Stably non-synchronizable maps of the plane

Pecora and Carroll presented a notion of synchronization where an (n-1)-dimensional nonautonomous system is constructed from a given $n$-dimensional dynamical system by imposing the evolution of one coordinate. They noticed that the resulting dynamics may be contracting even if the original dynamics are not. It is easy to construct flows or maps such that no coordinate has synchronizing properties, but this cannot be done in an open set of linear maps or flows in $\R^n$, $n\geq 2$. In this paper we give examples of real analytic homeomorphisms of $\R^2$ such that the non-synchronizability is stable in the sense that in a full $C^0$ neighborhood of the given map, no homeomorphism is synchronizable

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

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

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

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

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

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

DNA methylome analysis identifies accelerated epigenetic aging associated with postmenopausal breast cancer susceptibility

Aim of the study A vast majority of human malignancies are associated with ageing, and age is a strong predictor of cancer risk. Recently, DNA methylation-based marker of ageing, known as ‘epigenetic clock’, has been linked with cancer risk factors. This study aimed to evaluate whether the epigenetic clock is associated with breast cancer risk susceptibility and to identify potential epigenetics-based biomarkers for risk stratification. Methods Here, we profiled DNA methylation changes in a nested case–control study embedded in the European Prospective Investigation into Cancer and Nutrition (EPIC) cohort (n = 960) using the Illumina HumanMethylation 450K BeadChip arrays and used the Horvath age estimation method to calculate epigenetic age for these samples. Intrinsic epigenetic age acceleration (IEAA) was estimated as the residuals by regressing epigenetic age on chronological age. Results We observed an association between IEAA and breast cancer risk (OR, 1.04; 95% CI, 1.007–1.076, P = 0.016). One unit increase in IEAA was associated with a 4% increased odds of developing breast cancer (OR, 1.04; 95% CI, 1.007–1.076). Stratified analysis based on menopausal status revealed that IEAA was associated with development of postmenopausal breast cancers (OR, 1.07; 95% CI, 1.020–1.11, P = 0.003). In addition, methylome-wide analyses revealed that a higher mean DNA methylation at cytosine-phosphate-guanine (CpG) islands was associated with increased risk of breast cancer development (OR per 1 SD = 1.20; 95 %CI: 1.03–1.40, P = 0.02) whereas mean methylation levels at non-island CpGs were indistinguishable between cancer cases and controls. Conclusion Epigenetic age acceleration and CpG island methylation have a weak, but statistically significant, association with breast cancer susceptibility