Crisp sets as classes of discontinuous fuzzy sets

AbstractThis paper aims to show how, by using a threshold-based approach, a path from imprecise information to a crisp ‘decision’ can be developed. It deals with the problem of the logical transformation of a fuzzy set into a crisp set. Such threshold arises from the ideas of contradiction and separation, and allows us to prove that crisp sets can be structurally considered as classes of discontinuous fuzzy sets. It is also shown that continuous fuzzy sets are computationally indistinguishable from some kind of discontinuous fuzzy sets

New chemical profiles for the asteroseismology of ZZ Ceti stars

We compute new chemical profiles for the core and envelope of white dwarfs appropriate for pulsational studies of ZZ Ceti stars. These profiles are extracted from the complete evolution of progenitor stars, evolved through the main sequence and the thermally-pulsing asymptotic giant branch (AGB) stages, and from time-dependent element diffusion during white dwarf evolution. We discuss the importance of the initial-final mass relationship for the white dwarf carbon-oxygen composition. In particular, we find that the central oxygen abundance may be underestimated by about 15% if the white dwarf mass is assumed to be the hydrogen-free core mass before the first thermal pulse. We also discuss the importance for the chemical profiles expected in the outermost layers of ZZ Ceti stars of the computation of the thermally-pulsing AGB phase and of the phase in which element diffusion is relevant. We find a strong dependence of the outer layer chemical stratification on the stellar mass. In particular, in the less massive models, the double-layered structure in the helium layer built up during the thermally-pulsing AGB phase is not removed by diffusion by the time the ZZ Ceti stage is reached. Finally, we perform adiabatic pulsation calculations and discuss the implications of our new chemical profiles for the pulsational properties of ZZ Ceti stars. We find that the whole $g-$mode period spectrum and the mode-trapping properties of these pulsating white dwarfs as derived from our new chemical profiles are substantially different from those based on chemical profiles widely used in existing asteroseismological studies. Thus, we expect the asteroseismological models derived from our chemical profiles to be significantly different from those found thus far.Comment: 12 pages, 11 figures, 1 table. To be published in Ap

Evolution of white dwarf stars with high-metallicity progenitors: the role of 22Ne diffusion

Motivated by the strong discrepancy between the main sequence turn-off age and the white dwarf cooling age in the metal-rich open cluster NGC 6791, we compute a grid of white dwarf evolutionary sequences that incorporates for the first time the energy released by the processes of 22Ne sedimentation and of carbon/oxygen phase separation upon crystallization. The grid covers the mass range from 0.52 to 1.0 Msun, and it is appropriate for the study of white dwarfs in metal-rich clusters. The evolutionary calculations are based on a detailed and self-consistent treatment of the energy released from these two processes, as well as on the employment of realistic carbon/oxygen profiles, of relevance for an accurate evaluation of the energy released by carbon/oxygen phase separation. We find that 22Ne sedimentation strongly delays the cooling rate of white dwarfs stemming from progenitors with high metallicities at moderate luminosities, whilst carbon/oxygen phase separation adds considerable delays at low luminosities. Cooling times are sensitive to possible uncertainties in the actual value of the diffusion coefficient of 22Ne. Changing the diffusion coefficient by a factor of 2, leads to maximum age differences of approx. 8-20% depending on the stellar mass. We find that the magnitude of the delays resulting from chemical changes in the core is consistent with the slow down in the white dwarf cooling rate that is required to solve the age discrepancy in NGC 6791.Comment: 10 pages, 6 figures, to be published in The Astrophysical Journa

Evolution of white dwarf stars with high-metallicity progenitors: The role of 22Ne diffusion

Motivated by the strong discrepancy between the main-sequence turnoff age and the white dwarf cooling age in the metal-rich open cluster NGC 6791, we compute a grid of white dwarf evolutionary sequences that incorporates for the first time the energy released by the processes of 22Ne sedimentation and of carbon/oxygen phase separation upon crystallization. The grid covers the mass range from 0.52 to 1.0M⊙, and is appropriate for the study of white dwarfs in metal-rich clusters. The evolutionary calculations are based on a detailed and self-consistent treatment of the energy released from these two processes, as well as on the employment of realistic carbon/oxygen profiles, of relevance for an accurate evaluation of the energy released by carbon/oxygen phase separation. We find that 22Ne sedimentation strongly delays the cooling rate of white dwarfs stemming from progenitors with high metallicities at moderate luminosities, while carbon/oxygen phase separation adds considerable delays at lowluminosities. Cooling times are sensitive to possible uncertainties in the actual value of the diffusion coefficient of 22Ne. Changing the diffusion coefficient by a factor of 2 leads to maximum age differences of ≈8%-20% depending on the stellar mass. We find that the magnitude of the delays resulting from chemical changes in the core is consistent with the slowdown in the white dwarf cooling rate that is required to solve the age discrepancy in NGC 6791.Facultad de Ciencias Astronómicas y Geofísica

Drosophila DNA polymerase theta utilizes both helicase-like and polymerase domains during microhomology-mediated end joining and interstrand crosslink repair

Double strand breaks (DSBs) and interstrand crosslinks (ICLs) are toxic DNA lesions that can be repaired through multiple pathways, some of which involve shared proteins. One of these proteins, DNA Polymerase θ (Pol θ), coordinates a mutagenic DSB repair pathway named microhomology-mediated end joining (MMEJ) and is also a critical component for bypass or repair of ICLs in several organisms. Pol θ contains both polymerase and helicase-like domains that are tethered by an unstructured central region. While the role of the polymerase domain in promoting MMEJ has been studied extensively both in vitro and in vivo, a function for the helicase-like domain, which possesses DNA-dependent ATPase activity, remains unclear. Here, we utilize genetic and biochemical analyses to examine the roles of the helicase-like and polymerase domains of Drosophila Pol θ. We demonstrate an absolute requirement for both polymerase and ATPase activities during ICL repair in vivo. However, similar to mammalian systems, polymerase activity, but not ATPase activity, is required for ionizing radiation-induced DSB repair. Using a site-specific break repair assay, we show that overall end-joining efficiency is not affected in ATPase-dead mutants, but there is a significant decrease in templated insertion events. In vitro, Pol θ can efficiently bypass a model unhooked nitrogen mustard crosslink and promote DNA synthesis following microhomology annealing, although ATPase activity is not required for these functions. Together, our data illustrate the functional importance of the helicase-like domain of Pol θ and suggest that its tethering to the polymerase domain is important for its multiple functions in DNA repair and damage tolerance

Optimization of topical cidofovir penetration using microparticles.

Edelfosine is the prototype molecule of a family of anticancer drugs collectively known as synthetic alkyl-lysophospholipids. This drug holds promise as a selective antitumor agent, and a number of preclinical assays are in progress. In this study, we observe the accumulation of edelfosine in brain tissue after its oral administration in Compritol® and Precirol® lipid nanoparticles (LN). The high accumulation of edelfosine in brain was due to the inhibition of P-glycoprotein by Tween® 80, as verified using a P-glycoprotein drug interaction assay. Moreover, these LN were tested in vitro against the C6 glioma cell line, which was later employed to establish an in vivo xenograft mouse model of glioma. In vitro studies revealed that edelfosine-loaded LN induced an antiproliferative effect in C6 glioma cell line. In addition, in vivo oral administration of drug-loaded LN in NMRI nude mice bearing a C6 glioma xenograft tumor induced a highly significant reduction in tumor growth (p < 0.01) 14 days after the beginning of the treatment. Our results showed that Tween® 80 coated Compritol® and Precirol® LN can effectively inhibit the growth of C6 glioma cells in vitro and suggest that edelfosine-loaded LN represent an attractive option for the enhancement of antitumor activity on brain tumors in vivo

The white-dwarf cooling sequence of NGC 6791: A unique tool for stellar evolution

Context. NGC 6791 is a well-studied, metal-rich open cluster that is so close to us that it can be imaged down to luminosities fainter than that of the termination of its white-dwarf cooling sequence, thus allowing for an in-depth study of its white dwarf population. Aims. White dwarfs carry important information about the history of the cluster. We use observations of the white-dwarf cooling sequence to constrain important properties of the cluster stellar population, such as the existence of a putative population of massive helium-core white dwarfs, and the properties of a large population of unresolved binary white dwarfs. We also investigate the use of white dwarfs to disclose the presence of cluster subpopulations with a different initial chemical composition, and we obtain an upper bound to the fraction of hydrogen-deficient white dwarfs. Methods. We use a Monte Carlo simulator that employs up-to-date evolutionary cooling sequences for white dwarfs with hydrogenrich and hydrogen-deficient atmospheres, with carbon-oxygen and helium cores. The cooling sequences for carbon-oxygen cores account for the delays introduced by both 22Ne sedimentation in the liquid phase and by carbon-oxygen phase separation upon crystallization. Results. We do not find evidence for a substantial fraction of helium-core white dwarfs, and hence our results support the suggestion that the origin of the bright peak of the white-dwarf luminosity function can only be attributed to a population of unresolved binary white dwarfs. Moreover, our results indicate that if this hypothesis is at the origin of the bright peak, the number distribution of secondary masses of the population of unresolved binaries has to increase with increasing mass ratio between the secondary and primary components of the progenitor system. We also find that the observed cooling sequence appears to be able to constrain the presence of progenitor subpopulations with different chemical compositions and the fraction of hydrogen-deficient white dwarfs. Conclusions. Our simulations place interesting constraints on important characteristics of the stellar populations of NGC 6791. In particular, we find that the fraction of single helium-core white dwarfs must be smaller than 5%, that a subpopulation of stars with zero metallicity must be ≤ 12%, while if the adopted metallicity of the subpopulation is solar the upper limit is ∼8%. Finally, we also find that the fraction of hydrogen-deficient white dwarfs in this particular cluster is surprinsingly small (≤6%).Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

An upper limit to the secular variation of the gravitational constant from white dwarf stars

A variation of the gravitational constant over cosmological ages modifies the main sequence lifetimes and white dwarf cooling ages. Using an state-of-the-art stellar evolutionary code we compute the effects of a secularly varying G on the main sequence ages and, employing white dwarf cooling ages computed taking into account the effects of a running G, we place constraints on the rate of variation of Newton's constant. This is done using the white dwarf luminosity function and the distance of the well studied open Galactic cluster NGC 6791. We derive an upper bound G'/G ~ -1.8 10^{-12} 1/yr. This upper limit for the secular variation of the gravitational constant compares favorably with those obtained using other stellar evolutionary properties, and can be easily improved if deep images of the cluster allow to obtain an improved white dwarf luminosity function.Comment: 15 pages, 4 figures, accepted for publication in JCA

New cooling sequences for old white dwarfs

We present full evolutionary calculations appropriate for the study of hydrogen-rich DA white dwarfs. This is done by evolving white dwarf progenitors from the zero-age main sequence, through the core hydrogen-burning phase, the helium-burning phase, and the thermally pulsing asymptotic giant branch phase to the white dwarf stage. Complete evolutionary sequences are computed for a wide range of stellar masses and for two different metallicities, Z = 0.01, which is representative of the solar neighborhood, and Z = 0.001, which is appropriate for the study of old stellar systems, like globular clusters. During the white dwarf cooling stage, we self-consistently compute the phase in which nuclear reactions are still important, the diffusive evolution of the elements in the outer layers and, finally, we also take into account all the relevant energy sources in the deep interior of the white dwarf, such as the release of latent heat and the release of gravitational energy due to carbon-oxygen phase separation upon crystallization. We also provide colors and magnitudes for these sequences, based on a new set of improved non-gray white dwarf model atmospheres, which include the most up-to-date physical inputs like the Lyα quasi-molecular opacity. The calculations are extended down to an effective temperature of 2500 K. Our calculations provide a homogeneous set of evolutionary cooling tracks appropriate for mass and age determinations of old DA white dwarfs and for white dwarf cosmochronology of the different Galactic populations.Facultad de Ciencias Astronómicas y Geofísica

New chemical profiles for the asteroseismology of ZZ CETI stars

We compute new chemical profiles for the core and envelope of white dwarfs appropriate for pulsational studies of ZZ Ceti stars. These profiles are extracted from the complete evolution of progenitor stars, evolved through the main sequence and the thermally pulsing asymptotic giant branch (AGB) stages, and from time-dependent element diffusion during white dwarf evolution. We discuss the importance of the initial-final mass relationship for the white dwarf carbon-oxygen composition. In particular, we find that the central oxygen abundance may be underestimated by about 15% if the white dwarf mass is assumed to be the hydrogen-free core mass before the first thermal pulse. We also discuss the importance for the chemical profiles expected in the outermost layers of ZZ Ceti stars of the computation of the thermally pulsing AGB phase and of the phase in which element diffusion is relevant. We find a strong dependence of the outer layer chemical stratification on the stellar mass. In particular, in the less massive models, the double-layered structure in the helium layer built up during the thermally pulsing AGB phase is not removed by diffusion by the time the ZZ Ceti stage is reached. Finally, we perform adiabatic pulsation calculations and discuss the implications of our new chemical profiles for the pulsational properties of ZZ Ceti stars. We find that the whole g-mode period spectrum and the mode-trapping properties of these pulsating white dwarfs as derived from our new chemical profiles are substantially different from those based on chemical profiles widely used in existing asteroseismological studies. Thus, we expect the asteroseismological models derived from our chemical profiles to be significantly different from those found thus far.Facultad de Ciencias Astronómicas y Geofísica