Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an e-machine--is the minimal one consistent with accurate prediction. We establish several results on e-machine...

It has been well-known since the pioneering work of Claude Shannon in the 1940s that a message transmitted with optimal efficiency over a channel of limited bandwidth is indistinguishable from random noise to a receiver who is unfamiliar with the language in which the message is written. In this...

A criterion based on conditional probabilities, related to the concept of algorithmic distance, is used to detect correlated mutations at noncontiguous sites on sequences. We apply this criterion to the problem of analyzing correlations between sites in protein sequences, however, the analysis...

We compare and contrast three different, but complementary views of "structure" and "pattern" in spatial processes. For definiteness and analytical clarity we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions....

We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the L tetromino, and the T tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each of these. For the T tetromino, we also derive a lower...