6,571 research outputs found
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
Timing interactions in social simulations: The voter model
The recent availability of huge high resolution datasets on human activities
has revealed the heavy-tailed nature of the interevent time distributions. In
social simulations of interacting agents the standard approach has been to use
Poisson processes to update the state of the agents, which gives rise to very
homogeneous activity patterns with a well defined characteristic interevent
time. As a paradigmatic opinion model we investigate the voter model and review
the standard update rules and propose two new update rules which are able to
account for heterogeneous activity patterns. For the new update rules each node
gets updated with a probability that depends on the time since the last event
of the node, where an event can be an update attempt (exogenous update) or a
change of state (endogenous update). We find that both update rules can give
rise to power law interevent time distributions, although the endogenous one
more robustly. Apart from that for the exogenous update rule and the standard
update rules the voter model does not reach consensus in the infinite size
limit, while for the endogenous update there exist a coarsening process that
drives the system toward consensus configurations.Comment: Book Chapter, 23 pages, 9 figures, 5 table
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Distributed anonymous discrete function computation
We propose a model for deterministic distributed function computation by a
network of identical and anonymous nodes. In this model, each node has bounded
computation and storage capabilities that do not grow with the network size.
Furthermore, each node only knows its neighbors, not the entire graph. Our goal
is to characterize the class of functions that can be computed within this
model. In our main result, we provide a necessary condition for computability
which we show to be nearly sufficient, in the sense that every function that
satisfies this condition can at least be approximated. The problem of computing
suitably rounded averages in a distributed manner plays a central role in our
development; we provide an algorithm that solves it in time that grows
quadratically with the size of the network
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