2,935 research outputs found
Evolutionary accessibility of modular fitness landscapes
A fitness landscape is a mapping from the space of genetic sequences, which
is modeled here as a binary hypercube of dimension , to the real numbers. We
consider random models of fitness landscapes, where fitness values are assigned
according to some probabilistic rule, and study the statistical properties of
pathways to the global fitness maximum along which fitness increases
monotonically. Such paths are important for evolution because they are the only
ones that are accessible to an adapting population when mutations occur at a
low rate. The focus of this work is on the block model introduced by A.S.
Perelson and C.A. Macken [Proc. Natl. Acad. Sci. USA 92:9657 (1995)] where the
genome is decomposed into disjoint sets of loci (`modules') that contribute
independently to fitness, and fitness values within blocks are assigned at
random. We show that the number of accessible paths can be written as a product
of the path numbers within the blocks, which provides a detailed analytic
description of the path statistics. The block model can be viewed as a special
case of Kauffman's NK-model, and we compare the analytic results to simulations
of the NK-model with different genetic architectures. We find that the mean
number of accessible paths in the different versions of the model are quite
similar, but the distribution of the path number is qualitatively different in
the block model due to its multiplicative structure. A similar statement
applies to the number of local fitness maxima in the NK-models, which has been
studied extensively in previous works. The overall evolutionary accessibility
of the landscape, as quantified by the probability to find at least one
accessible path to the global maximum, is dramatically lowered by the modular
structure.Comment: 26 pages, 12 figures; final version with some typos correcte
The magnetic reversal in dot arrays recognized by the self-organized adaptive neural network
The remagnetization dynamics of monolayer dot array superlattice XY 2-D spin
model with dipole-dipole interactions is simulated. Within the proposed model
of array, the square dots are described by the spatially modulated
exchange-couplings. The dipole-dipole interactions are approximated by the
hierarchical sums and spin dynamics is considered in regime of the
Landau-Lifshitz equation. The simulation of reversal for spins
exhibits formation of nonuniform intra-dot configurations with nonlinear
wave/anti-wave pairs developed at intra-dot and inter-dot scales. Several
geometric and parametric dependences are calculated and compared with
oversimplified four-spin model of reversal. The role of initial conditions and
the occurrence of coherent rotation mode is also investigated. The emphasis is
on the classification of intra-dot or inter-dot (interfacial) magnetic
configurations done by adaptive neural network with varying number of neurons.Comment: 16 figure
Ambient cosmology and spacetime singularities
We present a new approach to the issues of spacetime singularities and cosmic
censorship in general relativity. This is based on the idea that standard
4-dimensional spacetime is the conformal infinity of an ambient metric for the
5-dimensional Einstein equations with fluid sources. We then find that the
existence of spacetime singularities in four dimensions is constrained by
asymptotic properties of the ambient 5-metric, while the non-degeneracy of the
latter crucially depends on cosmic censorship holding on the boundary.Comment: v3: 32 pages, longer version to appear in the EPJC, main idea made
explicit, various mathematical and physical explanations adde
Compressed self-avoiding walks, bridges and polygons
We study various self-avoiding walks (SAWs) which are constrained to lie in
the upper half-plane and are subjected to a compressive force. This force is
applied to the vertex or vertices of the walk located at the maximum distance
above the boundary of the half-space. In the case of bridges, this is the
unique end-point. In the case of SAWs or self-avoiding polygons, this
corresponds to all vertices of maximal height. We first use the conjectured
relation with the Schramm-Loewner evolution to predict the form of the
partition function including the values of the exponents, and then we use
series analysis to test these predictions.Comment: 29 pages, 6 figure
Statistical Physics of Evolutionary Trajectories on Fitness Landscapes
Random walks on multidimensional nonlinear landscapes are of interest in many
areas of science and engineering. In particular, properties of adaptive
trajectories on fitness landscapes determine population fates and thus play a
central role in evolutionary theory. The topography of fitness landscapes and
its effect on evolutionary dynamics have been extensively studied in the
literature. We will survey the current research knowledge in this field,
focusing on a recently developed systematic approach to characterizing path
lengths, mean first-passage times, and other statistics of the path ensemble.
This approach, based on general techniques from statistical physics, is
applicable to landscapes of arbitrary complexity and structure. It is
especially well-suited to quantifying the diversity of stochastic trajectories
and repeatability of evolutionary events. We demonstrate this methodology using
a biophysical model of protein evolution that describes how proteins maintain
stability while evolving new functions
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