210 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
Numerical evidence against a conjecture on the cover time of planar graphs
We investigate a conjecture on the cover times of planar graphs by means of
large Monte Carlo simulations. The conjecture states that the cover time
of a planar graph of vertices and maximal degree
is lower bounded by with , with equality holding for some geometries. We tested this
conjecture on the regular honeycomb (), regular square (), regular
elongated triangular (), and regular triangular () lattices, as well
as on the nonregular Union Jack lattice (, ).
Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as
an equality for most of these lattices, with an interesting issue in the case
of the Union Jack lattice. The data for the honeycomb lattice, however,
violates the bound with the conjectured constant. The empirical probability
distribution function of the cover time for the square lattice is also briefly
presented, since very little is known about cover time probability distribution
functions in general.Comment: Typeset in RevTEX 4.1, 4 pages, 3 figure
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