Rationality of the moduli spaces of plane curves of sufficiently large degree

We prove that the moduli space of plane curves of degree d is rational for all sufficiently large d.Comment: 18 pages; 1 figure; Macaulay2 scripts used can be found at http://www.uni-math.gwdg.de/bothmer/rationality/ or at the end of the latex source fil

Large scale patterns in vertical distribution and behavior of mesopelagic scattering layers

Recent studies suggest that previous estimates of mesopelagic biomasses are severely biased, with the new, higher estimates underlining the need to unveil behaviourally mediated coupling between shallow and deep ocean habitats. We analysed vertical distribution and diel vertical migration (DVM) of mesopelagic acoustic scattering layers (SLs) recorded at 38 kHz across oceanographic regimes encountered during the circumglobal Malaspina expedition. Mesopelagic SLs were observed in all areas covered, but vertical distributions and DVM patterns varied markedly. The distribution of mesopelagic backscatter was deepest in the southern Indian Ocean (weighted mean daytime depth: WMD 590 m) and shallowest at the oxygen minimum zone in the eastern Pacific (WMD 350 m). DVM was evident in all areas covered, on average ~50% of mesopelagic backscatter made daily excursions from mesopelagic depths to shallow waters. There were marked differences in migrating proportions between the regions, ranging from ~20% in the Indian Ocean to ~90% in the Eastern Pacific. Overall the data suggest strong spatial gradients in mesopelagic DVM patterns, with implied ecological and biogeochemical consequences. Our results suggest that parts of this spatial variability can be explained by horizontal patterns in physical-chemical properties of water masses, such as oxygen, temperature and turbidity.En prensa2,927

Molecular identification of Palearctic members of Anopheles maculipennis in northern Iran

BACKGROUND: Members of Anopheles maculipennis complex are effective malaria vectors in Europe and the Caspian Sea region in northern Iran, where malaria has been re-introduced since 1994. The current study has been designed in order to provide further evidence on the status of species composition and to identify more accurately the members of the maculipennis complex in northern Iran. METHODS: The second internal transcribed spacer of ribosomal DNA (rDNA-ITS2) was sequenced in 28 out of 235 specimens that were collected in the five provinces of East Azerbayjan, Ardebil, Guilan, Mazandaran and Khorassan in Iran. RESULTS: The length of the ITS2 ranged from 283 to 302 bp with a GC content of 49.33 – 54.76%. No intra-specific variations were observed. Construction of phylogenetic tree based on the ITS2 sequence revealed that the six Iranian members of the maculipennis complex could be easily clustered into three groups: the An. atroparvus – Anopheles labranchiae group; the paraphyletic group of An. maculipennis, An. messeae, An. persiensis; and An. sacharovi as the third group. CONCLUSION: Detection of three species of the An. maculipennis complex including An. atroparvus, An. messae and An. labranchiae, as shown as new records in northern Iran, is somehow alarming. A better understanding of the epidemiology of malaria on both sides of the Caspian Sea may be provided by applying the molecular techniques to the correct identification of species complexes, to the detection of Plasmodium composition in Anopheles vectors and to the status of insecticide resistance by looking to related genes

Proof-theoretic analysis by iterated reflection

Progressions of iterated reflection principles can be used as a tool for ordinal analysis of formal systems. Technically, in some sense, they replace the use of omega-rule. We compare the information obtained by this kind of analysis with the results obtained by the more usual proof-theoretic techniques. In some cases the techniques of iterated reflection principles allows to obtain sharper results, e.g., to define proof-theoretic ordinals relevant to logical complexity Π 0 1. We provide a more general version of the fine structure formulas for iterated reflection principles (due to U. Schmerl [24]). This allows us, in a uniform manner, to analyze main fragments of arithmetic axiomatized by restricted forms of induction, including IΣn, IΣ − n, IΠ − n and their combinations. We also obtain new conservation results relating the hierarchies of uniform and local reflection principles. In particular, we show that (for a sufficiently broad class of theories T) the uniform Σ1-reflection principle for T is Σ2-conservative over the corresponding local reflection principle. This bears some corollaries on the hierarchies of restricted induction schemata in arithmetic and provides a key tool for our generalization of Schmerl’s theorem.