236 research outputs found
Two-dimensional projections of an hypercube
We present a method to project a hypercube of arbitrary dimension on the
plane, in such a way as to preserve, as well as possible, the distribution of
distances between vertices. The method relies on a Montecarlo optimization
procedure that minimizes the squared difference between distances in the plane
and in the hypercube, appropriately weighted. The plane projections provide a
convenient way of visualization for dynamical processes taking place on the
hypercube.Comment: 4 pages, 3 figures, Revtex
Estimating the conditions for polariton condensation in organic thin-film microcavities
We examine the possibility of observing Bose condensation of a confined
two-dimensional polariton gas in an organic quantum well. We deduce a suitable
parameterization of a model Hamiltonian based upon the cavity geometry, the
biexciton binding energy, and similar spectroscopic and structural data. By
converting the sum-over-states to a semiclassical integration over
-dimensional phase space, we show that while an ideal 2-D Bose gas will not
undergo condensation, an interacting gas with the Bogoliubov dispersion
close to will undergo Bose condensation at a given
critical density and temperature. We show that is sensitive
to both the cavity geometry and to the biexciton binding energy. In particular,
for strongly bound biexcitons, the non-linear interaction term appearing in the
Gross-Pitaevskii equation becomes negative and the resulting ground state will
be a localized soliton state rather than a delocalized Bose condensate.Comment: 2 figure
Production of a pseudo-scalar Higgs boson at hadron colliders at next-to-next-to leading order
The production cross section for pseudo-scalar Higgs bosons at hadron
colliders is computed at next-to-next-to-leading order (NNLO) in QCD. The
pseudo-scalar Higgs is assumed to couple only to top quarks. The NNLO effects
are evaluated using an effective lagrangian where the top quarks are integrated
out. The NNLO corrections are similar in size to those found for scalar Higgs
boson production.Comment: 20 pages, 6 figures, JHEP style, Minor changes, Journal reference
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Combinatorial expression for universal Vassiliev link invariant
The most general R-matrix type state sum model for link invariants is
constructed. It contains in itself all R-matrix invariants and is a generating
function for "universal" Vassiliev link invariants. This expression is more
simple than Kontsevich's expression for the same quantity, because it is
defined combinatorially and does not contain any integrals, except for an
expression for "the universal Drinfeld's associator".Comment: 20 page
Smooth operator? Understanding and visualising mutation bias
The potential for mutation operators to adversely affect the behaviour of evolutionary algorithms is demonstrated for both real-valued and discrete-valued genotypes. Attention is drawn to the utility of effective visualisation techniques and explanatory concepts in identifying and understanding these biases. The skewness of a mutation distribution is identified as a crucial determinant of its bias. For redundant discrete genotype-phenotype mappings intended to exploit neutrality in genotype space, it is demonstrated that in addition to the mere extent of phenotypic connectivity achieved by these schemes, the distribution of phenotypic connectivity may be critical in determining whether neutral networks improve the ability of an evolutionary algorithm overall. Mutation operators lie at the heart of evolutionary algorithms. They corrupt the reproduction of genotypes, introducing the variety that fuels natural selection. However, until recently, the process of mutation has taken..
Damage Spreading During Domain Growth
We study damage spreading in models of two-dimensional systems undergoing
first order phase transitions. We consider several models from the same
non-conserved order parameter universality class, and find unexpected
differences between them. An exact solution of the Ohta-Jasnow-Kawasaki model
yields the damage growth law , where in
dimensions. In contrast, time-dependent Ginzburg-Landau simulations and Ising
simulations in using heat-bath dynamics show power-law growth, but with
an exponent of approximately , independent of the system sizes studied.
In marked contrast, Metropolis dynamics shows damage growing via , although the damage difference grows as . PACS: 64.60.-i, 05.50.+qComment: 4 pags of revtex3 + 3 postscript files appended as a compressed and
uuencoded file. UIB940320
Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution
We compare and contrast the long-time dynamical properties of two
individual-based models of biological coevolution. Selection occurs via
multispecies, stochastic population dynamics with reproduction probabilities
that depend nonlinearly on the population densities of all species resident in
the community. New species are introduced through mutation. Both models are
amenable to exact linear stability analysis, and we compare the analytic
results with large-scale kinetic Monte Carlo simulations, obtaining the
population size as a function of an average interspecies interaction strength.
Over time, the models self-optimize through mutation and selection to
approximately maximize a community fitness function, subject only to
constraints internal to the particular model. If the interspecies interactions
are randomly distributed on an interval including positive values, the system
evolves toward self-sustaining, mutualistic communities. In contrast, for the
predator-prey case the matrix of interactions is antisymmetric, and a nonzero
population size must be sustained by an external resource. Time series of the
diversity and population size for both models show approximate 1/f noise and
power-law distributions for the lifetimes of communities and species. For the
mutualistic model, these two lifetime distributions have the same exponent,
while their exponents are different for the predator-prey model. The difference
is probably due to greater resilience toward mass extinctions in the food-web
like communities produced by the predator-prey model.Comment: 26 pages, 12 figures. Discussion of early-time dynamics added. J.
Math. Biol., in pres
Pareto Local Optima of Multiobjective NK-Landscapes with Correlated Objectives
International audienceIn this paper, we conduct a fitness landscape analysis for multiobjective combinatorial optimization, based on the local optima of multiobjective NK-landscapes with objective correlation. In single-objective optimization, it has become clear that local optima have a strong impact on the performance of metaheuristics. Here, we propose an extension to the multiobjective case, based on the Pareto dominance. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives and the correlation degree between objective functions on the number of Pareto local optima
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