1,570 research outputs found
Relaxation of monotone coupling conditions: Poisson approximation and beyond
It is well-known that assumptions of monotonicity in size-bias couplings may
be used to prove simple, yet powerful, Poisson approximation results. Here we
show how these assumptions may be relaxed, establishing explicit Poisson
approximation bounds (depending on the first two moments only) for random
variables which satisfy an approximate version of these monotonicity
conditions. These are shown to be effective for models where an underlying
random variable of interest is contaminated with noise. We also give explicit
Poisson approximation bounds for sums of associated or negatively associated
random variables. Applications are given to epidemic models, extremes, and
random sampling. Finally, we also show how similar techniques may be used to
relax the assumptions needed in a Poincar\'e inequality and in a normal
approximation result.Comment: 19 page
Infrared Period-Luminosity Relations of Evolved Variable Stars in the Large Magellanic Cloud
We combine variability information from the MAssive Compact Halo Objects
(MACHO) survey of the Large Magellanic Cloud (LMC) with infrared photometry
from the Spitzer Space Telescope Surveying the Agents of a Galaxy's Evolution
(SAGE) survey to create a dataset of ~30 000 variable red sources. We
photometrically classify these sources as being on the first ascent of the Red
Giant Branch (RGB), or as being in one of three stages along the Asymptotic
Giant Branch (AGB): oxygen-rich, carbon-rich, or highly reddened with
indeterminate chemistry ("extreme" AGB candidates). We present linear
period-luminosity relationships for these sources using 8 separate infrared
bands (J, H, K, 3.6, 4.5, 5.8, 8.0, and 24 micron) as proxies for the
luminosity. We find that the wavelength dependence of the slope of the
period-luminosity relationship is different for different photometrically
determined classes of AGB stars. Stars photometrically classified as O-rich
show the least variation of slope with wavelength, while dust enshrouded
extreme AGB stars show a pronounced trend toward steeper slopes with increasing
wavelength. We find that O-rich AGB stars pulsating in the fundamental mode
obey a period-magnitude relation with a slope of -3.41 +/- 0.04 when magnitude
is measured in the 3.6 micron band, in contrast to C-rich AGB stars, which obey
a relation of slope -3.77 +/- 0.05
Web invariants for flamingo Specht modules
Webs yield an especially important realization of certain Specht modules,
irreducible representations of symmetric groups, as they provide a pictorial
basis with a convenient diagrammatic calculus. In recent work, the last three
authors associated polynomials to noncrossing partitions without singleton
blocks, so that the corresponding polynomials form a web basis of the pennant
Specht module . These polynomials were interpreted as
global sections of a line bundle on a 2-step partial flag variety.
Here, we both simplify and extend this construction. On the one hand, we show
that these polynomials can alternatively be situated in the homogeneous
coordinate ring of a Grassmannian, instead of a 2-step partial flag variety,
and can be realized as tensor invariants of classical (but highly nonplanar)
tensor diagrams. On the other hand, we extend these ideas from the pennant
Specht module to more general flamingo Specht modules
. In the hook case , we obtain a spanning set that can
be restricted to a basis in various ways. In the case , we obtain a basis
of a well-behaved subspace of , but not of the entire
module.Comment: 32 pages, 7 figure
SDSS J210014.12+004446.0: A New Dwarf Nova with Quiescent Superhumps?
We report follow-up observations of the Sloan Digital Sky Survey Cataclysmic
Variable SDSS J210014.12+004446.0 (hereafter SDSS J2100). We obtained
photometry and spectroscopy in both outburst and quiescent states, providing
the first quiescent spectrum of this source. In both states, non-sinusoidal
photometric modulations are apparent, suggestive of superhumps, placing SDSS
J2100 in the SU UMa subclass of dwarf novae. However, the periods during
outburst and quiescence differ significantly, being 2.099 plus or minus 0.002
hr and 1.96 plus or minus 0.02 hr respectively. Our phase-resolved spectroscopy
during outburst yielded an estimate of about 2 hr for the orbital period,
consistent with the photometry. The presence of the shorter period modulation
at quiescence is unusual, but not unique. Another atypical feature is the
relative weakness of the Balmer emission lines in quiescence. Overall, we find
a close similarity between SDSS J2100 and the well-studied superhump
cataclysmic Variable V503 Cygni. By analogy, we suggest that the quiescent
modulation is due to a tilted accretion disk -- producing negative superhumps
-- and the modulation in outburst is due to positive superhumps from the
precession of an elliptical disk.Comment: 6 pages, 5 eps figures, accepted by PASP Dec. 16th, 200
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