What is a pattern? How do we come to recognize patterns never seen before? Quantifying
the notion of pattern and formalizing the process of pattern discovery go right to the heart of …

Stochastic processes are as ubiquitous throughout the quantitative sciences as they are
notorious for being difficult to simulate and predict. In this Letter, we propose a unitary …

We review recent progress in applying information-theoretic and computation-theoretic
measures to describe material structure that transcends previous methods based on exact …

Computational mechanics quantifies structure in a stochastic process via its causal states,
leading to the process's minimal, optimal predictor—the ϵ-machine ϵ-machine. We extend …

We introduce a Bayesian approach to discovering patterns in structurally complex
processes. The proposed method of Bayesian structural inference (BSI) relies on a set of …

We give exact formulae for a wide family of complexity measures that capture the
organization of hidden nonlinear processes. The spectral decomposition of operator-valued …

In stochastic modeling, there has been a significant effort towards finding predictive models
that predict a stochastic process' future using minimal information from its past. Meanwhile …

Power spectral densities are a common, convenient, and powerful way to analyze signals,
so much so that they are now broadly deployed across the sciences and engineering—from …

The ubiquitous nature of thermal fluctuations poses a limitation on the identification of crystal
structures. However, the trajectory of an atom carries a fingerprint of its surroundings. This …

Abstract Conway's Game of Life (GoL), a famous 2D cellular automaton (CA), is extended to
allow evolution by associating genetic information with individual live cells, that specifies …