5,572 research outputs found
Age of Information: Whittle Index for Scheduling Stochastic Arrivals
Age of information is a new concept that characterizes the freshness of
information at end devices. This paper studies the age of information from a
scheduling perspective. We consider a wireless broadcast network where a
base-station updates many users on stochastic information arrivals. Suppose
that only one user can be updated for each time. In this context, we aim at
developing a transmission scheduling algorithm for minimizing the long-run
average age. To develop a low-complexity transmission scheduling algorithm, we
apply the Whittle's framework for restless bandits. We successfully derive the
Whittle index in a closed form and establish the indexability. Based on the
Whittle index, we propose a scheduling algorithm, while experimentally showing
that it closely approximates an age-optimal scheduling algorithm.Comment: ISIT 201
Energy Estimates and Gravitational Collapse
We study the cancelations in the energy estimates for Einstein vacuum
equations in order to prove the formation of black holes along evolutions. The
novelty of the paper is that, we completely avoid using rotation vector fields
to establish the global existence theorem of the solution. More precisely, we
use only canonical null directions as commutators to derive energy estimates at
the level of one derivatives of null curvature components.Comment: 2 figures, 40 page
Non-existence of multiple-black-hole solutions close to Kerr-Newman
We show that a stationary asymptotically flat electro-vacuum solution of
Einstein's equations that is everywhere locally "almost isometric" to a
Kerr-Newman solution cannot admit more than one event horizon. Axial symmetry
is not assumed. In particular this implies that the assumption of a single
event horizon in Alexakis-Ionescu-Klainerman's proof of perturbative uniqueness
of Kerr black holes is in fact unnecessary.Comment: Version 2: improved presentation; no changes to the result. Version
3: corrected an oversight in the historical review. Version 4: version
accepted for publicatio
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