Oversampling in shift-invariant spaces with a rational sampling period

8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología

A test for asymptotic giant branch evolution theories: Planetary Nebulae in the Large Magellanic Cloud

We used a new generation of asymptotic giant branch (AGB) stellar models that include dust formation in the stellar winds to find the links between evolutionary models and the observed properties of a homogeneous sample of Large Magellanic Cloud (LMC) planetary nebulae (PNe). Comparison between the evolutionary yields of elements such as CNO and the corresponding observed chemical abundances is a powerful tool to shed light on evolutionary processes such as hot bottom burning (HBB) and third dredge-up (TDU). We found that the occurrence of HBB is needed to interpret the nitrogen-enriched (log(N/H)+12>8) PNe. In particular, N-rich PNe with the lowest carbon content are nicely reproduced by AGB models of mass M >=6 Mo, whose surface chemistry reflects the pure effects of HBB. PNe with log(N/H)+12<7.5 correspond to ejecta of stars that have not experienced HBB, with initial mass below about 3 Mo. Some of these stars show very large carbon abundances, owing to the many TDU episodes experienced. We found from our LMC PN sample that there is a threshold to the amount of carbon accumulated at AGB surfaces, log(C/H)+12<9. Confirmation of this constraint would indicate that, after the C-star stage is reached,AGBs experience only a few thermal pulses, which suggests a rapid loss of the external mantle, probably owing to the effects of radiation pressure on carbonaceous dust particles present in the circumstellar envelope. The implications of these findings for AGB evolution theories and the need to extend the PN sample currently available are discussed.Comment: 12 pages, 4 figures, 1 table, accepted for publication in MNRAS (2015 July 13; in original form 2015 June 9

Planetary Nebulae in the Small Magellanic Cloud

We analyse the planetary nebulae (PNe) population of the Small Magellanic Cloud (SMC), based on evolutionary models of stars with metallicities in the range $10^{-3} \leq Z \leq 4\times 10^{-3}$ and mass $0.9 M\odot < M < 8M\odot$, evolved through the asymptotic giant branch (AGB) phase. The models used account for dust formation in the circumstellar envelope. To characterise the PNe sample of the SMC, we compare the observed abundances of the various species with the final chemical composition of the AGB models: this study allows us to identify the progenitors of the PNe observed, in terms of mass and chemical composition. According to our interpretation, most of the PNe descend from low-mass ($M < 2 M\odot$) stars, which become carbon rich, after experiencing repeated third dredge-up episodes, during the AGB phase. A fraction of the PNe showing the signature of advanced CNO processing are interpreted as the progeny of massive AGB stars, with mass above $\sim 6 M\odot$, undergoing strong hot bottom burning. The differences with the chemical composition of the PNe population of the Large Magellanic Cloud (LMC) is explained on the basis of the diverse star formation history and age-metallicity relation of the two galaxies. The implications of the present study for some still highly debated points regarding the AGB evolution are also commented.Comment: Accepted for publication in MNRAS, 11 pages, 4 figure

On the nature of the most obscured C-rich AGB stars in the Magellanic Clouds

The stars in the Magellanic Clouds with the largest degree of obscuration are used to probe the highly uncertain physics of stars in the asymptotic giant branch (AGB) phase of evolution. Carbon stars in particular, provide key information on the amount of third dredge-up (TDU) and mass loss. We use two independent stellar evolution codes to test how a different treatment of the physics affects the evolution on the AGB. The output from the two codes are used to determine the rates of dust formation in the circumstellar envelope, where the method used to determine the dust is the same for each case. The stars with the largest degree of obscuration in the LMC and SMC are identified as the progeny of objects of initial mass $2.5-3~M_{\odot}$ and $\sim 1.5~M_{\odot}$, respectively. This difference in mass is motivated by the difference in the star formation histories of the two galaxies, and offers a simple explanation of the redder infrared colours of C-stars in the LMC compared to their counterparts in the SMC. The comparison with the Spitzer colours of C-rich AGB stars in the SMC shows that a minimum surface carbon mass fraction $X(C) \sim 5\times 10^{-3}$ must have been reached by stars of initial mass around $1.5~M_{\odot}$. Our results confirm the necessity of adopting low-temperature opacities in stellar evolutionary models of AGB stars. These opacities allow the stars to obtain mass-loss rates high enough ($\gtrsim 10^{-4}M_{\odot}/yr$) to produce the amount of dust needed to reproduce the Spitzer coloursComment: 14 pages, 5 figures, 1 table; accepted for publication in MNRAS Main Journa

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

Role of 5 α -dihydrotestosterone in testicular development of gilthead seabream following finasteride administration

In teleosts, spermatogenesis is regulated by pituitary gonadotropins and sex steroids. 5α-dihydrotestosterone (DHT), derived from testosterone (T) through the action of 5α-reductase, has recently been suggested to play a physiologically important role in some fish species. In this study, gilthead seabream, Sparus aurata L., males received an implant of 1μg T/g body mass (bm) or vehicle alone and, 7 days later, 1 mg finasteride (FIN, an inhibitor of 5α-reductase)/kg bm or vehicle. Serum levels of T, 11-ketotestosterone (11KT), DHT and 17β-estradiol (E2), and the mRNA levels of the main enzymes involved in their synthesis, were analysed. T promoted a transient increase in the serum levels of T, 11KT and E2 but a decrease in those of DHT at day 15 following T injection, in accordance with the up-regulation of mRNA levels of the enzymes involved in T transformation to 11KT (coding genes: cyp11b1 and hsd11b) and the down-regulation of mRNA levels of the enzyme responsible for T transformation to DHT (coding gene:srd5a). Interestingly, a similar effect was observed when FIN was in- jected. However, when fish were injected with T and FIN successively (T + FIN), control levels were not re-covered at the end of the experimental period (28 days). DHT seems to regulate E2 serum levels via the down-regulation of mRNA levels of aromatase (coding gene:cyp19a1a), which is needed for the transformation of T into E2. The testis histology, together with the proliferative rates recorded upon T, FIN or T + FIN treatment, suggests that DHT is involved in the onset of the meiotic phase of spermatogenesis.Versión del edito