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Designs for graphs with six vertices and nine edges
The design spectrum has been determined for eleven of the 21 graphs with six vertices and nine edges. In this paper we completely solve the design spectrum problem for the remaining ten graphs
Bulge Globular Clusters in Spiral Galaxies
There is now strong evidence that the metal-rich globular clusters (GC) near
the center of our Galaxy are associated with the Galactic bulge rather than the
disk as previously thought. Here we extend the concept of bulge GCs to the GC
systems of nearby spiral galaxies. In particular, the kinematic and metallicity
properties of the GC systems favor a bulge rather than a disk origin. The
number of metal-rich GCs normalized by the bulge luminosity is roughly constant
(i.e. bulge S_N ~ 1) in nearby spirals, and this value is similar to that for
field ellipticals when only the red (metal--rich) GCs are considered. We argue
that the metallicity distributions of GCs in spiral and elliptical galaxies are
remarkably similar, and that they obey the same correlation of mean GC
metallicity with host galaxy mass. We further suggest that the metal-rich GCs
in spirals are the direct analogs of the red GCs seen in ellipticals. The
formation of a bulge/spheroidal stellar system is accompanied by the formation
of metal-rich GCs. The similarities between GC systems in spiral and elliptical
galaxies appear to be greater than the differences.Comment: 5 pages, Latex, 2 figures, 1 table, Accepted for publication in ApJ
Letter
The Southern Vilnius Photometric System. IV. The E Regions Standard Stars
This paper is the fourth in a series on the extension of the Vilnius
photometric system to the southern hemisphere. Observations were made of 60
stars in the Harvard Standard E regions to increase a set of standard stars.Comment: 6 pages, TeX, requires 2 macros (baltic2.tex, baltic4.tex) included
no figures, to be published in Baltic Astronomy, Vol 6, pp1-6 (1997
Approximate Bayesian computation via the energy statistic
Approximate Bayesian computation (ABC) has become an essential part of the
Bayesian toolbox for addressing problems in which the likelihood is
prohibitively expensive or entirely unknown, making it intractable. ABC defines
a pseudo-posterior by comparing observed data with simulated data,
traditionally based on some summary statistics, the elicitation of which is
regarded as a key difficulty. Recently, using data discrepancy measures has
been proposed in order to bypass the construction of summary statistics. Here
we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the
so-called two-sample energy statistic. We establish a new asymptotic result for
the case where both the observed sample size and the simulated data sample size
increase to infinity, which highlights to what extent the data discrepancy
measure impacts the asymptotic pseudo-posterior. The result holds in the broad
setting of IS-ABC methodologies, thus generalizing previous results that have
been established only for rejection ABC algorithms. Furthermore, we propose a
consistent V-statistic estimator of the energy statistic, under which we show
that the large sample result holds, and prove that the rejection ABC algorithm,
based on the energy statistic, generates pseudo-posterior distributions that
achieves convergence to the correct limits, when implemented with rejection
thresholds that converge to zero, in the finite sample setting. Our proposed
energy statistic based ABC algorithm is demonstrated on a variety of models,
including a Gaussian mixture, a moving-average model of order two, a bivariate
beta and a multivariate -and- distribution. We find that our proposed
method compares well with alternative discrepancy measures.Comment: 25 pages, 6 figures, 5 table
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