47,661 research outputs found
Kolmogorov complexity spectrum for use in analysis of UV-B radiation time series
We have used the Kolmogorov complexity and sample entropy measures to
estimate the complexity of the UV-B radiation time series in the Vojvodina
region (Serbia) for the period 1990-2007. We defined the Kolmogorov complexity
spectrum and have introduced the Kolmogorov complexity spectrum highest value
(KLM). We have established the UV-B radiation time series on the basis of their
daily sum (dose) for seven representative places in this region using (i)
measured data, (ii) data calculated via a derived empirical formula and (iii)
data obtained by a parametric UV radiation model. We have calculated the
Kolmogorov complexity (KL) based on the Lempel-Ziv Algorithm (LZA), KLM and
Sample Entropy (SE) values for each time series. We have divided the period
1990-2007 into two sub-intervals: (a) 1990-1998 and (b)1999-2007 and calculated
the KL, KLM and SE values for the various time series in these sub-intervals.
It is found that during the period 1999-2007, there is a decrease in the KL,
KLM and SE, comparing to the period 1990-1998. This complexity loss may be
attributed to (i) the increased human intervention in the post civil war period
causing increase of the air pollution and (ii) the increased cloudiness due to
climate changes.Comment: 10 pages, 1 figure, 1 table. arXiv admin note: substantial text
overlap with arXiv:1301.2039; This paper has been accepted in Modern Physics
Letters B on Aug 14, 201
Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy
We develop information-theoretic measures of spatial structure and pattern in
more than one dimension. As is well known, the entropy density of a
two-dimensional configuration can be efficiently and accurately estimated via a
converging sequence of conditional entropies. We show that the manner in which
these conditional entropies converge to their asymptotic value serves as a
measure of global correlation and structure for spatial systems in any
dimension. We compare and contrast entropy-convergence with mutual-information
and structure-factor techniques for quantifying and detecting spatial
structure.Comment: 11 pages, 5 figures,
http://www.santafe.edu/projects/CompMech/papers/2dnnn.htm
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Factorization and escorting in the game-theoretical approach to non-extensive entropy measures
The game-theoretical approach to non-extensive entropy measures of
statistical physics is based on an abstract measure of complexity from which
the entropy measure is derived in a natural way. A wide class of possible
complexity measures is considered and a property of factorization investigated.
The property reflects a separation between the system being observed and the
observer. Apparently, the property is also related to escorting. It is shown
that only those complexity measures which are connected with Tsallis entropy
have the factorization property.Comment: 7 pages, revtex4. For NEXT2005 proceeding
The Ambiguity of Simplicity
A system's apparent simplicity depends on whether it is represented
classically or quantally. This is not so surprising, as classical and quantum
physics are descriptive frameworks built on different assumptions that capture,
emphasize, and express different properties and mechanisms. What is surprising
is that, as we demonstrate, simplicity is ambiguous: the relative simplicity
between two systems can change sign when moving between classical and quantum
descriptions. Thus, notions of absolute physical simplicity---minimal structure
or memory---at best form a partial, not a total, order. This suggests that
appeals to principles of physical simplicity, via Ockham's Razor or to the
"elegance" of competing theories, may be fundamentally subjective, perhaps even
beyond the purview of physics itself. It also raises challenging questions in
model selection between classical and quantum descriptions. Fortunately,
experiments are now beginning to probe measures of simplicity, creating the
potential to directly test for ambiguity.Comment: 7 pages, 6 figures, http://csc.ucdavis.edu/~cmg/compmech/pubs/aos.ht
Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction
Virtually all questions that one can ask about the behavioral and structural
complexity of a stochastic process reduce to a linear algebraic framing of a
time evolution governed by an appropriate hidden-Markov process generator. Each
type of question---correlation, predictability, predictive cost, observer
synchronization, and the like---induces a distinct generator class. Answers are
then functions of the class-appropriate transition dynamic. Unfortunately,
these dynamics are generically nonnormal, nondiagonalizable, singular, and so
on. Tractably analyzing these dynamics relies on adapting the recently
introduced meromorphic functional calculus, which specifies the spectral
decomposition of functions of nondiagonalizable linear operators, even when the
function poles and zeros coincide with the operator's spectrum. Along the way,
we establish special properties of the projection operators that demonstrate
how they capture the organization of subprocesses within a complex system.
Circumventing the spurious infinities of alternative calculi, this leads in the
sequel, Part II, to the first closed-form expressions for complexity measures,
couched either in terms of the Drazin inverse (negative-one power of a singular
operator) or the eigenvalues and projection operators of the appropriate
transition dynamic.Comment: 24 pages, 3 figures, 4 tables; current version always at
http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt1.ht
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