math studies. The team’s approximate $5 million, 5-year-long project is entitled “Intelligent Information Systems Institute.” Dr. Gomes, who is director of the institute, said the institute seeks to help break down problems and foster new ideas. To do this, the institute combines approaches and faculty from different disciplines such as operations research, math, computer science, physics, and more. Networks, she explained, are complex problem solvers, processors, and distributors of information. “Mathematically speaking, in a very basic sense, a network can be viewed as collection of nodes and a set of arcs or links connecting the nodes” Dr. Gomes said. “In this sense, networks are everywhere. A good example of a network is the World Wide Web. The nodes correspond to the Web pages and the arcs correspond to the hyperlinks between the Web pages.” Other network examples include airlines, power grids, and friends, she said. Problems, Dr. Gomes explained, from the simple to the complex, have critical nodes or variables which are key to solving the problems. “If you can figure out what the critical nodes are, you can solve the problems,” she said. A key issue, Dr. Gomes said, is to identify the ‘back doors’ that most problems have. A back door could be, for example, a solution that is available but has been overlooked. “Once you identify critical nodes, computational math can be used to solve various problems. “What our research has shown so far is a number of problems have just a few critical nodes. If you get them right, the rest is easily solved. That’s where computational math can help,” Dr. Gomes said. Dr. Gomes explained the institute model for problem solving can be applied to a wide variety of areas to include scheduling, transportation, and social network systems.