5 research outputs found
Chaotic Crystallography: How the physics of information reveals structural order in materials
We review recent progress in applying information- and computation-theoretic
measures to describe material structure that transcends previous methods based
on exact geometric symmetries. We discuss the necessary theoretical background
for this new toolset and show how the new techniques detect and describe novel
material properties. We discuss how the approach relates to well known
crystallographic practice and examine how it provides novel interpretations of
familiar structures. Throughout, we concentrate on disordered materials that,
while important, have received less attention both theoretically and
experimentally than those with either periodic or aperiodic order.Comment: 9 pages, two figures, 1 table;
http://csc.ucdavis.edu/~cmg/compmech/pubs/ChemOpinion.ht
Reductions of Hidden Information Sources
In all but special circumstances, measurements of time-dependent processes
reflect internal structures and correlations only indirectly. Building
predictive models of such hidden information sources requires discovering, in
some way, the internal states and mechanisms. Unfortunately, there are often
many possible models that are observationally equivalent. Here we show that the
situation is not as arbitrary as one would think. We show that generators of
hidden stochastic processes can be reduced to a minimal form and compare this
reduced representation to that provided by computational mechanics--the
epsilon-machine. On the way to developing deeper, measure-theoretic foundations
for the latter, we introduce a new two-step reduction process. The first step
(internal-event reduction) produces the smallest observationally equivalent
sigma-algebra and the second (internal-state reduction) removes sigma-algebra
components that are redundant for optimal prediction. For several classes of
stochastic dynamical systems these reductions produce representations that are
equivalent to epsilon-machines.Comment: 12 pages, 4 figures; 30 citations; Updates at
http://www.santafe.edu/~cm
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Chaotic Crystallography: How the physics of information reveals structural order in materials
We review recent progress in applying information- and computation-theoretic
measures to describe material structure that transcends previous methods based on exact
geometric symmetries. We discuss the necessary theoretical background for this new toolset
and show how the new techniques detect and describe novel material properties. We discuss
how the approach relates to well known crystallographic practice and examine how it
provides novel interpretations of familiar structures. Throughout, we concentrate on
disordered materials that, while important, have received less attention both theoretically
and experimentally than those with either periodic or aperiodic order
Understanding and Designing Complex Systems: Response to "A framework for optimal high-level descriptions in science and engineering---preliminary report"
We recount recent history behind building compact models of nonlinear, complex
processes and identifying their relevant macroscopic patterns or "macrostates". We give a
synopsis of computational mechanics, predictive rate-distortion theory, and the role of
information measures in monitoring model complexity and predictive performance.
Computational mechanics provides a method to extract the optimal minimal predictive model
for a given process. Rate-distortion theory provides methods for systematically
approximating such models. We end by commenting on future prospects for developing a
general framework that automatically discovers optimal compact models. As a response to the
manuscript cited in the title above, this brief commentary corrects potentially misleading
claims about its state space compression method and places it in a broader historical
setting