31,371 research outputs found
Simply modified GKL density classifiers that reach consensus faster
The two-state Gacs-Kurdyumov-Levin (GKL) cellular automaton has been a staple
model in the study of complex systems due to its ability to classify binary
arrays of symbols according to their initial density. We show that a class of
modified GKL models over extended neighborhoods, but still involving only three
cells at a time, achieves comparable density classification performance but in
some cases reach consensus more than twice as fast. Our results suggest the
time to consensus (relative to the length of the CA) as a complementary measure
of density classification performance.Comment: Short note, 3 pages, 1 table, 2 composite figures, 18 reference
Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density
We investigate the sensitivity of the composite cellular automaton of H.
Fuk\'{s} [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density
classification performance of the resulting probabilistic cellular automaton
(PCA) numerically. We conclude that the composite PCA performs the density
classification task reliably only up to very small levels of noise. In
particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an
imperfect classifier, for any level of noise. While the original composite CA
is nonergodic, analyses of relaxation times indicate that its noisy version is
an ergodic automaton, with the relaxation times decaying algebraically over an
extended range of parameters with an exponent very close (possibly equal) to
the mean-field value.Comment: Typeset in REVTeX 4.1, 5 pages, 5 figures, 2 tables, 1 appendix.
Version v2 corresponds to the published version of the manuscrip
Electromagnetic surface wave propagation in a metallic wire and the Lambert function
We revisit the solution due to Sommerfeld of a problem in classical
electrodynamics, namely, that of the propagation of an electromagnetic axially
symmetric surface wave (a low-attenuation single TM mode) in a
cylindrical metallic wire, and his iterative method to solve the transcendental
equation that appears in the determination of the propagation wave number from
the boundary conditions. We present an elementary analysis of the convergence
of Sommerfeld's iterative solution of the approximate problem and compare it
with both the numerical solution of the exact transcendental equation and the
solution of the approximate problem by means of the Lambert function.Comment: REVTeX double column, 9 pages, 3 figures, minor differences between
v3 and published version; "Editor's Pick" for June 2019 edition of AJ
Near-Rationality, Heterogeneity and Aggregate Consumption
The simple permanent income model provides a good description of the medium-long run behavior of aggregate nondurables consumption, while it fails in describing its short run behavior. In this paper I present a non-representative agent model with near-rational microeconomic units that simultaneously explains the observed excess smoothness of consumption to wealth innovations, the excess sensitivity of consumption to lagged income changes, as well as small conditional asymmetries found in the data. In spite of the presence of large non-diversifiable idiosyncratic uncertainty, the estimated dollar equivalent utility cost of the micreconomic near-rational strategy required to explain the aggregate facts is only 0.26y percent of consumption per year, where y is the coefficient of relative risk aversion.
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