Partition of unity interpolation using stable kernel-based techniques

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, the approach consists in computing, for each PU subdomain, a stable basis. Such technique, taking advantage of the local scheme, leads to a significant benefit in terms of stability, especially for flat kernels. Furthermore, an optimized searching procedure is applied to build the local stable bases, thus rendering the method more efficient

RBF approximation of large datasets by partition of unity and local stabilization

We present an algorithm to approximate large dataset by Radial Basis Function (RBF) techniques. The method couples a fast domain decomposition procedure with a localized stabilization method. The resulting algorithm can efficiently deal with large problems and it is robust with respect to the typical instability of kernel methods

Very Large Telescope Observations of the peculiar globular cluster NGC6712. Discovery of a UV, H-alpha excess star in the core

We present results from multi-band observations in the central region of the cluster NGC6712 with the ESO-Very Large Telescope. Using high resolution images we have identified three UV-excess stars. In particular two of them are within the cluster core, a few arcsec apart: the first object is star "S" which previous studies identified as the best candidate to the optical counterpart to the luminous X-ray source detected in this cluster. The other UV object shows clearcut H-alpha emission and, for this reason, is an additional promising interacting binary candidate (a quiescent LMXB or a CV). The presence of two unrelated interacting binary systems a few arcsec apart in the core of this low-density cluster is somewhat surprising and supports the hypothesis that the (internal) dynamical history of the cluster and/or the (external) interaction with the Galaxy might play a fundamental role in the formation of these peculiar objects.Comment: 15 pages, 3 figures. ApJL in pres

Greedy kernel methods for accelerating implicit integrators for parametric ODEs

We present a novel acceleration method for the solution of parametric ODEs by single-step implicit solvers by means of greedy kernel-based surrogate models. In an offline phase, a set of trajectories is precomputed with a high-accuracy ODE solver for a selected set of parameter samples, and used to train a kernel model which predicts the next point in the trajectory as a function of the last one. This model is cheap to evaluate, and it is used in an online phase for new parameter samples to provide a good initialization point for the nonlinear solver of the implicit integrator. The accuracy of the surrogate reflects into a reduction of the number of iterations until convergence of the solver, thus providing an overall speedup of the full simulation. Interestingly, in addition to providing an acceleration, the accuracy of the solution is maintained, since the ODE solver is still used to guarantee the required precision. Although the method can be applied to a large variety of solvers and different ODEs, we will present in details its use with the Implicit Euler method for the solution of the Burgers equation, which results to be a meaningful test case to demonstrate the method's features

WIYN Open Cluster Study 1: Deep Photometry of NGC 188

We have employed precise V and I photometry of NGC 188 at WIYN to explore the cluster luminosity function (LF) and study the cluster white dwarfs (WDs). Our photometry is offset by V = 0.052 (fainter) from Sandage (1962) and Eggen & Sandage (1969). All published photometry for the past three decades have been based on these two calibrations, which are in error by 0.05 +- 0.01. We employ the Pinsonneault etal (1998) fiducial main sequence to derive a cluster distance modulus of 11.43 +- 0.08. We report observations that are >= 50% complete to V = 24.6 and find that the cluster central-field LF peaks at M_I ~ 3 to 4. This is unlike the solar neighborhood LF and unlike the LFs of dynamically unevolved portions of open and globular clusters, which rise continuously until M_I ~ 9.5. Although we find that >= 50% of the unresolved cluster objects are multiple systems, their presence cannot account for the shape of the NGC 188 LF. For theoretical reasons (Terlevich 1987; Vesperini & Heggie 1997) having to do with the survivability of NGC 188 we believe the cluster is highly dynamically evolved and that the missing low luminosity stars are either in the cluster outskirts or have left the cluster altogether. We identify nine candidate WDs, of which we expect three to six are bona fide cluster WDs. The luminosities of the faintest likely WD indicates an age (Bergeron, Wesemael, & Beauchamp 1995) of 1.14 +- 0.09 Gyrs. This is a lower limit to the cluster age and observations probing to V = 27 or 28 will be necessary to find the faintest cluster WDs and independently determine the cluster age. While our age limit is not surprising for this ~6 Gyr old cluster, our result demonstrates the value of the WD age technique with its very low internal errors. (abridged)Comment: 26 pages, uuencoded gunzip'ed latex + 16 postscrip figures, to be published in A

An HST search for planets in the lower Main Sequence of the globular cluster NGC 6397

Searches for planetary transits carried out in open and globular clusters have yielded to date only a handful of weak, unconfirmed candidates. These results have been interpreted either as being insignificant, or as evidence that the cluster chemical or dynamical environment inhibits the planetary formation or survival. Most campaigns were limited by small sample statistics or systematics from ground-based photometry. In this work we performed a search for transiting planets and variables in a deep stellar field of NGC 6397 imaged by HST-ACS for 126 orbits. We analyzed 5,078 light curves, including a pure sample of 2,215 cluster-member M0-M9 dwarfs. The light curves have been corrected for systematic trends and inspected with several tools. No high-significance planetary candidate is detected. We compared this null detection with the most recent results from Kepler, showing that no conclusive evidence of lower planet incidence can be drawn. However, a very small photometric jitter is measured for early-M cluster members (<~2 mmag on 98% of them), which may be worth targeting in the near future with more optimized campaigns. Twelve variable stars are reported for the first time.Comment: 10 pages, 6 figures, 1 table; accepted for publication in A&A on February 16, 2012. Typos corrected. One figure and a short final note adde

Stable interpolation with exponential-polynomial splines and node selection via greedy algorithms

In this work we extend some ideas about greedy algorithms, which are well-established tools for, e.g., kernel bases, and exponential-polynomial splines whose main drawback consists in possible overfitting and consequent oscillations of the approximant. To partially overcome this issue, we develop some results on theoretically optimal interpolation points. Moreover, we introduce two algorithms which perform an adaptive selection of the spline interpolation points based on the minimization either of the sample residuals (f-greedy), or of an upper bound for the approximation error based on the spline Lebesgue function (λ-greedy). Both methods allow us to obtain an adaptive selection of the sampling points, i.e., the spline nodes. While the f-greedy selection is tailored to one specific target function, the λ-greedy algorithm enables us to define target-data-independent interpolation nodes

Variable stars in the open cluster NGC 6791 and its surrounding field

Aims: This work presents a high--precision variability survey in the field of the old, super metal-rich open cluster NGC 6791. Methods: The data sample consists of more than 75,000 high-precision CCD time series measurements in the V band obtained mainly at the Canada-France-Hawaii Telescope, with additional data from S. Pedro Martir and Loiano observatories, over a time span of ten nights. The field covers an area of 42x28 arcmin^2. Results: We have discovered 260 new variables and re-determined periods and amplitudes of 70 known variable stars. By means of a photometric evaluation of the membership in NGC 6791, and a preliminary membership based on the proper motions, we give a full description of the variable content of the cluster and surrounding field in the range 16<V<23.5. Accurate periods can be given for the variables with P<4.0 d, while for ones with longer periods the limited time-baseline hampered precise determinations. We categorized the entire sample as follows: 6 pulsating, 3 irregular, 3 cataclysmic, 89 rotational variables and 61 eclipsing systems; moreover, we detected 168 candidate variables for which we cannot give a variability class since their periods are much longer than our time baseline. Conclusions: On the basis of photometric considerations, and of the positions of the stars with respect to the center of the cluster, we inferred that 11 new variable stars are likely members of the cluster, for 22 stars the membership is doubtful and 137 are likely non-members. We also detected an outburst of about 3 mag in the light curve of a very faint blue star belonging to the cluster and we suggest that this star could be a new U Gem (dwarf nova) cataclysmic variable.Comment: 24 pages, 19 Figures, A&A accepte

GENETIC AND PRODUCTIVE CHARACTERIZATION OF THE BURLINA CATTLE BREED

The Burlina (BUR) is a local Italian cattle breed, its main feature is to be a small sized animal well adapted to live in difficult environment such as mountain areas. Nowadays only 350 cows are enrolled in the Italian Herd Book due to its substitution by more productive breeds. This study proposes a phenotypic and genetic characterization of the BUR breed in comparison with Holstein Friesian (HFR) and Brown Swiss (BSW). The comparison of productive traits showed lower production than HFR and BSW as well as longer productive life and more favourable reproductive traits in BUR animals. The genetic analyses, performed by microsatellites markers, showed the high level of heterozygosity and the genetic distinctiveness of BUR. These findings approve the feasibility of a conservation scheme and suggest the profitability of breeding BUR, especially in difficult environment where the low production can be compensated by longevity and the economic loss by the added value of its typical dairy production