11,381 research outputs found
Doppler effect of gamma-ray bursts in the fireball framework
The influence of the Doppler effect in the fireball framework on the spectrum
of gamma-ray bursts is investigated. The study shows that the shape of the
expected spectrum of an expanding fireball remains almost the same as that of
the corresponding rest frame spectrum for constant radiations of the
bremsstrahlung, Comptonized, and synchrotron mechanisms as well as for that of
the GRB model. The peak flux spectrum and the peak frequency are obviously
correlated. When the value of the Lorentz factor becomes 10 times larger, the
flux of fireballs would be several orders of magnitude larger. The expansion
speed of fireballs is a fundamental factor of the enhancement of the flux of
gamma-ray bursts.Comment: 19 pages, 13 figure
Clustering with diversity
We consider the {\em clustering with diversity} problem: given a set of
colored points in a metric space, partition them into clusters such that each
cluster has at least points, all of which have distinct colors.
We give a 2-approximation to this problem for any when the objective
is to minimize the maximum radius of any cluster. We show that the
approximation ratio is optimal unless , by providing a matching
lower bound. Several extensions to our algorithm have also been developed for
handling outliers. This problem is mainly motivated by applications in
privacy-preserving data publication.Comment: Extended abstract accepted in ICALP 2010. Keywords: Approximation
algorithm, k-center, k-anonymity, l-diversit
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