We analyze how difficult it is to synchronize to a periodic sequence whose structure is known, when an observer is initially unaware of the sequence's phase. We examine the transient information T, a recently introduced information-theoretic quantity that measures the uncertainty an observer...

Using an information-theoretic framework, we examine how an intelligent agent, given an accurate model of its environment, synchronizes to the environment — i.e., comes to know in which state the environment is. We show that the total uncertainty experienced by the agent during the process is...

We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its environment. We introduce natural measures of the...

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to stochastic and deterministic processes by using a...

We critique the measure of complexity introduced by Shiner, Davison, and Landsberg in Ref. [1]. In particular, we point out that it is over-universal, in the sense that it has the same dependence on disorder for structurally distinct systems. We also point out a misinterpretation of a result...

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 review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, L\`opez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another measure of statistical complexity $C_{\rm LMC}$ that, like...

We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second, statistical complexity, measures the amount of memory...