Professor Shields and others have recently found many new interpretations of entropy in such diverse areas as string matching in DNA analysis, prefix generation and Hausdorf dimension, recurrence and waiting time problems in probability theory, Markov order estimation, statistical problems associated with recognizing a process from its sample paths, and hypothesis testing. In his project, Professor Shields will extend and sharpen these recent results and will further develop the theoretical properties of processes which have connections with entropy. Professor Shields' work is on the interface between abstract and applied information theory. The concept of entropy, originally developed in physics, and of crucial importance for the second law of thermodynamics, is the mathematical realization of the vague idea of disorder or lack of information. This concept continues to bear fruit in many fields including those mentioned above.
