A Continuous Injection Plasma Model for the X-Ray/Radio Knots in Kpc-Scale Jets of AGN

We consider the evolution of a spherically expanding plasma cloud, where there is continuous injection of non-thermal electrons. We compute the time dependent electron distribution and resultant photon spectra taking into account synchrotron, adiabatic and inverse Compton cooling. This model is different from previous works where, instead of a continuous injection of particles, a short injection period was assumed. We apply this model to the radio/optical knots in the large scale jets of AGN, detected in X-rays by {\it Chandra} and find that the overall broadband spectral features can be reproduced. It is shown that for some sources, constraints on the X-ray spectral index (by a longer {\it Chandra} observation) will be able to differentiate between the different models. This in turn will put a strong constraint on the acceleration mechanism active in these sources.Comment: Accepted for publications in the Astrophysical Journal Letter

Black Hole Entropy from Spin One Punctures

Recent suggestion, that the emission of a quantum of energy corresponding to the asymptotic value of quasinormal modes of a Schwarzschild black hole should be associated with the loss of spin one punctures from the black hole horizon, fixes the Immirzi parameter to a definite value. We show that saturating the horizon with spin one punctures reproduces the earlier formula for the black hole entropy, including the $ln (area)$ correction with definite coefficient (- 3/2) for large area.Comment: 4 pages. RevTe

Optimizing Information Freshness in Wireless Networks under General Interference Constraints

Age of information (AoI) is a recently proposed metric for measuring information freshness. AoI measures the time that elapsed since the last received update was generated. We consider the problem of minimizing average and peak AoI in a wireless networks, consisting of a set of source-destination links, under general interference constraints. When fresh information is always available for transmission, we show that a stationary scheduling policy is peak age optimal. We also prove that this policy achieves average age that is within a factor of two of the optimal average age. In the case where fresh information is not always available, and packet/information generation rate has to be controlled along with scheduling links for transmission, we prove an important separation principle: the optimal scheduling policy can be designed assuming fresh information, and independently, the packet generation rate control can be done by ignoring interference. Peak and average AoI for discrete time G/Ber/1 queue is analyzed for the first time, which may be of independent interest

BTZ Black Hole Entropy from Ponzano-Regge Gravity

The entropy of the BTZ black hole is computed in the Ponzano-Regge formulation of three-dimensional lattice gravity. It is seen that the correct semi-classical behaviour of entropy is reproduced by states that correspond to all possible triangulations of the Euclidean black hole.Comment: 11 pages LaTeX, 3 eps figures, some minor clarifications added, result unchange

Reductions for the Stable Set Problem

One approach to finding a maximum stable set (MSS) in a graph is to try to reduce the size of the problem by transforming the problem into an equivalent problem on a smaller graph. This paper introduces several new reductions for the MSS problem, extends several well-known reductions to the maximum weight stable set (MWSS) problem, demonstrates how reductions for the generalized stable set problem can be used in conjunction with probing to produce powerful new reductions for both the MSS and MWSS problems, and shows how hypergraphs can be used to expand the capabilities of clique projections. The effectiveness of these new reduction techniques are illustrated on the DIMACS benchmark graphs, planar graphs, and a set of challenging MSS problems arising from Steiner Triple Systems

Quantum Aspects of Black Hole Entropy

This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based N=2 supergravity are also discussed, albeit more briefly.Comment: 13 Pages Revtex with 3 eps figures; based on plenary talk given at the International Conference on Gravitation and Cosmology, Kharagpur, India, January, 2000 One reference adde