The category of local algebras and points proches

Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed

Polarizations and differential calculus in affine spaces

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as linearity, iterability, Leibniz and chain rules, are shared -- at the finite level -- by the polarization operators. We give these results by means of explicit general formulae, which are valid at any order $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-th derivatives (without resorting to the usual recursive definition), and the above mentioned properties will be recovered directly in the limit. Polynomial functions will allow us to produce a coordinate free version of Taylor's formula

Nutritional challenges of substituting farmed animals for wild fish in human diets

Wild fisheries provide billions of people with a key source of multiple essential nutrients. As fisheries plateau or decline, nourishing more people will partially rely on shifting consumption to farmed animals. The environmental implications of transitions among animal-sourced foods have been scrutinized, but their nutritional substitutability remains unclear. We compared concentrations of six essential dietary nutrients across \u3e5000 species of wild fishes, aquaculture, poultry and livestock species, representing \u3e65% of animals consumed globally. Wild fishes are both more nutrient-dense and variable than farmed animals; achieving recommended intake of all nutrients with farmed species could require consuming almost four times more biomass than with wild fish. The challenge of substituting farmed animals for wild fishes are magnified in fishery-dependent nations with high biodiversity and prevalence of malnutrition. Ultimately, the better ability of wild fishes to meet multiple nutrients simultaneously underscores the importance of drawing upon a diverse portfolio of animal- and plant-based foods as societies seek to offset changes in fisheries while achieving healthy and sustainable diets

Functional metathesis catalyst through ring closing enyne metathesis: one pot protocol for living heterotelechelic polymers

Enyne ring closing metathesis has been used to synthesize functional group carrying metathesis catalysts from a commercial (Ru-benzylidene) Grubbs’ catalysts. The new Grubbs-type ruthenium carbene was used to synthesize living heterotelechelic ROMP polymers without any intermediate purification. Olefin metathesis with a mono substituted alkyne followed by ring closing metathesis with an allylic ether provided efficient access to new functional group carrying metathesis catalysts. Different functional benzylidene and alkylidene derivatives have been investigated in the synthesis of heterotelechelic polymers in one pot

A large stellar evolution database for population synthesis studies. II. Stellar models and isochrones for an alpha-enhanced metal distribution

[Abridged] We present a large, new set of stellar evolution models and isochrones for an alpha-enhanced metal distribution typical of Galactic halo and bulge stars; it represents a homogeneous extension of our stellar model library for a distribution already presented in Pietrinferni et al.(2004). The effect of the alpha-element enhancement has been properly taken into account in the nuclear network, opacity, equation of state and, for the first time, the bolometric corrections, and color transformations. This allows us to avoid the inconsistent use - common to all alpha-enhanced model libraries currently available - of scaled-solar bolometric corrections and color transformations for alpha-enhanced models and isochrones. We show how bolometric corrections to magnitudes obtained for the U,B portion of stellar spectra for T_{eff}<=6500K, are significantly affected by the metal mixture, especially at the higher metallicities. We also provide complete sets of evolutionary models for low-mass, He-burning stellar structures covering the whole metallicity range, to enable synthetic horizontal branch simulations. We compare our database with several widely used stellar model libraries from different authors, as well as with various observed color magnitude and color-color diagrams (Johnson-Cousins BVI and near infrared magnitudes, Stromgren colors) of Galactic field stars and globular clusters. We also test our isochrones comparing integrated optical colors and Surface Brightness Fluctuation magnitudes with selected globular cluster data. We find a general satisfactory agreement with the empirical constraints.Comment: 46 pages, 20 figures, ApJ in press, the whole database presented in this paper can be foud at http://www.te.astro.it/BASTI/index.ph

Modeling cancer genomic data in yeast reveals selection against ATM function during tumorigenesis

The DNA damage response (DDR) comprises multiple functions that collectively preserve genomic integrity and suppress tumorigenesis. The Mre11 complex and ATM govern a major axis of the DDR and several lines of evidence implicate that axis in tumor suppression. Components of the Mre11 complex are mutated in approximately five percent of human cancers. Inherited mutations of complex members cause severe chromosome instability syndromes, such as Nijmegen Breakage Syndrome, which is associated with strong predisposition to malignancy. And in mice, Mre11 complex mutations are markedly more susceptible to oncogene- induced carcinogenesis. The complex is integral to all modes of DNA double strand break (DSB) repair and is required for the activation of ATM to effect DNA damage signaling. To understand which functions of the Mre11 complex are important for tumor suppression, we undertook mining of cancer genomic data from the clinical sequencing program at Memorial Sloan Kettering Cancer Center, which includes the Mre11 complex among the 468 genes assessed. Twenty five mutations in MRE11 and RAD50 were modeled in S. cerevisiae and in vitro. The mutations were chosen based on recurrence and conservation between human and yeast. We found that a significant fraction of tumor-borne RAD50 and MRE11 mutations exhibited separation of function phenotypes wherein Tel1/ATM activation was severely impaired while DNA repair functions were mildly or not affected. At the molecular level, the gene products of RAD50 mutations exhibited defects in ATP binding and hydrolysis. The data reflect the importance of Rad50 ATPase activity for Tel1/ATM activation and suggest that inactivation of ATM signaling confers an advantage to burgeoning tumor cells