928 research outputs found
Cluster Expansion Method for Evolving Weighted Networks Having Vector-like Nodes
The Cluster Variation Method known in statistical mechanics and condensed
matter is revived for weighted bipartite networks. The decomposition of a
Hamiltonian through a finite number of components, whence serving to define
variable clusters, is recalled. As an illustration the network built from data
representing correlations between (4) macro-economic features, i.e. the so
called , of 15 EU countries, as (function) nodes, is
discussed. We show that statistical physics principles, like the maximum
entropy criterion points to clusters, here in a (4) variable phase space: Gross
Domestic Product (GDP), Final Consumption Expenditure (FCE), Gross Capital
Formation (GCF) and Net Exports (NEX). It is observed that the
entropy corresponds to a cluster which does explicitly include the GDP
but only the other (3) ''axes'', i.e. consumption, investment and trade
components. On the other hand, the entropy clustering scheme is
obtained from a coupling necessarily including GDP and FCE. The results confirm
intuitive economic theory and practice expectations at least as regards
geographical connexions. The technique can of course be applied to many other
cases in the physics of socio-economy networks.Comment: 7 pages, 2 figures, 20 references, 3 tables, submitted to FENS 07
Proceeding
On the strengths of connectivity and robustness in general random intersection graphs
Random intersection graphs have received much attention for nearly two
decades, and currently have a wide range of applications ranging from key
predistribution in wireless sensor networks to modeling social networks. In
this paper, we investigate the strengths of connectivity and robustness in a
general random intersection graph model. Specifically, we establish sharp
asymptotic zero-one laws for -connectivity and -robustness, as well as
the asymptotically exact probability of -connectivity, for any positive
integer . The -connectivity property quantifies how resilient is the
connectivity of a graph against node or edge failures. On the other hand,
-robustness measures the effectiveness of local diffusion strategies (that
do not use global graph topology information) in spreading information over the
graph in the presence of misbehaving nodes. In addition to presenting the
results under the general random intersection graph model, we consider two
special cases of the general model, a binomial random intersection graph and a
uniform random intersection graph, which both have numerous applications as
well. For these two specialized graphs, our results on asymptotically exact
probabilities of -connectivity and asymptotic zero-one laws for
-robustness are also novel in the literature.Comment: This paper about random graphs appears in IEEE Conference on Decision
and Control (CDC) 2014, the premier conference in control theor
Connectivity in Secure Wireless Sensor Networks under Transmission Constraints
In wireless sensor networks (WSNs), the Eschenauer-Gligor (EG) key
pre-distribution scheme is a widely recognized way to secure communications.
Although connectivity properties of secure WSNs with the EG scheme have been
extensively investigated, few results address physical transmission
constraints. These constraints reflect real-world implementations of WSNs in
which two sensors have to be within a certain distance from each other to
communicate. In this paper, we present zero-one laws for connectivity in WSNs
employing the EG scheme under transmission constraints. These laws help specify
the critical transmission ranges for connectivity. Our analytical findings are
confirmed via numerical experiments. In addition to secure WSNs, our
theoretical results are also applied to frequency hopping in wireless networks.Comment: Full version of a paper published in Annual Allerton Conference on
Communication, Control, and Computing (Allerton) 201
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