Trace ideals for Fourier integral operators with non-smooth symbols II

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann properties of such operators when acting on modulation spaces.Comment: 25 page

The functional VNTR MNS16A of the TERT gene is associated with human longevity in a population of Central Italy.

Telomerase, encoded by TERT, is the ribonucleoprotein polymerase that maintains telomere ends and it plays a crucial role in cellular senescence. TERT single nucleotide polymorphisms (SNPs) have been associated both with various malignancies and telomere length (TL). The association of TERT SNPs with longevity remains uncertain and varies with ethnicity. The aim of this study was to investigate whether the functional variable number of tandem repeat (VNTR) MNS16A of TERT is associated with longevity. METHODS: MNS16A genotypes have been determined for 1072 unrelated healthy individuals from Central Italy (18-106 years old) divided into three gender-specific age classes defined according to demographic information and accounting for the different survivals between sexes: for men (women), the first class consists of individuals 88 years old (>91 years old). TL was assessed using genomic DNA from whole blood of 72 selected individuals by a multiplex real-time PCR assay. RESULTS: MNS16A appears associated to longevity, showing significant associations in Comparison 2 (Age Class 3 vs. Age Class 2) under both additive (odds ratio [O.R.] 0.749; p=0.019) and dominant (O.R. 0.579; p=0.011) models. The MNS16A*L allele is significantly underrepresented in Age Class 3 (O.R. 0.759; p=0.020) compared to Age Class 2. A significant telomere attrition is reported along the three age classes (p=0.0001), that remains significant only in L*/L* genotype carriers (p=0.002) when the analysis was conducted according to MNS16A genotype. CONCLUSIONS: The TERT MNS16A*L allele appears negatively associated with longevity. The concomitant significant telomere cross sectional attrition rate observed for L*/L* genotype suggests that this polymorphism could influence human longevity by affecting TL

Green Plants in the Red: A Baseline Global Assessment for the IUCN Sampled Red List Index for Plants

Plants provide fundamental support systems for life on Earth and are the basis for all terrestrial ecosystems; a decline in plant diversity will be detrimental to all other groups of organisms including humans. Decline in plant diversity has been hard to quantify, due to the huge numbers of known and yet to be discovered species and the lack of an adequate baseline assessment of extinction risk against which to track changes. The biodiversity of many remote parts of the world remains poorly known, and the rate of new assessments of extinction risk for individual plant species approximates the rate at which new plant species are described. Thus the question ‘How threatened are plants?’ is still very difficult to answer accurately. While completing assessments for each species of plant remains a distant prospect, by assessing a randomly selected sample of species the Sampled Red List Index for Plants gives, for the first time, an accurate view of how threatened plants are across the world. It represents the first key phase of ongoing efforts to monitor the status of the world’s plants. More than 20% of plant species assessed are threatened with extinction, and the habitat with the most threatened species is overwhelmingly tropical rain forest, where the greatest threat to plants is anthropogenic habitat conversion, for arable and livestock agriculture, and harvesting of natural resources. Gymnosperms (e.g. conifers and cycads) are the most threatened group, while a third of plant species included in this study have yet to receive an assessment or are so poorly known that we cannot yet ascertain whether they are threatened or not. This study provides a baseline assessment from which trends in the status of plant biodiversity can be measured and periodically reassessed

Approximation of Fourier Integral Operators by Gabor multipliers

A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth phase and a symbol in the Sjoestrand class and use Gabor frames as wave packets. The almost diagonalization of such Fourier integral operators suggests a specific approximation by (a sum of) elementary operators, namely modified Gabor multipliers. We derive error estimates for such approximations. The methods are taken from time-frequency analysis.Comment: 22. page