Quantitative neuroscience: Models, algorithms, diagnostics, and therapeutic applications

Advances in the field of signal processing, nonlinear dynamics, statistics, and optimization theory, combined with marked improvement in instrumentation and development of computer systems, have made it possible to apply the power of mathematics to the task of understanding the human brain. This veritable revolution has already 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 techniques developed for the study of complex nonlinear systems and chaos are already being used to explore the complex nonlinear dynamics of human brain physiology. 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 function as well as the affects of diseases such as epilepsy, sleep disorders, movement disorders, and cognitive disorders that affect millions of people every year. Application of these powerful tools to the study of the human brain requires, by necessity, collaboration among scientists, engineers, neurobiologists and clinicians. Each discipline brings to the table unique knowledge, unique approaches to problem solving, and a unique language.