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

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

On the Globular Cluster IMF below 1 Solar Mass

(Abridged) Accurate luminosity functions (LF) for a dozen globular clusters have now been measured at or just beyond their half-light radius using HST. They span almost the entire cluster main sequence below ~ 0.75 Msolar. All these clusters exhibit LF that rise continuously from an absolute I magnitude M_I ~ 6 to a peak at M_I ~ 8.5-9 and then drop with increasing M_I. Transformation of the LF into mass functions (MF) by means of the most recent mass luminosity relations that are consistent with all presently available data on the physical properties of low mass, low metallicity stars shows that all the LF observed so far can be obtained from MF having the shape of a log-normal distribution with characteristic mass m_c=0.33 +/- 0.03 Msolar and standard deviation sigma = 1.81 +/- 0.19. After correction for the effects of mass segregation, the variation of the ratio of the number of higher to lower mass stars with cluster mass or any simple orbital parameter or the expected time to disruption recently computed for these clusters shows no statistically significant trend over a range of this last parameter of more than a factor of 100. We conclude that the global MF of these clusters have not been measurably modified by evaporation and tidal interactions with the Galaxy and, thus, should reflect the initial distribution of stellar masses. Since the log-normal function that we find is also very similar to the one obtained independently for much younger clusters and to the form expected theoretically, the implication seems to be unavoidable that it represents the true stellar IMF for this type of stars in this mass range.Comment: Accepted for publication in The Astrophysical Journal. Contains 28 pages with 6 figure

Analysis of Different Methodologies to Calculate Bouguer Gravity Anomalies in the Argentine Continental Margin

We have tested and used two methods to determine the Bouguer gravity anomaly in the area of the Argentine continental margin. The first method employs the relationship between the topography and gravity anomaly in the Fourier transform domain using Parker’s expression for different orders of expansion. The second method computes the complete Bouguer correction (Bullard A, B and C) with the Fortran code FA2BOUG2. The Bouguer slab correction (Bullard A), the curvature correction (Bullard B) and the terrain correction (Bullard C) are computed in several zones according to thedistances between the topography and the calculation point. In each zone, different approximations of the gravitationalattraction of rectangular or conic prisms are used according to the surrounding topography. Our calculations show that the anomaly generated by the fourth order in Parker’s expansion is actually compatible with the traditional Bouguer anomaly calculated with FA2BOUG, and that higher orders do not introduce significant changes. The comparison reveals that the difference between both methods in the Argentine continental margin has a quasi bimodal statistical distribution. The main disadvantage in using routines based on Parker's expansion is that an average value of the topography is needed for the calculation and, as the margin has an abrupt change of the topography in the continental slope area, it causes a bimodal distribution. It is worth noticing that, as expected, the most important differences between both methods are located over the continental slope both in complex structures such as part of the shared margin, as well as in isolated points where there are contributions from short wavelength or rugged topography.Fil: Pedraza de Marchi, Ana Carolina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Ghidella, Marta E.. Ministerio de Relaciones Exteriores, Comercio Interno y Culto. Dirección Nacional del Antártico. Instituto Antártico Argentino; ArgentinaFil: Tocho, Claudia. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Why haven't loose globular clusters collapsed yet?

We report on the discovery of a surprising observed correlation between the slope of the low-mass stellar global mass function (GMF) of globular clusters (GCs) and their central concentration parameter c=log(r_t/r_c), i.e. the logarithmic ratio of tidal and core radii. This result is based on the analysis of a sample of twenty Galactic GCs with solid GMF measurements from deep HST or VLT data. All the high-concentration clusters in the sample have a steep GMF, most likely reflecting their initial mass function. Conversely, low-concentration clusters tend to have a flatter GMF implying that they have lost many stars via evaporation or tidal stripping. No GCs are found with a flat GMF and high central concentration. This finding appears counter-intuitive, since the same two-body relaxation mechanism that causes stars to evaporate and the cluster to eventually dissolve should also lead to higher central density and possibly core-collapse. Therefore, more concentrated clusters should have lost proportionately more stars and have a shallower GMF than low concentration clusters, contrary to what is observed. It is possible that severely depleted GCs have also undergone core collapse and have already recovered a normal radial density profile. It is, however, more likely that GCs with a flat GMF have a much denser and smaller core than suggested by their surface brightness profile and may well be undergoing collapse at present. In either case, we may have so far seriously underestimated the number of post core-collapse clusters and many may be lurking in the Milky Way.Comment: Four pages, one figure, accepted for publication in ApJ Letter

The Mass Function of Main Sequence Stars in NGC6397 from Near IR and Optical High Resolution HST Observations

We have investigated the properties of the stellar mass function in the globular cluster NGC6397 using a large set of HST observations that include WFPC2 images in V and I, obtained at ~4' and 10' radial distances, and a series of deep images in the J and H bands obtained with the NIC2 and NIC3 cameras of NICMOS pointed to regions located ~4.5' and ~3.2' from the center. These observations span the region from ~1 to ~3 times the cluster's half-light radius. All luminosity functions, derived from color magniutde diagrams, increase with decreasing luminosity up to a peak at M_I~8.5 or M_H~7 and then precipitously drop well before photometric incompleteness becomes significant. Within the observational uncertainties, at M_I~12 or M_H~10.5 (~0.09 Msun) the luminosity functions are compatible with zero. By applying the best available mass- luminosity relation appropriate to the metallicity of NGC6397 to both the optical and IR data, we obtain a mass function that shows a break in slope at \~0.3 Msun. No single exponent power-law distribution is compatible with these data, regardless of the value of the exponent. We find that a dynamical model of the cluster can simultaneously reproduce all the luminosity functions observed throughout the cluster only if the IMF rises as m**-1.6 in the range 0.8-0.3 Msun and then drops as m**0.2 below ~0.3 Msun. Adopting a more physical log-normal distribution for the IMF, all these data taken together imply a best fit distribution with characteristic mass m_c~0.3 and sigma~1.8.Comment: 18 pages, 6 figures (ps). Accepted for publication in Ap

Jumping with variably scaled discontinuous kernels (VSDKs)

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Correction to: Jumping with variably scaled discontinuous kernels (VSDKs)

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Emerging roles of purinergic signaling in anti-cancer therapy resistance

Cancer is a complex disease with a rapid growing incidence and often characterized by a poor prognosis. Although impressive advances have been made in cancer treatments, resistance to therapy remains a critical obstacle for the improvement of patients outcome. Current treatment approaches as chemo-, radio-, and immuno-therapy deeply affect the tumor microenvironment (TME), inducing an extensive selective pressure on cancer cells through the activation of the immune system, the induction of cell death and the release of inflammatory and damage-associated molecular patterns (DAMPS), including nucleosides (adenosine) and nucleotides (ATP and ADP). To survive in this hostile environment, resistant cells engage a variety of mitigation pathways related to metabolism, DNA repair, stemness, inflammation and resistance to apoptosis. In this context, purinergic signaling exerts a pivotal role being involved in mitochondrial function, stemness, inflammation and cancer development. The activity of ATP and adenosine released in the TME depend upon the repertoire of purinergic P2 and adenosine receptors engaged, as well as, by the expression of ectonucleotidases (CD39 and CD73) on tumor, immune and stromal cells. Besides its well established role in the pathogenesis of several tumors and in host–tumor interaction, purinergic signaling has been recently shown to be profoundly involved in the development of therapy resistance. In this review we summarize the current advances on the role of purinergic signaling in response and resistance to anti-cancer therapies, also describing the translational applications of combining conventional anticancer interventions with therapies targeting purinergic signaling

Mass accretion rates from multiband photometry in the Carina Nebula: The case of Trumpler 14

open8siWe present a study of the mass accretion rates of pre-main sequence (PMS) stars in the cluster Trumpler 14 (Tr 14) in the Carina Nebula. Using optical multiband photometry we were able to identify 356 PMS stars showing Hα excess emission with equivalent width EW(Hα) > 20 Å. We interpret this observational feature as an indication that these objects are still actively accreting gas from their circumstellar medium. From a comparison of the HR diagram with PMS evolutionary models we derive ages and masses of the PMS stars. We find that most of the PMS objects are younger than 10 Myr with a median age of ~3 Myr. Surprisingly, we also find that ~20% of the mass accreting objects are older than 10 Myr. For each PMS star in Trumpler 14 we determine the mass accretion rate (Ṁacc) and discuss its dependence on mass and age. We finally combine the optical photometry with near-IR observations to build the spectral energy distribution (SED) for each PMS star in Tr 14. The analysis of the SEDs suggests the presence of transitional discs in which a large amount of gas is still present and sustains accretion onto the PMS object at ages older than 10 Myr. Our results, discussed in light of recent recent discoveries with Herschel of transitional discs containing a massive gas component around the relatively old PMS stars TW Hydrae, 49 Ceti, and HD 95086, support a new scenario n which old and evolved debris discs still host a significant amount of gas.openBeccari, G.; De Marchi, G.; Panagia, N.; Valenti, E.; Carraro, G.; Romaniello, M.; Zoccali, M.; Weidner, C.Beccari, G.; De Marchi, G.; Panagia, N.; Valenti, E.; Carraro, Giovanni; Romaniello, M.; Zoccali, M.; Weidner, C