Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

Genome-to-genome analysis highlights the effect of the human innate and adaptive immune systems on the hepatitis C virus

Outcomes of hepatitis C virus (HCV) infection and treatment depend on viral and host genetic factors. Here we use human genome-wide genotyping arrays and new whole-genome HCV viral sequencing technologies to perform a systematic genome-to-genome study of 542 individuals who were chronically infected with HCV, predominantly genotype 3. We show that both alleles of genes encoding human leukocyte antigen molecules and genes encoding components of the interferon lambda innate immune system drive viral polymorphism. Additionally, we show that IFNL4 genotypes determine HCV viral load through a mechanism dependent on a specific amino acid residue in the HCV NS5A protein. These findings highlight the interplay between the innate immune system and the viral genome in HCV control

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the grey matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising, 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9–0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease-course longitudinal studies

High summer temperatures amplify functional differences between coral- and algae-dominated reef communities

Shifts from coral to algal dominance are expected to increase in tropical coral reefs as a result of anthropogenic disturbances. The consequences for key ecosystem functions such as primary productivity, calcification, and nutrient recycling are poorly understood, particularly under changing environmental conditions. We used a novel in situ incubation approach to compare functions of coral- and algae-dominated communities in the central Red Sea bimonthly over an entire year. In situ gross and net community primary productivity, calcification, dissolved organic carbon fluxes, dissolved inorganic nitrogen fluxes, and their respective activation energies were quantified to describe the effects of seasonal changes. Overall, coral-dominated communities exhibited 30% lower net productivity and 10 times higher calcification than algae-dominated communities. Estimated activation energies indicated a higher thermal sensitivity of coral-dominated communities. In these communities, net productivity and calcification were negatively correlated with temperature (>40% and >65% reduction, respectively, with +5 degrees C increase from winter to summer), whereas carbon losses via respiration and dissolved organic carbon release more than doubled at higher temperatures. In contrast, algae-dominated communities doubled net productivity in summer, while calcification and dissolved organic carbon fluxes were unaffected. These results suggest pronounced changes in community functioning associated with coral-algal phase shifts. Algae-dominated communities may outcompete coral-dominated communities because of their higher productivity and carbon retention to support fast biomass accumulation while compromising the formation of important reef framework structures. Higher temperatures likely amplify these functional differences, indicating a high vulnerability of ecosystem functions of coral-dominated communities to temperatures even below coral bleaching thresholds. Our results suggest that ocean warming may not only cause but also amplify coral-algal phase shifts in coral reefs.Peer reviewe

On the definition of a unique effective temperature for non-equilibrium critical systems

We consider the problem of the definition of an effective temperature via the long-time limit of the fluctuation-dissipation ratio (FDR) after a quench from the disordered state to the critical point of an O(N) model with dissipative dynamics. The scaling forms of the response and correlation functions of a generic observable are derived from the solutions of the corresponding Renormalization Group equations. We show that within the Gaussian approximation all the local observables have the same FDR, allowing for a definition of a unique effective temperature. This is no longer the case when fluctuations are taken into account beyond that approximation, as shown by a computation up to the first order in the epsilon-expansion for two quadratic observables. This implies that, contrarily to what often conjectured, a unique effective temperature can not be defined for this class of models.Comment: 32 pages, 5 figures. Minor changes, published versio

Integrating environmental variability to broaden the research on coral responses to future ocean conditions

Our understanding of the response of reef-building corals to changes in their physical environment is largely based on laboratory experiments, analysis of long-term field data, and model projections. Experimental data provide unique insights into how organisms respond to variation of environmental drivers. However, an assessment of how well experimental conditions cover the breadth of environmental conditions and variability where corals live successfully is missing. Here, we compiled and analyzed a globally distributed dataset of in-situ seasonal and diurnal variability of key environmental drivers (temperature, pCO2, and O2) critical for the growth and livelihood of reef-building corals. Using a meta-analysis approach, we compared the variability of environmental conditions assayed in coral experimental studies to current and projected conditions in their natural habitats. We found that annual temperature profiles projected for the end of the 21st century were characterized by distributional shifts in temperatures with warmer winters and longer warm periods in the summer, not just peak temperatures. Furthermore, short-term hourly fluctuations of temperature and pCO2 may regularly expose corals to conditions beyond the projected average increases for the end of the 21st century. Coral reef sites varied in the degree of coupling between temperature, pCO2, and dissolved O2, which warrants site-specific, differentiated experimental approaches depending on the local hydrography and influence of biological processes on the carbonate system and O2 availability. Our analysis highlights that a large portion of the natural environmental variability at short and long timescales is underexplored in experimental designs, which may provide a path to extend our understanding on the response of corals to global climate change