2,566 research outputs found
XY model in small-world networks
The phase transition in the XY model on one-dimensional small-world networks
is investigated by means of Monte-Carlo simulations. It is found that
long-range order is present at finite temperatures, even for very small values
of the rewiring probability, suggesting a finite-temperature transition for any
nonzero rewiring probability. Nature of the phase transition is discussed in
comparison with the globally-coupled XY model.Comment: 5 pages, accepted in PR
Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks
The aim of the study was to compare the epidemic spread on static and dynamic
small-world networks. The network was constructed as a 2-dimensional
Watts-Strogatz model (500x500 square lattice with additional shortcuts), and
the dynamics involved rewiring shortcuts in every time step of the epidemic
spread. The model of the epidemic is SIR with latency time of 3 time steps. The
behaviour of the epidemic was checked over the range of shortcut probability
per underlying bond 0-0.5. The quantity of interest was percolation threshold
for the epidemic spread, for which numerical results were checked against an
approximate analytical model. We find a significant lowering of percolation
thresholds for the dynamic network in the parameter range given. The result
shows that the behaviour of the epidemic on dynamic network is that of a static
small world with the number of shortcuts increased by 20.7 +/- 1.4%, while the
overall qualitative behaviour stays the same. We derive corrections to the
analytical model which account for the effect. For both dynamic and static
small-world we observe suppression of the average epidemic size dependence on
network size in comparison with finite-size scaling known for regular lattice.
We also study the effect of dynamics for several rewiring rates relative to
latency time of the disease.Comment: 13 pages, 6 figure
Path finding strategies in scale-free networks
We numerically investigate the scale-free network model of Barab{\'a}si and
Albert [A. L. Barab{\'a}si and R. Albert, Science {\bf 286}, 509 (1999)]
through the use of various path finding strategies. In real networks, global
network information is not accessible to each vertex, and the actual path
connecting two vertices can sometimes be much longer than the shortest one. A
generalized diameter depending on the actual path finding strategy is
introduced, and a simple strategy, which utilizes only local information on the
connectivity, is suggested and shown to yield small-world behavior: the
diameter of the network increases logarithmically with the network size
, the same as is found with global strategy. If paths are sought at random,
is found.Comment: 4 pages, final for
A Simple Model of Epidemics with Pathogen Mutation
We study how the interplay between the memory immune response and pathogen
mutation affects epidemic dynamics in two related models. The first explicitly
models pathogen mutation and individual memory immune responses, with contacted
individuals becoming infected only if they are exposed to strains that are
significantly different from other strains in their memory repertoire. The
second model is a reduction of the first to a system of difference equations.
In this case, individuals spend a fixed amount of time in a generalized immune
class. In both models, we observe four fundamentally different types of
behavior, depending on parameters: (1) pathogen extinction due to lack of
contact between individuals, (2) endemic infection (3) periodic epidemic
outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic
due to extremely low minima in the oscillations. We analyze both models to
determine the location of each transition. Our main result is that pathogens in
highly connected populations must mutate rapidly in order to remain viable.Comment: 9 pages, 11 figure
Large-scale structure of a nation-wide production network
Production in an economy is a set of firms' activities as suppliers and
customers; a firm buys goods from other firms, puts value added and sells
products to others in a giant network of production. Empirical study is lacking
despite the fact that the structure of the production network is important to
understand and make models for many aspects of dynamics in economy. We study a
nation-wide production network comprising a million firms and millions of
supplier-customer links by using recent statistical methods developed in
physics. We show in the empirical analysis scale-free degree distribution,
disassortativity, correlation of degree to firm-size, and community structure
having sectoral and regional modules. Since suppliers usually provide credit to
their customers, who supply it to theirs in turn, each link is actually a
creditor-debtor relationship. We also study chains of failures or bankruptcies
that take place along those links in the network, and corresponding
avalanche-size distribution.Comment: 17 pages with 8 figures; revised section VI and references adde
Structure of a large social network
We study a social network consisting of over individuals, with a
degree distribution exhibiting two power scaling regimes separated by a
critical degree , and a power law relation between degree and
local clustering. We introduce a growing random model based on a local
interaction mechanism that reproduces all of the observed scaling features and
their exponents. Our results lend strong support to the idea that several very
different networks are simultenously present in the human social network, and
these need to be taken into account for successful modeling.Comment: 5 pages, 5 figure
Scaling exponents and clustering coefficients of a growing random network
The statistical property of a growing scale-free network is studied based on
an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett.
86, 5401 (2001)], with the additional constraints of forbidden of
self-connection and multiple links of the same direction between any two nodes.
Scaling exponents in the range of 1-2 are obtained through Monte Carlo
simulations and various clustering coefficients are calculated, one of which,
, is of order , indicating the network resembles a
small-world. The out-degree distribution has an exponential cut-off for large
out-degree.Comment: six pages, including 5 figures, RevTex 4 forma
Sustaining productivity of tropical red snappers using new monitoring and reference points
OBJECTIVES:
1. Analyse current monitoring and logbook data sets, as well as survey and other information,to establish whether these data provide sufficient power to develop critical indicators of fishery performance.
2. Provide a risk analysis that examines the use of age structure and catch rate information for development of critical indicators, and response rules for those criteria, in the absence of other fishery information.
3. Develop a monitoring program that uses commercial vessels from the fishery to provide independent data
Correlation effects in a simple model of small-world network
We analyze the effect of correlations in a simple model of small world
network by obtaining exact analytical expressions for the distribution of
shortest paths in the network. We enter correlations into a simple model with a
distinguished site, by taking the random connections to this site from an Ising
distribution. Our method shows how the transfer matrix technique can be used in
the new context of small world networks.Comment: 10 pages, 3 figure
Search in Power-Law Networks
Many communication and social networks have power-law link distributions,
containing a few nodes which have a very high degree and many with low degree.
The high connectivity nodes play the important role of hubs in communication
and networking, a fact which can be exploited when designing efficient search
algorithms. We introduce a number of local search strategies which utilize high
degree nodes in power-law graphs and which have costs which scale sub-linearly
with the size of the graph. We also demonstrate the utility of these strategies
on the Gnutella peer-to-peer network.Comment: 17 pages, 14 figure
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