Coursemaster: Dr. Amin Kayali
Dates: Begins Tuesday September 6, 2005 at 2pm
The course is offered for a period of 10 weeks with one session (90 minutes/session) per week.
The tools and methods of mathematics and physics have become an integral part of many disciplines including neuroscience. The theory group at the HNL is planning to offer two courses to cover mathematical and physical topics important for any individual working in scientific research with a special emphasis on concrete information processing problems in biological systems.
The first course is divided into three parts. Part one familiarizes students with some aspects of statistical mechanics. Part two covers a few concrete problems in biophysics that will introduce physical and mathematical concepts important for studying molecular signaling and biochemical networks. Part three focuses on methods useful for data analysis in many domains including independent component analysis, principal component analysis, and singular value decomposition all applied to generic problems in 'image' reconstruction.
Part II of the course will focus on information theory and inference. It will be offered in the spring.
To our knowledge, there is no single textbook that covers the material in the course. The following sources will be useful. In the early parts of the course we will follow the spirit of the course notes developed by Bill Bialek at Princeton University for a graduate course that covers biophysics and information theory with application to neural systems.
- W. Bialek, PHY562 lecture notes, Department of Physics, Princeton University, Available at "http://www.princeton.edu/~wbialek/PHY562/PHY562_home.html".
- G. Arfken and H. Weber, Mathematical Methods for Physicists. 5th edition, Academic Press, New York (2000).
- L. Reichl, A Modern Course in Statistical Physics, John Wiley & Sons Inc., New York (1998).
- A. Hyvarinen, J. Karhunen and E. Oja, Independent Component Analysis, John Wiley & Sons Inc., New York (2001).
- W. Press, S. Teukolsky, W. Vetterling and B. Flannery, Numerical Recipes in FORTRAN, CUP, New York (1992).
- L. D. Landau and E. M. Lifshitz "Statistical Physics: Part 1", Pergamon Press, Oxford (1981).
- T. Hill, "Statistical Thermodynamics", Dover Publication, New York (1987).