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.

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

Crohn's Disease and Early Exposure to Domestic Refrigeration

Environmental risk factors playing a causative role in Crohn's Disease (CD) remain largely unknown. Recently, it has been suggested that refrigerated food could be involved in disease development. We thus conducted a pilot case control study to explore the association of CD with the exposure to domestic refrigeration in childhood.Using a standard questionnaire we interviewed 199 CD cases and 207 age-matched patients with irritable bowel syndrome (IBS) as controls. Cases and controls were followed by the same gastroenterologists of tertiary referral clinics in Tehran, Iran. The questionnaire focused on the date of the first acquisition of home refrigerator and freezer. Data were analysed by a multivariate logistic model. The current age was in average 34 years in CD cases and the percentage of females in the case and control groups were respectively 48.3% and 63.7%. Patients were exposed earlier than controls to the refrigerator (X2 = 9.9, df = 3, P = 0.04) and refrigerator exposure at birth was found to be a risk factor for CD (OR = 2.08 (95% CI: 1.01-4.29), P = 0.05). Comparable results were obtained looking for the exposure to freezer at home. Finally, among the other recorded items reflecting the hygiene and comfort at home, we also found personal television, car and washing machine associated with CD.This study supports the opinion that CD is associated with exposure to domestic refrigeration, among other household factors, during childhood

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