71,473 research outputs found
On the Existence of General Factors in Regular Graphs
Let be a graph, and a set function
associated with . A spanning subgraph of is called an -factor if
the degree of any vertex in belongs to the set . This paper
contains two results on the existence of -factors in regular graphs. First,
we construct an -regular graph without some given -factor. In
particular, this gives a negative answer to a problem recently posed by Akbari
and Kano. Second, by using Lov\'asz's characterization theorem on the existence
of -factors, we find a sharp condition for the existence of general
-factors in -graphs, in terms of the maximum and minimum of .
The result reduces to Thomassen's theorem for the case that consists of
the same two consecutive integers for all vertices , and to Tutte's theorem
if the graph is regular in addition.Comment: 10 page
Nonparametric inference procedure for percentiles of the random effects distribution in meta-analysis
To investigate whether treating cancer patients with
erythropoiesis-stimulating agents (ESAs) would increase the mortality risk,
Bennett et al. [Journal of the American Medical Association 299 (2008)
914--924] conducted a meta-analysis with the data from 52 phase III trials
comparing ESAs with placebo or standard of care. With a standard parametric
random effects modeling approach, the study concluded that ESA administration
was significantly associated with increased average mortality risk. In this
article we present a simple nonparametric inference procedure for the
distribution of the random effects. We re-analyzed the ESA mortality data with
the new method. Our results about the center of the random effects distribution
were markedly different from those reported by Bennett et al. Moreover, our
procedure, which estimates the distribution of the random effects, as opposed
to just a simple population average, suggests that the ESA may be beneficial to
mortality for approximately a quarter of the study populations. This new
meta-analysis technique can be implemented with study-level summary statistics.
In contrast to existing methods for parametric random effects models, the
validity of our proposal does not require the number of studies involved to be
large. From the results of an extensive numerical study, we find that the new
procedure performs well even with moderate individual study sample sizes.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS280 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Study on the spectrum of the injected relativistic protons
About 10TeV gamma-ray emission within 10 pc region from the Galactic Center
had been reported by 4 independent groups. Considering that this TeV gamma-ray
emission is produced via a hadronic model, and the relativistic protons came
from the tidal disruption of stars by massive black holes, we investigate the
spectral nature of the injected relativistic protons required by the hadronic
model. The calculation was carried on the tidal disruption of the different
types of stars and the different propagation mechanisms of protons in the
interstellar medium. Compared with the observation data from HESS, we find for
the best fitting that the power-law index of the spectrum of the injected
protons is about -1.9, when a red giant star is tidally disrupted, and the
effective confinement of protons diffusion mechanism is adopted.Comment: 2 pages, IAU Symposium 25
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