328 research outputs found
Shearer's point process, the hard-sphere model and a continuum Lov\'asz Local Lemma
A point process is R-dependent, if it behaves independently beyond the
minimum distance R. This work investigates uniform positive lower bounds on the
avoidance functions of R-dependent simple point processes with a common
intensity. Intensities with such bounds are described by the existence of
Shearer's point process, the unique R-dependent and R-hard-core point process
with a given intensity. This work also presents several extensions of the
Lov\'asz Local Lemma, a sufficient condition on the intensity and R to
guarantee the existence of Shearer's point process and exponential lower
bounds. Shearer's point process shares combinatorial structure with the
hard-sphere model with radius R, the unique R-hard-core Markov point process.
Bounds from the Lov\'asz Local Lemma convert into lower bounds on the radius of
convergence of a high-temperature cluster expansion of the hard-sphere model.
This recovers a classic result of Ruelle on the uniqueness of the Gibbs measure
of the hard-sphere model via an inductive approach \`a la Dobrushin
Avoidance Coupling
We examine the question of whether a collection of random walks on a graph
can be coupled so that they never collide. In particular, we show that on the
complete graph on n vertices, with or without loops, there is a Markovian
coupling keeping apart Omega(n/log n) random walks, taking turns to move in
discrete time.Comment: 13 pages, 3 figure
Improving Resource Efficiency with Partial Resource Muting for Future Wireless Networks
We propose novel resource allocation algorithms that have the objective of
finding a good tradeoff between resource reuse and interference avoidance in
wireless networks. To this end, we first study properties of functions that
relate the resource budget available to network elements to the optimal utility
and to the optimal resource efficiency obtained by solving max-min utility
optimization problems. From the asymptotic behavior of these functions, we
obtain a transition point that indicates whether a network is operating in an
efficient noise-limited regime or in an inefficient interference-limited regime
for a given resource budget. For networks operating in the inefficient regime,
we propose a novel partial resource muting scheme to improve the efficiency of
the resource utilization. The framework is very general. It can be applied not
only to the downlink of 4G networks, but also to 5G networks equipped with
flexible duplex mechanisms. Numerical results show significant performance
gains of the proposed scheme compared to the solution to the max-min utility
optimization problem with full frequency reuse.Comment: 8 pages, 9 figures, to appear in WiMob 201
Shearer's point process, the hard-sphere model, and a continuum Lovász local lemma
A point process is R-dependent if it behaves independently beyond the minimum
distance R. In this paper we investigate uniform positive lower bounds on the avoidance
functions of R-dependent simple point processes with a common intensity. Intensities
with such bounds are characterised by the existence of Shearer’s point process, the unique
R-dependent and R-hard-core point process with a given intensity. We also present
several extensions of the Lovász local lemma, a sufficient condition on the intensity
andR to guarantee the existence of Shearer’s point process and exponential lower bounds.
Shearer’s point process shares a combinatorial structure with the hard-sphere model with
radius R, the unique R-hard-core Markov point process. Bounds from the Lovász local
lemma convert into lower bounds on the radius of convergence of a high-temperature
cluster expansion of the hard-sphere model. This recovers a classic result of Ruelle
(1969) on the uniqueness of the Gibbs measure of the hard-sphere model via an inductive
approach of Dobrushin (1996)
Conservative collision prediction and avoidance for stochastic trajectories in continuous time and space
Existing work in multi-agent collision prediction and avoidance typically
assumes discrete-time trajectories with Gaussian uncertainty or that are
completely deterministic. We propose an approach that allows detection of
collisions even between continuous, stochastic trajectories with the only
restriction that means and variances can be computed. To this end, we employ
probabilistic bounds to derive criterion functions whose negative sign provably
is indicative of probable collisions. For criterion functions that are
Lipschitz, an algorithm is provided to rapidly find negative values or prove
their absence. We propose an iterative policy-search approach that avoids prior
discretisations and yields collision-free trajectories with adjustably high
certainty. We test our method with both fixed-priority and auction-based
protocols for coordinating the iterative planning process. Results are provided
in collision-avoidance simulations of feedback controlled plants.Comment: This preprint is an extended version of a conference paper that is to
appear in \textit{Proceedings of the 13th International Conference on
Autonomous Agents and Multiagent Systems (AAMAS 2014)
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