Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat

Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions

Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBS's) among a continuum of conventional Andreev bound states. The distinct feature of these MBS's lies in the $4\pi$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r\!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_2$Se$_3$ exhibit a fractional ac Josephson effect acting on the first Shapiro step only. With a modified resistively shunted junction model, we demonstrate that the resilience of higher order odd Shapiro steps can be accounted for by thermal poisoning driven by Joule overheating. Furthermore, we uncover a residual supercurrent at the nodes between Shapiro lobes, which provides a direct and novel signature of the current carried by the MBS. Our findings showcase the crucial role of thermal effects in topological Josephson junctions and lend support to the Majorana origin of the partial suppression of odd Shapiro steps.Comment: Revised article and Supplemental materia

Global surfaces of section in the planar restricted 3-body problem

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The approach relies on recent global methods in symplectic geometry and contrasts sharply with the perturbative methods used until now.Comment: 11 pages, 1 figur

Surface water monitoring in small water bodies: potential and limits of multi-sensor Landsat time series

Hydrometric monitoring of small water bodies (1–10&thinsp;ha) remains rare, due to their limited size and large numbers, preventing accurate assessments of their agricultural potential or their cumulative influence in watershed hydrology. Landsat imagery has shown its potential to support mapping of small water bodies, but the influence of their limited surface areas, vegetation growth, and rapid flood dynamics on long-term surface water monitoring remains unquantified. A semi-automated method is developed here to assess and optimize the potential of multi-sensor Landsat time series to monitor surface water extent and mean water availability in these small water bodies. Extensive hydrometric field data (1999–2014) for seven small reservoirs within the Merguellil catchment in central Tunisia and SPOT imagery are used to calibrate the method and explore its limits. The Modified Normalised Difference Water Index (MNDWI) is shown out of six commonly used water detection indices to provide high overall accuracy and threshold stability during high and low floods, leading to a mean surface area error below 15&thinsp;%. Applied to 546 Landsat 5, 7, and 8 images over 1999–2014, the method reproduces surface water extent variations across small lakes with high skill (R2 = 0.9) and a mean root mean square error (RMSE) of 9300&thinsp;m2. Comparison with published global water datasets reveals a mean RMSE of 21&thinsp;800&thinsp;m2 (+134&thinsp;%) on the same lakes and highlights the value of a tailored MNDWI approach to improve hydrological monitoring in small lakes and reduce omission errors of flooded vegetation. The rise in relative errors due to the larger proportion and influence of mixed pixels restricts surface water monitoring below 3&thinsp;ha with Landsat (Normalised RMSE&thinsp; = &thinsp;27&thinsp;%). Interferences from clouds and scan line corrector failure on ETM+ after 2003 also decrease the number of operational images by 51&thinsp;%, reducing performance on lakes with rapid flood declines. Combining Landsat observations with 10&thinsp;m pansharpened Sentinel-2 imagery further reduces RMSE to 5200&thinsp;m2, displaying the increased opportunities for surface water monitoring in small water bodies after 2015.</p

PHYMYCO-DB: A curated database for analyses of fungal diversity and evolution.

International audienceBackground: In environmental sequencing studies, fungi can be identified based on nucleic acid sequences, using either highly variable sequences as species barcodes or conserved sequences containing a high-quality phylogenetic signal. For the latter, identification relies on phylogenetic analyses and the adoption of the phylogenetic species concept. Such analysis requires that the reference sequences are well identified and deposited in public-access databases. However, many entries in the public sequence databases are problematic in terms of quality and reliability and these data require screening to ensure correct phylogenetic interpretation. Methods and Principal Findings: To facilitate phylogenetic inferences and phylogenetic assignment, we introduce a fungal sequence database. The database PHYMYCO-DB comprises fungal sequences from GenBank that have been filtered to satisfy stringent sequence quality criteria. For the first release, two widely used molecular taxonomic markers were chosen: the nuclear SSU rRNA and EF1-a gene sequences. Following the automatic extraction and filtration, a manual curation is performed to remove problematic sequences while preserving relevant sequences useful for phylogenetic studies. As a result of curation, ,20% of the automatically filtered sequences have been removed from the database. To demonstrate how PHYMYCO-DB can be employed, we test a set of environmental Chytridiomycota sequences obtained from deep sea samples. Conclusion: PHYMYCO-DB offers the tools necessary to: (i) extract high quality fungal sequences for each of the 5 fungal phyla, at all taxonomic levels, (ii) extract already performed alignments, to act as 'reference alignments', (iii) launch alignments of personal sequences along with stored data. A total of 9120 SSU rRNA and 672 EF1-a high-quality fungal sequences are now available. The PHYMYCO-DB is accessible through the URL http://phymycodb.genouest.org/

Specific trends in phosphate glass crystallization

This paper focusses on investigating and comparing the congruent crystallization of phosphate glasses with different degrees of polymerization. The study was performed both on powders, with different size fractions, and coarse particles which can be assimilated to bulk. From DSC experiments, corroborated by SEM analysis, it was demonstrated that LiPO3 crystallizes from surface whereas LiGe2(PO4)3 crystallizes in the whole volume. Sn2P2O7 presented both phenomena, the nucleation time lag being short enough to observe internal crystallization at the laboratory time scale. Using the non-isothermal Ozawa method, the kinetic parameters of the overall devitrification process were determined in terms of the Avrami exponent and of the activation energy for crystallization. The temperature of the maximum nucleation rate was calculated by using the nucleation adiabatic theory. For the achievement of this calculation, the heat capacity temperature dependence up to melting was determined from DSC experiments. The results were found in a good agreement with the SEM observation and the results of the non-isothermal crystallization study.acceptedVersionPeer reviewe

Symplectically degenerate maxima via generating functions

We provide a simple proof of a theorem due to Nancy Hingston, asserting that symplectically degenerate maxima of any Hamiltonian diffeomorphism of the standard symplectic 2d-torus are non-isolated contractible periodic points or their action is a non-isolated point of the average-action spectrum. Our argument is based on generating functions.Comment: 25 pages, thoroughly revised version, new titl

Cross-resistance to elvitegravir and dolutegravir in 502 patients failing on raltegravir: a French national study of raltegravir-experienced HIV-1-infected patients

OBJECTIVES: The objectives of this study were to determine the prevalence and patterns of resistance to integrase strand transfer inhibitors (INSTIs) in patients experiencing virological failure on raltegravir-based ART and the impact on susceptibility to INSTIs (raltegravir, elvitegravir and dolutegravir). PATIENTS AND METHODS: Data were collected from 502 treatment-experienced patients failing a raltegravir-containing regimen in a multicentre study. Reverse transcriptase, protease and integrase were sequenced at failure for each patient. INSTI resistance-associated mutations investigated were those included in the last ANRS genotypic algorithm (v23). RESULTS: Among the 502 patients, at failure, median baseline HIV-1 RNA (viral load) was 2.9 log10 copies/mL. Patients had been previously exposed to a median of five NRTIs, one NNRTI and three PIs. Seventy-one percent harboured HIV-1 subtype B and the most frequent non-B subtype was CRF02_AG (13.3%). The most frequent mutations observed were N155H/S (19.1%), Q148G/H/K/R (15.4%) and Y143C/G/H/R/S (6.7%). At failure, viruses were considered as fully susceptible to all INSTIs in 61.0% of cases, whilst 38.6% were considered as resistant to raltegravir, 34.9% to elvitegravir and 13.9% to dolutegravir. In the case of resistance to raltegravir, viruses were considered as susceptible to elvitegravir in 11% and to dolutegravir in 64% of cases. High HIV-1 viral load at failure (P &lt; 0.001) and low genotypic sensitivity score of the associated treatment with raltegravir (P &lt; 0.001) were associated with the presence of raltegravir-associated mutations at failure. Q148 mutations were selected more frequently in B subtypes versus non-B subtypes (P = 0.004). CONCLUSIONS: This study shows that a high proportion of viruses remain susceptible to dolutegravir in the case of failure on a raltegravir-containing regimen

Detecting differential allelic expression using high-resolution melting curve analysis: application to the breast cancer susceptibility gene CHEK2

<p>Abstract</p> <p>Background</p> <p>The gene <it>CHEK2 </it>encodes a checkpoint kinase playing a key role in the DNA damage pathway. Though <it>CHEK2 </it>has been identified as an intermediate breast cancer susceptibility gene, only a small proportion of high-risk families have been explained by genetic variants located in its coding region. Alteration in gene expression regulation provides a potential mechanism for generating disease susceptibility. The detection of differential allelic expression (DAE) represents a sensitive assay to direct the search for a functional sequence variant within the transcriptional regulatory elements of a candidate gene. We aimed to assess whether <it>CHEK2 </it>was subject to DAE in lymphoblastoid cell lines (LCLs) from high-risk breast cancer patients for whom no mutation in <it>BRCA1</it> or <it>BRCA2</it> had been identified.</p> <p>Methods</p> <p>We implemented an assay based on high-resolution melting (HRM) curve analysis and developed an analysis tool for DAE assessment.</p> <p>Results</p> <p>We observed allelic expression imbalance in 4 of the 41 LCLs examined. All four were carriers of the truncating mutation 1100delC. We confirmed previous findings that this mutation induces non-sense mediated mRNA decay. In our series, we ruled out the possibility of a functional sequence variant located in the promoter region or in a regulatory element of <it>CHEK2 </it>that would lead to DAE in the transcriptional regulatory milieu of freely proliferating LCLs.</p> <p>Conclusions</p> <p>Our results support that HRM is a sensitive and accurate method for DAE assessment. This approach would be of great interest for high-throughput mutation screening projects aiming to identify genes carrying functional regulatory polymorphisms.</p