70 research outputs found
Scale-free networks resistant to intentional attacks
We study the detailed mechanism of the failure of scale-free networks under
intentional attacks. Although it is generally accepted that such networks are
very sensitive to targeted attacks, we show that for a particular type of
structure such networks surprisingly remain very robust even under removal of a
large fraction of their nodes, which in some cases can be up to 70%. The degree
distribution of these structures is such that for small values of the
degree the distribution is constant with , up to a critical value ,
and thereafter it decays with with the usual power law. We describe in
detail a model for such a scale-free network with this modified degree
distribution, and we show both analytically and via simulations, that this
model can adequately describe all the features and breakdown characteristics of
these attacks. We have found several experimental networks with such features,
such as for example the IMDB actors collaboration network or the citations
network, whose resilience to attacks can be accurately described by our model.Comment: 5 pages, 4 figure
Reaction-diffusion processes on correlated and uncorrelated scale-free networks
We compare reaction-diffusion processes of the type on scale-free
networks created with either the configuration model or the uncorrelated
configuration model. We show via simulations that except for the difference in
the behavior of the two models, different results are observed within the same
model when the minimum number of connections for a node varies from to . This difference is attributed to the varying local
properties of the two systems. In all cases we are able to identify a power law
behavior of the density decay with time with an exponent , considerably
larger than its lattice counterpart
Fractal behavior of correlated random walk on percolating clusters
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70722/2/JCPSA6-84-2-1047-1.pd
Fractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three‐dimensional lattices
We perform random walk simulations on binary three‐dimensional simple cubic lattices covering the entire ratio of open/closed sites (fraction p) from the critical percolation threshold to the perfect crystal. We observe fractal behavior at the critical point and derive the value of the number‐of‐sites‐visited exponent, in excellent agreement with previous work or conjectures, but with a new and improved computational algorithm that extends the calculation to the long time limit. We show the crossover to the classical Euclidean behavior in these lattices and discuss its onset as a function of the fraction p. We compare the observed trends with the two‐dimensional case.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70154/2/JCPSA6-83-6-3099-1.pd
Exciton percolation and exciton coherence
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69756/2/JCPSA6-66-7-3301-1.pd
A network approach for the scientific collaboration in the European Framework Programs
We construct the networks of collaboration between partners for projects
carried out with the support of European Commission Framework Programs FP5 and
FP6. We analyze in detail these networks, not only in terms of total number of
projects, but also for the different tools employed, the different geographical
partitions, and the different thematic areas. For all cases we find a scale
free behavior, as expected for such social networks, and also reported in the
literature. In comparing FP5 to FP6, we show that despite a decrease in the
number of signed contracts, and the total number of unique partners, there is
an increase in the average number of collaborative partners per institution.
Furthermore, we establish a measure for the central role (hub) for each
country, by using the Minimum Spanning Tree (MST), which we construct in detail
for each thematic area (e.g. Informatics, Nanoscience, Life Sciences, etc.).
The importance of these network hubs is highlighted, as this information can be
used by policy planners in designing future research plans regarding the
distribution of available funds.Comment: 6 pages, 4 figure
Nature of segregation of reactants in diffusion controlled A+B reactions: Role of mobility in forming compact clusters
We investigate the A+B=0 bimolecular chemical reaction taking place in
low-dimensional spaces when the mobilities of the two reacting species are not
equal. While the case of different reactant mobilities has been previously
reported as not affecting the scaling of the reactant densities with time, but
only the pre-exponential factor, the mechanism for this had not been explained
before. By using Monte-Carlo simulations we show that the nature of segregation
is very different when compared to the normal case of equal reactant
mobilities. The clusters of the mobile species are statistically homogeneous
and randomly distributed in space, but the clusters of the less mobile species
are much more compact and restricted in space. Due to the asymmetric
mobilities, the initial symmetric random density fluctuations in time turn into
asymmetric density fluctuations. We explain this trend by calculating the
correlation functions for the positions of particles for the several different
cases
Static and dynamic behavior of multiplex networks under interlink strength variation
It has recently been suggested \cite{Radicchi2013} that in a two-level
multiplex network, a gradual change in the value of the "interlayer" strength
can provoke an abrupt structural transition. The critical point at
which this happens is system-dependent. In this article, we show in a similar
way as in \cite{Garrahan2014} that this is a consequence of the graph Laplacian
formalism used in \cite{Radicchi2013}. We calculate the evolution of as
a function of system size for ER and RR networks. We investigate the behavior
of structural measures and dynamical processes of a two-level system as a
function of , by Monte-Carlo simulations, for simple particle diffusion and
for reaction-diffusion systems. We find that as increases there is a smooth
transition from two separate networks to a single one. We cannot find any
abrupt change in static or dynamic behavior of the underlying system.Comment: 8 pages, 5 figure
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