The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.Comment: LaTex file, 1 figure, submitted to J. Phys.

A birational mapping with a strange attractor: Post critical set and covariant curves

We consider some two-dimensional birational transformations. One of them is a birational deformation of the H\'enon map. For some of these birational mappings, the post critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic two-form. One may have also an infinite post critical set yielding a covariant curve which is not algebraic (transcendent). For two of the birational mappings considered, the post critical set is not infinite and we claim that there is no algebraic covariant curve and no preserved meromorphic two-form. For these two mappings with non infinite post critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.Comment: 26 pages, 11 figure

Comparative performances of machine learning methods for classifying Crohn Disease patients using genome-wide genotyping data

© 2019, The Author(s). Crohn Disease (CD) is a complex genetic disorder for which more than 140 genes have been identified using genome wide association studies (GWAS). However, the genetic architecture of the trait remains largely unknown. The recent development of machine learning (ML) approaches incited us to apply them to classify healthy and diseased people according to their genomic information. The Immunochip dataset containing 18,227 CD patients and 34,050 healthy controls enrolled and genotyped by the international Inflammatory Bowel Disease genetic consortium (IIBDGC) has been re-analyzed using a set of ML methods: penalized logistic regression (LR), gradient boosted trees (GBT) and artificial neural networks (NN). The main score used to compare the methods was the Area Under the ROC Curve (AUC) statistics. The impact of quality control (QC), imputing and coding methods on LR results showed that QC methods and imputation of missing genotypes may artificially increase the scores. At the opposite, neither the patient/control ratio nor marker preselection or coding strategies significantly affected the results. LR methods, including Lasso, Ridge and ElasticNet provided similar results with a maximum AUC of 0.80. GBT methods like XGBoost, LightGBM and CatBoost, together with dense NN with one or more hidden layers, provided similar AUC values, suggesting limited epistatic effects in the genetic architecture of the trait. ML methods detected near all the genetic variants previously identified by GWAS among the best predictors plus additional predictors with lower effects. The robustness and complementarity of the different methods are also studied. Compared to LR, non-linear models such as GBT or NN may provide robust complementary approaches to identify and classify genetic markers

Synthetic Associations Are Unlikely to Account for Many Common Disease Genome-Wide Association Signals

Synthetic associations have been posited as a possible explanation for missing heritability in complex disease. We show several lines of evidence which suggest that, while possible, these synthetic associations are not common

First light of the VLT planet finder SPHERE. I. Detection and characterization of the sub-stellar companion GJ 758 B

GJ758 B is a brown dwarf companion to a nearby (15.76 pc) solar-type, metal-rich (M/H = +0.2 dex) main-sequence star (G9V) that was discovered with Subaru/HiCIAO in 2009. From previous studies, it has drawn attention as being the coldest (~600K) companion ever directly imaged around a neighboring star. We present new high-contrast data obtained during the commissioning of the SPHERE instrument at the VLT. The data was obtained in Y-, J-, H-, and Ks-bands with the dual-band imaging (DBI) mode of IRDIS, providing a broad coverage of the full near-infrared (near-IR) range at higher contrast and better spectral sampling than previously reported. In this new set of high-quality data, we report the re-detection of the companion, as well as the first detection of a new candidate closer-in to the star. We use the new 8 photometric points for an extended comparison of GJ758 B with empirical objects and 4 families of atmospheric models. From comparison to empirical object, we estimate a T8 spectral type, but none of the comparison object can accurately represent the observed near-IR fluxes of GJ758 B. From comparison to atmospheric models, we attribute a Teff = 600K $\pm$ 100K, but we find that no atmospheric model can adequately fit all the fluxes of GJ758 B. The photometry of the new candidate companion is broadly consistent with L-type objects, but a second epoch with improved photometry is necessary to clarify its status. The new astrometry of GJ758 B shows a significant proper motion since the last epoch. We use this result to improve the determination of the orbital characteristics using two fitting approaches, Least-Square Monte Carlo and Markov Chain Monte Carlo. Finally, we analyze the sensitivity of our data to additional closer-in companions and reject the possibility of other massive brown dwarf companions down to 4-5 AU. [abridged]Comment: 20 pages, 15 figures. Accepted for publication in A&

SPHERE: the exoplanet imager for the Very Large Telescope

Observations of circumstellar environments to look for the direct signal of exoplanets and the scattered light from disks has significant instrumental implications. In the past 15 years, major developments in adaptive optics, coronagraphy, optical manufacturing, wavefront sensing and data processing, together with a consistent global system analysis have enabled a new generation of high-contrast imagers and spectrographs on large ground-based telescopes with much better performance. One of the most productive is the Spectro-Polarimetic High contrast imager for Exoplanets REsearch (SPHERE) designed and built for the ESO Very Large Telescope (VLT) in Chile. SPHERE includes an extreme adaptive optics system, a highly stable common path interface, several types of coronagraphs and three science instruments. Two of them, the Integral Field Spectrograph (IFS) and the Infra-Red Dual-band Imager and Spectrograph (IRDIS), are designed to efficiently cover the near-infrared (NIR) range in a single observation for efficient young planet search. The third one, ZIMPOL, is designed for visible (VIR) polarimetric observation to look for the reflected light of exoplanets and the light scattered by debris disks. This suite of three science instruments enables to study circumstellar environments at unprecedented angular resolution both in the visible and the near-infrared. In this work, we present the complete instrument and its on-sky performance after 4 years of operations at the VLT.Comment: Final version accepted for publication in A&