13,712 research outputs found
Relativistic effects on the observed AGN luminosity distribution
Recently Zhang (2005) has proposed a model to account for the well
established effect that the fraction of type-II AGNs is anti-correlated with
the observed X-ray luminosity; the model consists of an X-ray emitting
accretion disk coaligned to the dusty torus within the standard AGN unification
model. In this paper the model is refined by including relativistic effects of
the observed X-ray radiations from the vicinity of the supermassive black hole
in an AGN. The relativistic corrections improve the combined fitting results of
the observed luminosity distribution and the type-II AGN fraction, though the
improvement is not significant. The type-II AGN fraction prefers non- or mildly
spinning black hole cases and rules out the extremely spinning case.Comment: 9 pages, 4 figures, accepted for publication in PAS
On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
In decentralized consensus optimization, a connected network of agents
collaboratively minimize the sum of their local objective functions over a
common decision variable, where their information exchange is restricted
between the neighbors. To this end, one can first obtain a problem
reformulation and then apply the alternating direction method of multipliers
(ADMM). The method applies iterative computation at the individual agents and
information exchange between the neighbors. This approach has been observed to
converge quickly and deemed powerful. This paper establishes its linear
convergence rate for decentralized consensus optimization problem with strongly
convex local objective functions. The theoretical convergence rate is
explicitly given in terms of the network topology, the properties of local
objective functions, and the algorithm parameter. This result is not only a
performance guarantee but also a guideline toward accelerating the ADMM
convergence.Comment: 11 figures, IEEE Transactions on Signal Processing, 201
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