Duality properties of Gorringe-Leach equations

In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold-Vassiliev type. The specific associated conserved quantities (Laplace-Runge-Lenz vector and Fradkin-Jauch-Hill tensor) are then dual reflections one of the othe

CDH1 mutation distribution and type suggests genetic differences between the etiology of orofacial clefting and gastric cancer

Pathogenic variants in CDH1, encoding epithelial cadherin (E-cadherin), have been implicated in hereditary diffuse gastric cancer (HDGC), lobular breast cancer, and both syndromic and non-syndromic cleft lip/palate (CL/P). Despite the large number of CDH1 mutations described, the nature of the phenotypic consequence of such mutations is currently not able to be predicted, creating significant challenges for genetic counselling. This study collates the phenotype and molecular data for available CDH1 variants that have been classified, using the American College of Medical Genetics and Genomics criteria, as at least ‘likely pathogenic’, and correlates their molecular and structural characteristics to phenotype. We demonstrate that CDH1 variant type and location differ between HDGC and CL/P, and that there is clustering of CL/P variants within linker regions between the extracellular domains of the cadherin protein. While these differences do not provide for exact prediction of the phenotype for a given mutation, they may contribute to more accurate assessments of risk for HDGC or CL/P for individuals with specific CDH1 variants

The MSX1 allele 4 homozygous child exposed to smoking at periconception is most sensitive in developing nonsyndromic orofacial clefts

Nonsyndromic orofacial clefts (OFC) are common birth defects caused by certain genes interacting with environmental factors. Mutations and association studies indicate that the homeobox gene MSX1 plays a role in human clefting. In a Dutch case-control triad study (mother, father, and child), we investigated interactions between MSX1 and the parents' periconceptional lifestyle in relation to the risk of OFC in their offspring. We s