1,818 research outputs found
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
Control of Multilayer Networks
The controllability of a network is a theoretical problem of relevance in a
variety of contexts ranging from financial markets to the brain. Until now,
network controllability has been characterized only on isolated networks, while
the vast majority of complex systems are formed by multilayer networks. Here we
build a theoretical framework for the linear controllability of multilayer
networks by mapping the problem into a combinatorial matching problem. We found
that correlating the external signals in the different layers can significantly
reduce the multiplex network robustness to node removal, as it can be seen in
conjunction with a hybrid phase transition occurring in interacting Poisson
networks. Moreover we observe that multilayer networks can stabilize the fully
controllable multiplex network configuration that can be stable also when the
full controllability of the single network is not stable
On the Mean Residence Time in Stochastic Lattice-Gas Models
A heuristic law widely used in fluid dynamics for steady flows states that
the amount of a fluid in a control volume is the product of the fluid influx
and the mean time that the particles of the fluid spend in the volume, or mean
residence time. We rigorously prove that if the mean residence time is
introduced in terms of sample-path averages, then stochastic lattice-gas models
with general injection, diffusion, and extraction dynamics verify this law.
Only mild assumptions are needed in order to make the particles distinguishable
so that their residence time can be unambiguously defined. We use our general
result to obtain explicit expressions of the mean residence time for the Ising
model on a ring with Glauber + Kawasaki dynamics and for the totally asymmetric
simple exclusion process with open boundaries
Optimal equilibria of the best shot game
We consider any network environment in which the "best shot game" is played.
This is the case where the possible actions are only two for every node (0 and
1), and the best response for a node is 1 if and only if all her neighbors play
0. A natural application of the model is one in which the action 1 is the
purchase of a good, which is locally a public good, in the sense that it will
be available also to neighbors. This game typically exhibits a great
multiplicity of equilibria. Imagine a social planner whose scope is to find an
optimal equilibrium, i.e. one in which the number of nodes playing 1 is
minimal. To find such an equilibrium is a very hard task for any non-trivial
network architecture. We propose an implementable mechanism that, in the limit
of infinite time, reaches an optimal equilibrium, even if this equilibrium and
even the network structure is unknown to the social planner.Comment: submitted to JPE
Loop corrections in spin models through density consistency
Computing marginal distributions of discrete or semidiscrete Markov random
fields (MRFs) is a fundamental, generally intractable problem with a vast
number of applications in virtually all fields of science. We present a new
family of computational schemes to approximately calculate the marginals of
discrete MRFs. This method shares some desirable properties with belief
propagation, in particular, providing exact marginals on acyclic graphs, but it
differs with the latter in that it includes some loop corrections; i.e., it
takes into account correlations coming from all cycles in the factor graph. It
is also similar to the adaptive Thouless-Anderson-Palmer method, but it differs
with the latter in that the consistency is not on the first two moments of the
distribution but rather on the value of its density on a subset of values. The
results on finite-dimensional Isinglike models show a significant improvement
with respect to the Bethe-Peierls (tree) approximation in all cases and with
respect to the plaquette cluster variational method approximation in many
cases. In particular, for the critical inverse temperature of the
homogeneous hypercubic lattice, the expansion of
around of the proposed scheme is exact up to the order,
whereas the two latter are exact only up to the order.Comment: 12 pages, 3 figures, 1 tabl
Statics and dynamics of selfish interactions in distributed service systems
We study a class of games which model the competition among agents to access
some service provided by distributed service units and which exhibit congestion
and frustration phenomena when service units have limited capacity. We propose
a technique, based on the cavity method of statistical physics, to characterize
the full spectrum of Nash equilibria of the game. The analysis reveals a large
variety of equilibria, with very different statistical properties. Natural
selfish dynamics, such as best-response, usually tend to large-utility
equilibria, even though those of smaller utility are exponentially more
numerous. Interestingly, the latter actually can be reached by selecting the
initial conditions of the best-response dynamics close to the saturation limit
of the service unit capacities. We also study a more realistic stochastic
variant of the game by means of a simple and effective approximation of the
average over the random parameters, showing that the properties of the
average-case Nash equilibria are qualitatively similar to the deterministic
ones.Comment: 30 pages, 10 figure
Predicting epidemic evolution on contact networks from partial observations
The massive employment of computational models in network epidemiology calls
for the development of improved inference methods for epidemic forecast. For
simple compartment models, such as the Susceptible-Infected-Recovered model,
Belief Propagation was proved to be a reliable and efficient method to identify
the origin of an observed epidemics. Here we show that the same method can be
applied to predict the future evolution of an epidemic outbreak from partial
observations at the early stage of the dynamics. The results obtained using
Belief Propagation are compared with Monte Carlo direct sampling in the case of
SIR model on random (regular and power-law) graphs for different observation
methods and on an example of real-world contact network. Belief Propagation
gives in general a better prediction that direct sampling, although the quality
of the prediction depends on the quantity under study (e.g. marginals of
individual states, epidemic size, extinction-time distribution) and on the
actual number of observed nodes that are infected before the observation time
Optimal Equilibria of the Best Shot Game
We consider any network environment in which the “best shot game” is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A natural application of the model is one in which the action 1 is the purchase of a good, which is locally a public good, in the sense that it will be available also to neighbors. This game will typically exhibit a great multiplicity of equilibria. Imagine a social planner whose scope is to find an optimal equilibrium, i.e. one in which the number of nodes playing 1 is minimal. To find such an equilibrium is a very hard task for any non-trivial network architecture. We propose an implementable mechanism that, in the limit of infinite time, reaches an optimal equilibrium, even if this equilibrium and even the network structure is unknown to the social planner.Networks, Best Shot Game, Simulated Annealing
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