The principle goal of computational mechanics is to define pattern and structure so that the
organization of complex systems can be detected and quantified. Computational mechanics …

Erwin Schrödinger famously and presciently ascribed the vehicle transmitting the hereditary
information underlying life to an 'aperiodic crystal'. We compare and contrast this, only later …

Renewal processes are broadly used to model stochastic behavior consisting of isolated
events separated by periods of quiescence, whose durations are specified by a given …

Recurrent networks are trained to memorize their input better, often in the hopes that such
training will increase the ability of the network to predict. We show that networks designed to …

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 …

Decomposing a complicated system into its constituent parts—reductionism—is one of
science's most powerful strategies for analysis and understanding. Large-scale systems with …

This article reviews the Markov theoretic description of one-dimensional aperiodic crystals,
describing the stacking-faulted crystal polytype as a special case of an aperiodic crystal …

This is the second contribution in a series of papers dealing with dynamical models in
equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status …

Extrinsic faulting has been discussed previously within the so-called difference method and
random walk calculation. In this contribution it is revisited under the framework of …

A mathematical framework is presented to represent turbostratic disorder in materials like
carbon blacks, smectites and twisted n-layer graphene. In particular, the set of all possible …