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