18,087 research outputs found
The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications
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 developed from efforts in the 1970s and
early 1980s to identify strange attractors as the mechanism driving weak fluid
turbulence via the method of reconstructing attractor geometry from measurement
time series and in the mid-1980s to estimate equations of motion directly from
complex time series. In providing a mathematical and operational definition of
structure it addressed weaknesses of these early approaches to discovering
patterns in natural systems.
Since then, computational mechanics has led to a range of results from
theoretical physics and nonlinear mathematics to diverse applications---from
closed-form analysis of Markov and non-Markov stochastic processes that are
ergodic or nonergodic and their measures of information and intrinsic
computation to complex materials and deterministic chaos and intelligence in
Maxwellian demons to quantum compression of classical processes and the
evolution of computation and language.
This brief review clarifies several misunderstandings and addresses concerns
recently raised regarding early works in the field (1980s). We show that
misguided evaluations of the contributions of computational mechanics are
groundless and stem from a lack of familiarity with its basic goals and from a
failure to consider its historical context. For all practical purposes, its
modern methods and results largely supersede the early works. This not only
renders recent criticism moot and shows the solid ground on which computational
mechanics stands but, most importantly, shows the significant progress achieved
over three decades and points to the many intriguing and outstanding challenges
in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations;
http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht
Numerical Techniques for Finding the Distances of Quantum Codes
We survey the existing techniques for calculating code distances of classical
codes and apply these techniques to generic quantum codes. For classical and
quantum LDPC codes, we also present a new linked-cluster technique. It reduces
complexity exponent of all existing deterministic techniques designed for codes
with small relative distances (which include all known families of quantum LDPC
codes), and also surpasses the probabilistic technique for sufficiently high
code rates.Comment: 5 pages, 1 figure, to appear in Proceedings of ISIT 2014 - IEEE
International Symposium on Information Theory, Honolul
Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning
We introduce a simple analysis of the structural complexity of
infinite-memory processes built from random samples of stationary, ergodic
finite-memory component processes. Such processes are familiar from the well
known multi-arm Bandit problem. We contrast our analysis with
computation-theoretic and statistical inference approaches to understanding
their complexity. The result is an alternative view of the relationship between
predictability, complexity, and learning that highlights the distinct ways in
which informational and correlational divergences arise in complex ergodic and
nonergodic processes. We draw out consequences for the resource divergences
that delineate the structural hierarchy of ergodic processes and for processes
that are themselves hierarchical.Comment: 8 pages, 1 figure; http://csc.ucdavis.edu/~cmg/compmech/pubs/soi.pd
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