We are requesting the continuation of a training program in theoretical neuroscience with funds to support 4 predoctoral trainees. Our goal is to train students who combine exceptional skills in mathematics, statistics, modeling and machine learning with a deep understanding of neurobiology. The complexity of neural systems and of the data that we can now obtain demands researchers with these skills if we are to realize the neuroscience community's goals of achieving a mechanistic understanding of nervous system function and making significant progress in the treatment of neural disorders and mental illness. Training will occur at the Center for Theoretical Neuroscience at Columbia University, supported by the 6 faculty at the Center, faculty visitors to the Center, and 26 other faculty from the Departments of Neuroscience, Psychology, Biology, Biochemistry, Biomedical Engineering, and Statistics at Columbia. The Theory Center provides an exceptional environment in which pre-doctoral, post-doctoral and faculty researchers interact and collaborate extensively both within the Center and with researchers in experimental laboratories. Most trainees are members of the Columbia graduate program in Neurobiology and Behavior (with a small number drawn from other graduate programs) and take the courses that satisfy the requirements of that program. The required courses are augmented by a large selection of electives, including courses in theoretical neuroscience, statistics and machine learning. The goal of this training program is twofold: 1) To produce theoreticians who combine outstanding skills in analysis and model-building with a deep understanding and "sense" of biological neuroscience; and 2) To train experimentalist who are skilled at applying theoretical and computational methods in their research. This will be accomplished through extensive collaborations with outstanding experimental laboratories both at Columbia and elsewhere combined with training in state-of-the art theoretical methods. Whenever possible, students will be co-advised by both a member of the Theory Center faculty and a researcher from our associated experimental faculty, and they will be given desk space both in the Theory Center and in the laboratory of their experimental co-advisor. The opportunity to be involved in the operations of an outstanding laboratory and in the activities and intellectual atmosphere of a world-class theory center provides an exceptional training experience.