2,586 research outputs found
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
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
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
Efficient generation of random derangements with the expected distribution of cycle lengths
We show how to generate random derangements efficiently by two different
techniques: random restricted transpositions and sequential importance
sampling. The algorithm employing restricted transpositions can also be used to
generate random fixed-point-free involutions only, a.k.a. random perfect
matchings on the complete graph. Our data indicate that the algorithms generate
random samples with the expected distribution of cycle lengths, which we
derive, and for relatively small samples, which can actually be very large in
absolute numbers, we argue that they generate samples indistinguishable from
the uniform distribution. Both algorithms are simple to understand and
implement and possess a performance comparable to or better than those of
currently known methods. Simulations suggest that the mixing time of the
algorithm based on random restricted transpositions (in the total variance
distance with respect to the distribution of cycle lengths) is
with and the length of the
derangement. We prove that the sequential importance sampling algorithm
generates random derangements in time with probability of
failing.Comment: This version corrected and updated; 14 pages, 2 algorithms, 2 tables,
4 figure
- …