1,991 research outputs found
Information Spreading on Almost Torus Networks
Epidemic modeling has been extensively used in the last years in the field of
telecommunications and computer networks. We consider the popular
Susceptible-Infected-Susceptible spreading model as the metric for information
spreading. In this work, we analyze information spreading on a particular class
of networks denoted almost torus networks and over the lattice which can be
considered as the limit when the torus length goes to infinity. Almost torus
networks consist on the torus network topology where some nodes or edges have
been removed. We find explicit expressions for the characteristic polynomial of
these graphs and tight lower bounds for its computation. These expressions
allow us to estimate their spectral radius and thus how the information spreads
on these networks
Information Spreading on Almost Torus Networks
International audienceEpidemic modeling has been extensively used in the last years in the field of telecommunications and computer networks. We consider the popular Susceptible-Infected-Susceptible spreading model as the metric for information spreading. In this work, we analyze information spreading on a particular class of networks denoted almost torus networks and over the lattice which can be considered as the limit when the torus length goes to infinity. Almost torus networks consist on the torus network topology where some nodes or edges have been removed. We find explicit expressions for the characteristic polynomial of these graphs and tight lower bounds for its computation. These expressions allow us to estimate their spectral radius and thus how the information spreads on these networks
Effect of small-world topology on wave propagation on networks of excitable elements
We study excitation waves on a Newman-Watts small-world network model of
coupled excitable elements. Depending on the global coupling strength, we find
differing resilience to the added long-range links and different mechanisms of
propagation failure. For high coupling strengths, we show agreement between the
network and a reaction-diffusion model with additional mean-field term.
Employing this approximation, we are able to estimate the critical density of
long-range links for propagation failure.Comment: 19 pages, 8 figures and 5 pages supplementary materia
On the Role of Mobility for Multi-message Gossip
We consider information dissemination in a large -user wireless network in
which users wish to share a unique message with all other users. Each of
the users only has knowledge of its own contents and state information;
this corresponds to a one-sided push-only scenario. The goal is to disseminate
all messages efficiently, hopefully achieving an order-optimal spreading rate
over unicast wireless random networks. First, we show that a random-push
strategy -- where a user sends its own or a received packet at random -- is
order-wise suboptimal in a random geometric graph: specifically,
times slower than optimal spreading. It is known that this
gap can be closed if each user has "full" mobility, since this effectively
creates a complete graph. We instead consider velocity-constrained mobility
where at each time slot the user moves locally using a discrete random walk
with velocity that is much lower than full mobility. We propose a simple
two-stage dissemination strategy that alternates between individual message
flooding ("self promotion") and random gossiping. We prove that this scheme
achieves a close to optimal spreading rate (within only a logarithmic gap) as
long as the velocity is at least . The key
insight is that the mixing property introduced by the partial mobility helps
users to spread in space within a relatively short period compared to the
optimal spreading time, which macroscopically mimics message dissemination over
a complete graph.Comment: accepted to IEEE Transactions on Information Theory, 201
Free vacuum for loop quantum gravity
We linearize extended ADM-gravity around the flat torus, and use the
associated Fock vacuum to construct a state that could play the role of a free
vacuum in loop quantum gravity. The state we obtain is an element of the
gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a
natural consequence of the momentum cutoff of the original Fock state. It has
the form of a Gaussian superposition of spin networks. We show that the peak of
the Gaussian lies at weave-like states and derive a relation between the
coloring of the weaves and the cutoff scale. Our analysis indicates that the
peak weaves become independent of the cutoff length when the latter is much
smaller than the Planck length. By the same method, we also construct
multiple-graviton states. We discuss the possible use of these states for
deriving a perturbation series in loop quantum gravity.Comment: 30 pages, 3 diagrams, treatment of phase factor adde
Complex Contagions in Kleinberg's Small World Model
Complex contagions describe diffusion of behaviors in a social network in
settings where spreading requires the influence by two or more neighbors. In a
-complex contagion, a cluster of nodes are initially infected, and
additional nodes become infected in the next round if they have at least
already infected neighbors. It has been argued that complex contagions better
model behavioral changes such as adoption of new beliefs, fashion trends or
expensive technology innovations. This has motivated rigorous understanding of
spreading of complex contagions in social networks. Despite simple contagions
() that spread fast in all small world graphs, how complex contagions
spread is much less understood. Previous work~\cite{Ghasemiesfeh:2013:CCW}
analyzes complex contagions in Kleinberg's small world
model~\cite{kleinberg00small} where edges are randomly added according to a
spatial distribution (with exponent ) on top of a two dimensional grid
structure. It has been shown in~\cite{Ghasemiesfeh:2013:CCW} that the speed of
complex contagions differs exponentially when compared to when
.
In this paper, we fully characterize the entire parameter space of
except at one point, and provide upper and lower bounds for the speed of
-complex contagions. We study two subtly different variants of Kleinberg's
small world model and show that, with respect to complex contagions, they
behave differently. For each model and each , we show that there is
an intermediate range of values, such that when takes any of these
values, a -complex contagion spreads quickly on the corresponding graph, in
a polylogarithmic number of rounds. However, if is outside this range,
then a -complex contagion requires a polynomial number of rounds to spread
to the entire network.Comment: arXiv admin note: text overlap with arXiv:1404.266
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