9,259 research outputs found
Percolation transition in correlated hypergraphs
Correlations are known to play a crucial role in determining the structure of
complex networks. Here we study how their presence affects the computation of
the percolation threshold in random hypergraphs. In order to mimic the
correlation in real network, we build hypergraphs from a generalized hidden
variable ensembles and we study the percolation transition by mapping this
problem to the fully connected Potts model with heterogeneous couplings
Efficiently Controllable Graphs
We investigate graphs that can be disconnected into small components by
removing a vanishingly small fraction of their vertices. We show that when a
quantum network is described by such a graph, the network is efficiently
controllable, in the sense that universal quantum computation can be performed
using a control sequence polynomial in the size of the network while
controlling a vanishingly small fraction of subsystems. We show that networks
corresponding to finite-dimensional lattices are efficently controllable, and
explore generalizations to percolation clusters and random graphs. We show that
the classical computational complexity of estimating the ground state of
Hamiltonians described by controllable graphs is polynomial in the number of
subsystems/qubits
A Self-Organized Method for Computing the Epidemic Threshold in Computer Networks
In many cases, tainted information in a computer network can spread in a way
similar to an epidemics in the human world. On the other had, information
processing paths are often redundant, so a single infection occurrence can be
easily "reabsorbed". Randomly checking the information with a central server is
equivalent to lowering the infection probability but with a certain cost (for
instance processing time), so it is important to quickly evaluate the epidemic
threshold for each node. We present a method for getting such information
without resorting to repeated simulations. As for human epidemics, the local
information about the infection level (risk perception) can be an important
factor, and we show that our method can be applied to this case, too. Finally,
when the process to be monitored is more complex and includes "disruptive
interference", one has to use actual simulations, which however can be carried
out "in parallel" for many possible infection probabilities
Inhomogeneous percolation models for spreading phenomena in random graphs
Percolation theory has been largely used in the study of structural
properties of complex networks such as the robustness, with remarkable results.
Nevertheless, a purely topological description is not sufficient for a correct
characterization of networks behaviour in relation with physical flows and
spreading phenomena taking place on them. The functionality of real networks
also depends on the ability of the nodes and the edges in bearing and handling
loads of flows, energy, information and other physical quantities. We propose
to study these properties introducing a process of inhomogeneous percolation,
in which both the nodes and the edges spread out the flows with a given
probability.
Generating functions approach is exploited in order to get a generalization
of the Molloy-Reed Criterion for inhomogeneous joint site bond percolation in
correlated random graphs. A series of simple assumptions allows the analysis of
more realistic situations, for which a number of new results are presented. In
particular, for the site percolation with inhomogeneous edge transmission, we
obtain the explicit expressions of the percolation threshold for many
interesting cases, that are analyzed by means of simple examples and numerical
simulations. Some possible applications are debated.Comment: 28 pages, 11 figure
- …