174 research outputs found
Dynamic networks and directed percolation
We introduce a model for dynamic networks, where the links or the strengths
of the links change over time. We solve the model by mapping dynamic networks
to the problem of directed percolation, where the direction corresponds to the
evolution of the network in time. We show that the dynamic network undergoes a
percolation phase transition at a critical concentration , which decreases
with the rate at which the network links are changed. The behavior near
criticality is universal and independent of . We find fundamental network
laws are changed. (i) For Erd\H{o}s-R\'{e}nyi networks we find that the size of
the giant component at criticality scales with the network size for all
values of , rather than as . (ii) In the presence of a broad
distribution of disorder, the optimal path length between two nodes in a
dynamic network scales as , compared to in a static network.Comment: 10 pages 5 figures; corrected metadata onl
Structural crossover of polymers in disordered media
We present a unified scaling theory for the structural behavior of polymers
embedded in a disordered energy substrate. An optimal polymer configuration is
defined as the polymer configuration that minimizes the sum of interacting
energies between the monomers and the substrate. The fractal dimension of the
optimal polymer in the limit of strong disorder (SD) was found earlier to be
larger than the fractal dimension in weak disorder (WD). We introduce a scaling
theory for the crossover between the WD and SD limits. For polymers of various
sizes in the same disordered substrate we show that polymers with a small
number of monomers, N << N*, will behave as in SD, while large polymers with
length N >> N* will behave as in WD. This implies that small polymers will be
relatively more compact compared to large polymers even in the same substrate.
The crossover length N* is a function of \nu and a, where \nu is the
percolation correlation length exponent and a is the parameter which controls
the broadness of the disorder. Furthermore, our results show that the crossover
between the strong and weak disorder limits can be seen even within the same
polymer configuration. If one focuses on a segment of size n << N* within a
long polymer (N >> N*) that segment will have a higher fractal dimension
compared to a segment of size n >> N*
Towards designing robust coupled networks
Natural and technological interdependent systems have been shown to be highly
vulnerable due to cascading failures and an abrupt collapse of global
connectivity under initial failure. Mitigating the risk by partial
disconnection endangers their functionality. Here we propose a systematic
strategy of selecting a minimum number of autonomous nodes that guarantee a
smooth transition in robustness. Our method which is based on betweenness is
tested on various examples including the famous 2003 electrical blackout of
Italy. We show that, with this strategy, the necessary number of autonomous
nodes can be reduced by a factor of five compared to a random choice. We also
find that the transition to abrupt collapse follows tricritical scaling
characterized by a set of exponents which is independent on the protection
strategy
Inter-similarity between coupled networks
Recent studies have shown that a system composed from several randomly
interdependent networks is extremely vulnerable to random failure. However,
real interdependent networks are usually not randomly interdependent, rather a
pair of dependent nodes are coupled according to some regularity which we coin
inter-similarity. For example, we study a system composed from an
interdependent world wide port network and a world wide airport network and
show that well connected ports tend to couple with well connected airports. We
introduce two quantities for measuring the level of inter-similarity between
networks (i) Inter degree-degree correlation (IDDC) (ii) Inter-clustering
coefficient (ICC). We then show both by simulation models and by analyzing the
port-airport system that as the networks become more inter-similar the system
becomes significantly more robust to random failure.Comment: 4 pages, 3 figure
A New Analysis Method for Simulations Using Node Categorizations
Most research concerning the influence of network structure on phenomena
taking place on the network focus on relationships between global statistics of
the network structure and characteristic properties of those phenomena, even
though local structure has a significant effect on the dynamics of some
phenomena. In the present paper, we propose a new analysis method for phenomena
on networks based on a categorization of nodes. First, local statistics such as
the average path length and the clustering coefficient for a node are
calculated and assigned to the respective node. Then, the nodes are categorized
using the self-organizing map (SOM) algorithm. Characteristic properties of the
phenomena of interest are visualized for each category of nodes. The validity
of our method is demonstrated using the results of two simulation models. The
proposed method is useful as a research tool to understand the behavior of
networks, in particular, for the large-scale networks that existing
visualization techniques cannot work well.Comment: 9 pages, 8 figures. This paper will be published in Social Network
Analysis and Mining(www.springerlink.com
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