33,424 research outputs found
Number of adaptive steps to a local fitness peak
We consider a population of genotype sequences evolving on a rugged fitness
landscape with many local fitness peaks. The population walks uphill until it
encounters a local fitness maximum. We find that the statistical properties of
the walk length depend on whether the underlying fitness distribution has a
finite mean. If the mean is finite, all the walk length cumulants grow with the
sequence length but approach a constant otherwise. Experimental implications of
our analytical results are also discussed
Evolutionary dynamics on strongly correlated fitness landscapes
We study the evolutionary dynamics of a maladapted population of
self-replicating sequences on strongly correlated fitness landscapes. Each
sequence is assumed to be composed of blocks of equal length and its fitness is
given by a linear combination of four independent block fitnesses. A mutation
affects the fitness contribution of a single block leaving the other blocks
unchanged and hence inducing correlations between the parent and mutant
fitness. On such strongly correlated fitness landscapes, we calculate the
dynamical properties like the number of jumps in the most populated sequence
and the temporal distribution of the last jump which is shown to exhibit a
inverse square dependence as in evolution on uncorrelated fitness landscapes.
We also obtain exact results for the distribution of records and extremes for
correlated random variables
Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid
It is shown that Wen's effective theory correctly describes the
Tomonaga-Luttinger liquid at the edge of a system of non-interacting composite
fermions. However, the weak residual interaction between composite fermions
appears to be a relevant perturbation. The filling factor dependence of the
Tomonaga-Luttinger parameter is estimated for interacting composite fermions in
a microscopic approach and satisfactory agreement with experiment is achieved.
It is suggested that the electron field operator may not have a simple
representation in the effective one dimensional theory.Comment: 5 pages; accepted in Phys. Rev. Let
Persistence and the Random Bond Ising Model in Two Dimensions
We study the zero-temperature persistence phenomenon in the random bond Ising model on a square lattice via extensive numerical simulations. We find
strong evidence for ` blocking\rq regardless of the amount disorder present in
the system. The fraction of spins which {\it never} flips displays interesting
non-monotonic, double-humped behaviour as the concentration of ferromagnetic
bonds is varied from zero to one. The peak is identified with the onset of
the zero-temperature spin glass transition in the model. The residual
persistence is found to decay algebraically and the persistence exponent
over the range . Our results are
completely consistent with the result of Gandolfi, Newman and Stein for
infinite systems that this model has ` mixed\rq behaviour, namely positive
fractions of spins that flip finitely and infinitely often, respectively.
[Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]Comment: 9 pages, 5 figure
A Simple Method for Computing the Non-Linear Mass Correlation Function with Implications for Stable Clustering
We propose a simple and accurate method for computing analytically the mass
correlation function for cold dark matter and scale-free models that fits
N-body simulations over a range that extends from the linear to the strongly
non-linear regime. The method, based on the dynamical evolution of the pair
conservation equation, relies on a universal relation between the pair-wise
velocity and the smoothed correlation function valid for high and low density
models, as derived empirically from N-body simulations. An intriguing
alternative relation, based on the stable-clustering hypothesis, predicts a
power-law behavior of the mass correlation function that disagrees with N-body
simulations but conforms well to the observed galaxy correlation function if
negligible bias is assumed. The method is a useful tool for rapidly exploring a
wide span of models and, at the same time, raises new questions about large
scale structure formation.Comment: 10 pages, 3 figure
Extreme value distributions for weakly correlated fitnesses in block model
We study the limit distribution of the largest fitness for two models of
weakly correlated and identically distributed random fitnesses. The correlated
fitness is given by a linear combination of a fixed number of independent
random variables drawn from a common parent distribution. We find that for
certain class of parent distributions, the extreme value distribution for
correlated random variables can be related either to one of the known limit
laws for independent variables or the parent distribution itself. For other
cases, new limiting distributions appear. The conditions under which these
results hold are identified.Comment: Expanded, added reference
Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness
The activation gaps for fractional quantum Hall states at filling fractions
are computed for heterojunction, square quantum well, as well as
parabolic quantum well geometries, using an interaction potential calculated
from a self-consistent electronic structure calculation in the local density
approximation. The finite thickness is estimated to make 30% correction
to the gap in the heterojunction geometry for typical parameters, which
accounts for roughly half of the discrepancy between the experiment and
theoretical gaps computed for a pure two dimensional system. Certain model
interactions are also considered. It is found that the activation energies
behave qualitatively differently depending on whether the interaction is of
longer or shorter range than the Coulomb interaction; there are indications
that fractional Hall states close to the Fermi sea are destabilized for the
latter.Comment: 32 pages, 13 figure
Evolutionary dynamics of the most populated genotype on rugged fitness landscapes
We consider an asexual population evolving on rugged fitness landscapes which
are defined on the multi-dimensional genotypic space and have many local
optima. We track the most populated genotype as it changes when the population
jumps from a fitness peak to a better one during the process of adaptation.
This is done using the dynamics of the shell model which is a simplified
version of the quasispecies model for infinite populations and standard
Wright-Fisher dynamics for large finite populations. We show that the
population fraction of a genotype obtained within the quasispecies model and
the shell model match for fit genotypes and at short times, but the dynamics of
the two models are identical for questions related to the most populated
genotype. We calculate exactly several properties of the jumps in infinite
populations some of which were obtained numerically in previous works. We also
present our preliminary simulation results for finite populations. In
particular, we measure the jump distribution in time and find that it decays as
as in the quasispecies problem.Comment: Minor changes. To appear in Phys Rev
Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect
Motivated by the discovery of extremely low energy collective modes in the
fractional quantum Hall effect (Kang, Pinczuk {\em et al.}), with energies
below the Zeeman energy, we study theoretically the spin reversed excitations
for fractional quantum Hall states at and 3/7 and find qualitatively
different behavior than for . We find that a low-energy,
charge-neutral "spin roton," associated with spin reversed excitations that
involve a change in the composite-fermion Landau level index, has energy in
reasonable agreement with experiment.Comment: Postscript figures included. Accepted in Phys. Rev. B (Rapid
Communication
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