2,274 research outputs found
Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities
An extensive list of results for the ground state properties of spin glasses
on random graphs is presented. These results provide a timely benchmark for
currently developing theoretical techniques based on replica symmetry breaking
that are being tested on mean-field models at low connectivity. Comparison with
existing replica results for such models verifies the strength of those
techniques. Yet, we find that spin glasses on fixed-connectivity graphs (Bethe
lattices) exhibit a richer phenomenology than has been anticipated by theory.
Our data prove to be sufficiently accurate to speculate about some exact
results.Comment: 4 pages, RevTex4, 5 ps-figures included, related papers available at
http://www.physics.emory.edu/faculty/boettcher
Extremal Optimization for Graph Partitioning
Extremal optimization is a new general-purpose method for approximating
solutions to hard optimization problems. We study the method in detail by way
of the NP-hard graph partitioning problem. We discuss the scaling behavior of
extremal optimization, focusing on the convergence of the average run as a
function of runtime and system size. The method has a single free parameter,
which we determine numerically and justify using a simple argument. Our
numerical results demonstrate that on random graphs, extremal optimization
maintains consistent accuracy for increasing system sizes, with an
approximation error decreasing over runtime roughly as a power law t^(-0.4). On
geometrically structured graphs, the scaling of results from the average run
suggests that these are far from optimal, with large fluctuations between
individual trials. But when only the best runs are considered, results
consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers
available at http://www.physics.emory.edu/faculty/boettcher
Extremal Optimization of Graph Partitioning at the Percolation Threshold
The benefits of a recently proposed method to approximate hard optimization
problems are demonstrated on the graph partitioning problem. The performance of
this new method, called Extremal Optimization, is compared to Simulated
Annealing in extensive numerical simulations. While generally a complex
(NP-hard) problem, the optimization of the graph partitions is particularly
difficult for sparse graphs with average connectivities near the percolation
threshold. At this threshold, the relative error of Simulated Annealing for
large graphs is found to diverge relative to Extremal Optimization at equalized
runtime. On the other hand, Extremal Optimization, based on the extremal
dynamics of self-organized critical systems, reproduces known results about
optimal partitions at this critical point quite well.Comment: 7 pages, RevTex, 9 ps-figures included, as to appear in Journal of
Physics
Environmental factors influence both abundance and genetic diversity in a widespread bird species.
Genetic diversity is one of the key evolutionary variables that correlate with population size, being of critical importance for population viability and the persistence of species. Genetic diversity can also have important ecological consequences within populations, and in turn, ecological factors may drive patterns of genetic diversity. However, the relationship between the genetic diversity of a population and how this interacts with ecological processes has so far only been investigated in a few studies. Here, we investigate the link between ecological factors, local population size, and allelic diversity, using a field study of a common bird species, the house sparrow (Passer domesticus). We studied sparrows outside the breeding season in a confined small valley dominated by dispersed farms and small-scale agriculture in southern France. Population surveys at 36 locations revealed that sparrows were more abundant in locations with high food availability. We then captured and genotyped 891 house sparrows at 10 microsatellite loci from a subset of these locations (N = 12). Population genetic analyses revealed weak genetic structure, where each locality represented a distinct substructure within the study area. We found that food availability was the main factor among others tested to influence the genetic structure between locations. These results suggest that ecological factors can have strong impacts on both population size per se and intrapopulation genetic variation even at a small scale. On a more general level, our data indicate that a patchy environment and low dispersal rate can result in fine-scale patterns of genetic diversity. Given the importance of genetic diversity for population viability, combining ecological and genetic data can help to identify factors limiting population size and determine the conservation potential of populations
Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass
Sample-to-sample free energy fluctuations in spin-glasses display a markedly
different behaviour in finite-dimensional and fully-connected models, namely
Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random
graphs are in an intermediate situation between these two classes of models and
we investigate whether the nature of their free-energy fluctuations is Gaussian
or not. It has been argued that Gaussian behaviour is present whenever the
interactions are locally non-homogeneous, i.e. in most cases with the notable
exception of models with fixed connectivity and random couplings . We confirm these expectation by means of various analytical
results. In particular we unveil the connection between the spatial
fluctuations of the populations of populations of fields defined at different
sites of the lattice and the Gaussian nature of the free-energy fluctuations.
On the contrary on locally homogeneous lattices the populations do not
fluctuate over the sites and as a consequence the small-deviations of the free
energy are non-Gaussian and scales as in the Sherrington-Kirkpatrick model
Random Geometric Graphs
We analyse graphs in which each vertex is assigned random coordinates in a
geometric space of arbitrary dimensionality and only edges between adjacent
points are present. The critical connectivity is found numerically by examining
the size of the largest cluster. We derive an analytical expression for the
cluster coefficient which shows that the graphs are distinctly different from
standard random graphs, even for infinite dimensionality. Insights relevant for
graph bi-partitioning are included.Comment: 16 pages, 10 figures. Minor changes. Added reference
Exact Results for Spatio-Temporal Correlations in a Self-Organized Critical Model of Punctuated Equilibrium
We introduce a self-organized critical model of punctuated equilibrium with
many internal degrees of freedom () per site. We find exact solutions for
of cascade equations describing avalanche dynamics in the
steady state. This proves the existence of simple power laws with critical
exponents that verify general scaling relations for nonequilibrium phenomena.
Punctuated equilibrium is described by a Devil's staircase with a
characteristic exponent, where is the spatial
dimension.Comment: 4 pages, postscript, uuencoded, (two ps-figures included) Final
Version, to appear in PR
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