6,033 research outputs found
Two-dimensional cellular automata and the analysis of correlated time series
Correlated time series are time series that, by virtue of the underlying
process to which they refer, are expected to influence each other strongly. We
introduce a novel approach to handle such time series, one that models their
interaction as a two-dimensional cellular automaton and therefore allows them
to be treated as a single entity. We apply our approach to the problems of
filling gaps and predicting values in rainfall time series. Computational
results show that the new approach compares favorably to Kalman smoothing and
filtering
Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems
Most current methods for identifying coherent structures in
spatially-extended systems rely on prior information about the form which those
structures take. Here we present two new approaches to automatically filter the
changing configurations of spatial dynamical systems and extract coherent
structures. One, local sensitivity filtering, is a modification of the local
Lyapunov exponent approach suitable to cellular automata and other discrete
spatial systems. The other, local statistical complexity filtering, calculates
the amount of information needed for optimal prediction of the system's
behavior in the vicinity of a given point. By examining the changing
spatiotemporal distributions of these quantities, we can find the coherent
structures in a variety of pattern-forming cellular automata, without needing
to guess or postulate the form of that structure. We apply both filters to
elementary and cyclical cellular automata (ECA and CCA) and find that they
readily identify particles, domains and other more complicated structures. We
compare the results from ECA with earlier ones based upon the theory of formal
languages, and the results from CCA with a more traditional approach based on
an order parameter and free energy. While sensitivity and statistical
complexity are equally adept at uncovering structure, they are based on
different system properties (dynamical and probabilistic, respectively), and
provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv
requirements; write first author for higher-resolution version
Emerging properties of financial time series in the “Game of Life”
We explore the spatial complexity of Conway’s “Game of Life,” a prototypical cellular automaton by means of a geometrical procedure generating a two-dimensional random walk from a bidimensional lattice with periodical boundaries. The one-dimensional projection of this process is analyzed and it turns out that some of its statistical properties resemble the so-called stylized facts observed in financial time series. The scope and meaning of this result are discussed from the viewpoint of complex systems. In particular, we stress how the supposed peculiarities of financial time series are, often, overrated in their importance
Quantum Cellular Automata
Quantum cellular automata (QCA) are reviewed, including early and more recent
proposals. QCA are a generalization of (classical) cellular automata (CA) and
in particular of reversible CA. The latter are reviewed shortly. An overview is
given over early attempts by various authors to define one-dimensional QCA.
These turned out to have serious shortcomings which are discussed as well.
Various proposals subsequently put forward by a number of authors for a general
definition of one- and higher-dimensional QCA are reviewed and their properties
such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of
Complexity and Systems Scienc
Parrondo games as lattice gas automata
Parrondo games are coin flipping games with the surprising property that
alternating plays of two losing games can produce a winning game. We show that
this phenomenon can be modelled by probabilistic lattice gas automata.
Furthermore, motivated by the recent introduction of quantum coin flipping
games, we show that quantum lattice gas automata provide an interesting
definition for quantum Parrondo games.Comment: 12 pages, plain TeX, 10 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages); for related work see
http://math.ucsd.edu/~dmeyer/research.htm
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