194,442 research outputs found
Generalizations of the Tree Packing Conjecture
The Gy\'arf\'as tree packing conjecture asserts that any set of trees with
vertices has an (edge-disjoint) packing into the complete graph
on vertices. Gy\'arf\'as and Lehel proved that the conjecture holds in some
special cases. We address the problem of packing trees into -chromatic
graphs. In particular, we prove that if all but three of the trees are stars
then they have a packing into any -chromatic graph. We also consider several
other generalizations of the conjecture
Descendants of the first stars: the distinct chemical signature of second generation stars
Extremely metal-poor (EMP) stars in the Milky Way (MW) allow us to infer the
properties of their progenitors by comparing their chemical composition to the
metal yields of the first supernovae. This method is most powerful when applied
to mono-enriched stars, i.e. stars that formed from gas that was enriched by
only one previous supernova. We present a novel diagnostic to identify this
subclass of EMP stars. We model the first generations of star formation
semi-analytically, based on dark matter halo merger trees that yield MW-like
halos at the present day. Radiative and chemical feedback are included
self-consistently and we trace all elements up to zinc. Mono-enriched stars
account for only of second generation stars in our fiducial model
and we provide an analytical formula for this probability. We also present a
novel analytical diagnostic to identify mono-enriched stars, based on the metal
yields of the first supernovae. This new diagnostic allows us to derive our
main results independently from the specific assumptions made regarding Pop III
star formation, and we apply it to a set of observed EMP stars to demonstrate
its strengths and limitations. Our results may provide selection criteria for
current and future surveys and therefore contribute to a deeper understanding
of EMP stars and their progenitors.Comment: 18 pages, 20 figures, published in MNRA
Machine learning techniques to select Be star candidates. An application in the OGLE-IV Gaia south ecliptic pole field
Statistical pattern recognition methods have provided competitive solutions
for variable star classification at a relatively low computational cost. In
order to perform supervised classification, a set of features is proposed and
used to train an automatic classification system. Quantities related to the
magnitude density of the light curves and their Fourier coefficients have been
chosen as features in previous studies. However, some of these features are not
robust to the presence of outliers and the calculation of Fourier coefficients
is computationally expensive for large data sets. We propose and evaluate the
performance of a new robust set of features using supervised classifiers in
order to look for new Be star candidates in the OGLE-IV Gaia south ecliptic
pole field. We calculated the proposed set of features on six types of variable
stars and on a set of Be star candidates reported in the literature. We
evaluated the performance of these features using classification trees and
random forests along with K-nearest neighbours, support vector machines, and
gradient boosted trees methods. We tuned the classifiers with a 10-fold
cross-validation and grid search. We validated the performance of the best
classifier on a set of OGLE-IV light curves and applied this to find new Be
star candidates. The random forest classifier outperformed the others. By using
the random forest classifier and colour criteria we found 50 Be star candidates
in the direction of the Gaia south ecliptic pole field, four of which have
infrared colours consistent with Herbig Ae/Be stars. Supervised methods are
very useful in order to obtain preliminary samples of variable stars extracted
from large databases. As usual, the stars classified as Be stars candidates
must be checked for the colours and spectroscopic characteristics expected for
them
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