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...

We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of elementary one-dimensional cellular automaton rule 54. The CA's dominant regular domain filter is constructed to locate and classify defects in the domain....

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...

This Element develops an innovative combinatorial model of technological change and tests it with 2,000 years of data from global GDP data and US patents, thus generating the observed historical pattern of technological change. This Element models the Industrial Revolution as a combinatorial...

VanderWeele et al.'s paper is a useful contribution to the on-going scientific conversation about the detection of contagion from purely observational data. It is especially helpful as a corrective to some of the more extreme statements of Lyons (2011). Unfortunately, this paper, too, goes too...

The authors consider processes on social networks that can potentially involve three factors: homophily, or the formation of social ties due to matching individual traits; social contagion, also known as social influence; and the causal effect of an individual's covariates on his or her behavior...