6,102 research outputs found
The B36/S125 "2x2" Life-Like Cellular Automaton
The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D
square lattice much like Conway's Game of Life. Although it exhibits high-level
behaviour that is similar to Life, such as chaotic but eventually stable
evolution and the existence of a natural diagonal glider, the individual
objects that the rule contains generally look very different from their Life
counterparts. In this article, a history of notable discoveries in the 2x2 rule
is provided, and the fundamental patterns of the automaton are described. Some
theoretical results are derived along the way, including a proof that the speed
limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2,
respectively. A Margolus block cellular automaton that 2x2 emulates is
investigated, and in particular a family of oscillators made up entirely of 2 x
2 blocks are analyzed and used to show that there exist oscillators with period
2^m(2^k - 1) for any integers m,k \geq 1.Comment: 18 pages, 19 figure
On computational irreducibility and the predictability of complex physical systems
Using elementary cellular automata (CA) as an example, we show how to
coarse-grain CA in all classes of Wolfram's classification. We find that
computationally irreducible (CIR) physical processes can be predictable and
even computationally reducible at a coarse-grained level of description. The
resulting coarse-grained CA which we construct emulate the large-scale behavior
of the original systems without accounting for small-scale details. At least
one of the CA that can be coarse-grained is irreducible and known to be a
universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR
The rank of the semigroup of transformations stabilising a partition of a finite set
Let be a partition of a finite set . We say that a full
transformation preserves (or stabilizes) the partition
if for all there exists such that
. Let denote the semigroup of all full
transformations of that preserve the partition .
In 2005 Huisheng found an upper bound for the minimum size of the generating
sets of , when is a partition in which all of
its parts have the same size. In addition, Huisheng conjectured that his bound
was exact. In 2009 the first and last authors used representation theory to
completely solve Hisheng's conjecture.
The goal of this paper is to solve the much more complex problem of finding
the minimum size of the generating sets of , when
is an arbitrary partition. Again we use representation theory to
find the minimum number of elements needed to generate the wreath product of
finitely many symmetric groups, and then use this result to solve the problem.
The paper ends with a number of problems for experts in group and semigroup
theories
Comptonization and the Spectra of Accretion-Powered X-Ray Pulsars
Accretion-powered X-ray pulsars are among the most luminous X-ray sources in
the Galaxy. However, despite decades of theoretical and observational work
since their discovery, no satisfactory model for the formation of the observed
X-ray spectra has emerged. In this paper, we report on a self-consistent
calculation of the spectrum emerging from a pulsar accretion column that
includes an explicit treatment of the bulk and thermal Comptonization occurring
in the radiation-dominated shocks that form in the accretion flows. Using a
rigorous eigenfunction expansion method, we obtain a closed-form expression for
the Green's function describing the upscattering of monochromatic radiation
injected into the column. The Green's function is convolved with
bremsstrahlung, cyclotron, and blackbody source terms to calculate the emergent
photon spectrum. We show that energization of photons in the shock naturally
produces an X-ray spectrum with a relatively flat continuum and a high-energy
exponential cutoff. Finally, we demonstrate that our model yields good
agreement with the spectra of the bright pulsar Her X-1 and the low luminosity
pulsar X Per.Comment: 6 Pages, 2 Figures, To appear in "The Multicoloured Landscape of
Compact Objects and their Explosive Progenitors" (Cefalu, Sicily, June 2006).
Eds. L. Burderi et al. (New York: AIP
Choice mechanisms for past, temporally extended outcomes.
Accurate retrospection is critical in many decision scenarios ranging from investment banking to hedonic psychology. A notoriously difficult case is to integrate previously perceived values over the duration of an experience. Failure in retrospective evaluation leads to suboptimal outcome when previous experiences are under consideration for revisit. A biologically plausible mechanism underlying evaluation of temporally extended outcomes is leaky integration of evidence. The leaky integrator favours positive temporal contrasts, in turn leading to undue emphasis on recency. To investigate choice mechanisms underlying suboptimal outcome based on retrospective evaluation, we used computational and behavioural techniques to model choice between perceived extended outcomes with different temporal profiles. Second-price auctions served to establish the perceived values of virtual coins offered sequentially to humans in a rapid monetary gambling task. Results show that lesser-valued options involving successive growth were systematically preferred to better options with declining temporal profiles. The disadvantageous inclination towards persistent growth was mitigated in some individuals in whom a longer time constant of the leaky integrator resulted in fewer violations of dominance. These results demonstrate how focusing on immediate gains is less beneficial than considering longer perspectives.This research was supported by the Wellcome Trust Grants 095495 and 093270 and European Research Council Advanced Grant ERC-2011-AdG 293549.This is the final version. It was first published by Royal Society Publishing at http://rspb.royalsocietypublishing.org/content/282/1810/20141766
O(alpha_s^2) QCD corrections to the electroproduction of hadrons with high transverse momentum
We compute the order alpha_s^2 corrections to the one particle inclusive
electroproduction cross section of hadrons with non vanishing transverse
momentum. We perform the full calculation analytically, and obtain the
expression of the factorized (finite) cross section at this order. We compare
our results with H1 data on forward production of pi^0, and discuss the
phenomenological implications of the rather large higher order contributions
obtained in that case. Specifically, we analyze the cross section sensitivity
to the factorization and renormalization scales, and to the input fragmentation
functions, over the kinematical region covered by data. We conclude that the
data is well described by the O(alpha_s^2) predictions within the theoretical
uncertainties and without the inclusion of any physics content beyond the DGLAP
approach.Comment: 11 pages, LaTeX, 7 figure
On the numerical analysis of triplet pair production cross-sections and the mean energy of produced particles for modelling electron-photon cascade in a soft photon field
The double and single differential cross-sections with respect to positron
and electron energies as well as the total cross-section of triplet production
in the laboratory frame are calculated numerically in order to develop a Monte
Carlo code for modelling electron-photon cascades in a soft photon field. To
avoid numerical integration irregularities of the integrands, which are
inherent to problems of this type, we have used suitable substitutions in
combination with a modern powerful program code Mathematica allowing one to
achieve reliable higher-precission results. The results obtained for the total
cross-section closely agree with others estimated analytically or by a
different numerical approach. The results for the double and single
differential cross-sections turn out to be somewhat different from some
reported recently. The mean energy of the produced particles, as a function of
the characteristic collisional parameter (the electron rest frame photon
energy), is calculated and approximated by an analytical expression that
revises other known approximations over a wide range of values of the argument.
The primary-electron energy loss rate due to triplet pair production is shown
to prevail over the inverse Compton scattering loss rate at several (2)
orders of magnitude higher interaction energy than that predicted formerly.Comment: 18 pages, 8 figures, 2 tables, LaTex2e, Iopart.cls, Iopart12.clo,
Iopams.st
On the Kauffman bracket skein module of the quaternionic manifold
We use recoupling theory to study the Kauffman bracket skein module of the
quaternionic manifold over Z[A,A^{-1}] localized by inverting all the
cyclotomic polynomials. We prove that the skein module is spanned by five
elements. Using the quantum invariants of these skein elements and the Z_2
homology of the manifold, we determine that they are linearly independent.Comment: corrected summation signs in figures 14, 15, 17. Other minor change
Optimization of 2-d lattice cellular automata for pseudorandom number generation
This paper proposes a generalized approach to 2-d CA PRNGs – the 2-d lattice CA PRNG – by introducing vertical connections to arrays of 1-d CA. The structure of a 2-d lattice CA PRNG lies in between that of 1-d CA and 2-d CA grid PRNGs. With the generalized approach, 2-d lattice CA PRNG offers more 2-d CA PRNG variations. It is found that they can do better than the conventional 2-d CA grid PRNGs. In this paper, the structure and properties of 2-d lattice CA are explored by varying the number and location of vertical connections, and by searching for different 2-d array settings that can give good randomness based on Diehard test. To get the most out of 2-d lattice CA PRNGs, genetic algorithm is employed in searching for good neighborhood characteristics. By adopting an evolutionary approach, the randomness quality of 2-d lattice CA PRNGs is optimized. In this paper, a new metric, #rn is introduced as a way of finding a 2-d lattice CA PRNG with the least number of cells required to pass Diehard test. Following the introduction of the new metric #rn, a cropping technique is presented to further boost the CA PRNG performance. The cost and efficiency of 2-d lattice CA PRNG is compared with past works on CA PRNGs
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