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Advances in the field of signal processing, nonlinear dynamics, statistics, and optimization theory, combined with marked improvement in instrumenta- tion and development of computers systems, have made it possible to apply the power of mathematics to the task of understanding the human brain. This verita- ble revolution already has resulted in widespread availability of high resolution neuroimaging devices in clinical as well as research settings. Breakthroughs in functional imaging are not far behind. Mathematical tech- niques developed for the study of complex nonlinear systems and chaos already are being used to explore the complex nonlinear dynamics of human brain phys- iology. Global optimization is being applied to data mining expeditions in an effort to find knowledge in the vast amount of information being generated by neuroimaging and neurophysiological investigations. These breakthroughs in the ability to obtain, store and analyze large datasets offer, for the first time, exciting opportunities to explore the mechanisms underlying normal brain func- tion as well as the affects of diseases such as epilepsy, sleep disorders, movement disorders, and cognitive disorders that affect millions of people every year. Ap- plication of these powerful tools to the study of the human brain requires, by necessity, collaboration among scientists, engineers, neurobiologists and clini- cians. Each discipline brings to the table unique knowledge, unique approaches to problem solving, and a unique language.