1,136 research outputs found
Phase transition in hierarchy model of Bonabeau et al
The model of Bonabeau explains the emergence of social hierarchies from the
memory of fights in an initially egalitarian society. Introducing a feedback
from the social inequality into the probability to win a fight, we find a sharp
transition between egalitarian society at low population density and
hierarchical society at high population density.Comment: 3 pages including two figs.; for Int. J. Mod. Phys.
Probabilistic heuristics for disseminating information in networks
We study the problem of disseminating a piece of information through all the
nodes of a network, given that it is known originally only to a single node. In
the absence of any structural knowledge on the network other than the nodes'
neighborhoods, this problem is traditionally solved by flooding all the
network's edges. We analyze a recently introduced probabilistic algorithm for
flooding and give an alternative probabilistic heuristic that can lead to some
cost-effective improvements, like better trade-offs between the message and
time complexities involved. We analyze the two algorithms both mathematically
and by means of simulations, always within a random-graph framework and
considering relevant node-degree distributions
Local heuristics and the emergence of spanning subgraphs in complex networks
We study the use of local heuristics to determine spanning subgraphs for use
in the dissemination of information in complex networks. We introduce two
different heuristics and analyze their behavior in giving rise to spanning
subgraphs that perform well in terms of allowing every node of the network to
be reached, of requiring relatively few messages and small node bandwidth for
information dissemination, and also of stretching paths with respect to the
underlying network only modestly. We contribute a detailed mathematical
analysis of one of the heuristics and provide extensive simulation results on
random graphs for both of them. These results indicate that, within certain
limits, spanning subgraphs are indeed expected to emerge that perform well in
respect to all requirements. We also discuss the spanning subgraphs' inherent
resilience to failures and adaptability to topological changes
Applications and Sexual Version of a Simple Model for Biological Ageing
We use a simple model for biological ageing to study the mortality of the
population, obtaining a good agreement with the Gompertz law. We also simulate
the same model on a square lattice, considering different strategies of
parental care. The results are in agreement with those obtained earlier with
the more complicated Penna model for biological ageing. Finally, we present the
sexual version of this simple model.Comment: For Int.J.Mod.Phys.C Dec. 2001; 11 pages including 6 fig
Negative-weight percolation
We describe a percolation problem on lattices (graphs, networks), with edge
weights drawn from disorder distributions that allow for weights (or distances)
of either sign, i.e. including negative weights. We are interested whether
there are spanning paths or loops of total negative weight. This kind of
percolation problem is fundamentally different from conventional percolation
problems, e.g. it does not exhibit transitivity, hence no simple definition of
clusters, and several spanning paths/loops might coexist in the percolation
regime at the same time. Furthermore, to study this percolation problem
numerically, one has to perform a non-trivial transformation of the original
graph and apply sophisticated matching algorithms.
Using this approach, we study the corresponding percolation transitions on
large square, hexagonal and cubic lattices for two types of disorder
distributions and determine the critical exponents. The results show that
negative-weight percolation is in a different universality class compared to
conventional bond/site percolation. On the other hand, negative-weight
percolation seems to be related to the ferromagnet/spin-glass transition of
random-bond Ising systems, at least in two dimensions.Comment: v1: 4 pages, 4 figures; v2: 10 pages, 7 figures, added results, text
and reference
Phase transitions in diluted negative-weight percolation models
We investigate the geometric properties of loops on two-dimensional lattice
graphs, where edge weights are drawn from a distribution that allows for
positive and negative weights. We are interested in the appearance of spanning
loops of total negative weight. The resulting percolation problem is
fundamentally different from conventional percolation, as we have seen in a
previous study of this model for the undiluted case.
Here, we investigate how the percolation transition is affected by additional
dilution. We consider two types of dilution: either a certain fraction of edges
exhibit zero weight, or a fraction of edges is even absent. We study these
systems numerically using exact combinatorial optimization techniques based on
suitable transformations of the graphs and applying matching algorithms. We
perform a finite-size scaling analysis to obtain the phase diagram and
determine the critical properties of the phase boundary.
We find that the first type of dilution does not change the universality
class compared to the undiluted case whereas the second type of dilution leads
to a change of the universality class.Comment: 8 pages, 7 figure
Love kills: Simulations in Penna Ageing Model
The standard Penna ageing model with sexual reproduction is enlarged by
adding additional bit-strings for love: Marriage happens only if the male love
strings are sufficiently different from the female ones. We simulate at what
level of required difference the population dies out.Comment: 14 pages, including numerous figure
Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6
We consider the negative weight percolation (NWP) problem on hypercubic
lattice graphs with fully periodic boundary conditions in all relevant
dimensions from d=2 to the upper critical dimension d=6. The problem exhibits
edge weights drawn from disorder distributions that allow for weights of either
sign. We are interested in in the full ensemble of loops with negative weight,
i.e. non-trivial (system spanning) loops as well as topologically trivial
("small") loops. The NWP phenomenon refers to the disorder driven proliferation
of system spanning loops of total negative weight. While previous studies where
focused on the latter loops, we here put under scrutiny the ensemble of small
loops. Our aim is to characterize -using this extensive and exhaustive
numerical study- the loop length distribution of the small loops right at and
below the critical point of the hypercubic setups by means of two independent
critical exponents. These can further be related to the results of previous
finite-size scaling analyses carried out for the system spanning loops. For the
numerical simulations we employed a mapping of the NWP model to a combinatorial
optimization problem that can be solved exactly by using sophisticated matching
algorithms. This allowed us to study here numerically exact very large systems
with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at
http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text
overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174
Fast vectorized algorithm for the Monte Carlo Simulation of the Random Field Ising Model
An algoritm for the simulation of the 3--dimensional random field Ising model
with a binary distribution of the random fields is presented. It uses
multi-spin coding and simulates 64 physically different systems simultaneously.
On one processor of a Cray YMP it reaches a speed of 184 Million spin updates
per second. For smaller field strength we present a version of the algorithm
that can perform 242 Million spin updates per second on the same machine.Comment: 13 pp., HLRZ 53/9
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