The nature of distributed computation in complex systems has often been described in terms
of memory, communication and processing. This thesis presents a complete information …

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 …

We introduce an ambidextrous view of stochastic dynamical systems, comparing their
forward-time and reverse-time representations and then integrating them into a single time …

A stochastic process' statistical complexity stands out as a fundamental property: the
minimum information required to synchronize one process generator to another. How much …

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 …

In stochastic modeling, the excess entropy--the mutual information shared between a
processes past and future--represents the fundamental lower bound of the memory needed …

The predictive information required for proper trajectory sampling of a stochastic process
can be more efficiently transmitted via a quantum channel than a classical one. This recent …

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-
off between the precision to which these quantities are approximated, and the memory …

We adapt tools from information theory to analyze how an observer comes to synchronize
with the hidden states of a finitary, stationary stochastic process. We show that …

We consider two important time scales—the Markov and cryptic orders—that monitor how an
observer synchronizes to a finitary stochastic process. We show how to compute these …