Symmetric Variational Formulation of BIE for Domain Decomposition Problems in Elasticity – An SGBEM Approach for Nonconforming Discretizations of Curved Interfaces

An original approach to solve domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach, based on a new variational principle for such problems, yields a fully symmetric system of equations. A natural property of the proposed approach is its capability to deal with nonconforming discretizations along straight and curved interfaces, allowing in this way an independent meshing of non-overlapping subdomains to be performed. Weak coupling conditions of equilibrium and compatibility at an interface are obtained from the critical point conditions of the energy functional. Equilibrium is imposed through local traction (Neumann) boundary conditions prescribed on a subdomain situated at one side of the interface, and compatibility is imposed through local displacement (Dirichlet) boundary conditions prescribed on the other subdomain situated at the opposite side of the interface. No additional unknowns such as Lagrange multipliers are introduced. An SGBEM code for 2D elastic domain decomposition problems has been implemented. The effectiveness of the approach developed is documented by numerical examples involving non-matching linear boundary element meshes at the interfaces, where the accuracy is analyzed by comparing the numerical results obtained versus the analytical solutions and by evaluating the convergence rate of the error in the (discretized) integral L2-norm and maximum-normfor h-refinements of boundary element meshes. Finally, a theoretical analysis of a problem with an interior and an exterior subdomain is introduced to explain the observed behaviour of numerical results

A gene-wide investigation on polymorphisms in the taste receptor 2R14 (TAS2R14) and susceptibility to colorectal cancer

Background: Molecular sensing in the gastro-intestinal (GI) tract is responsible for the detection of ingested harmful drugs and toxins, thereby genetic polymorphisms affecting the capability of initiating these responses may be critical for the subsequent efficiency of the gut in eliminating possible threats to the organism. Although these fundamental control systems have been known for long time, the initial molecular recognition events that sense the chemical composition of the luminal contents of the GI tract have remained elusive. TAS2R14 is one of the better characterized members of the taste receptor family and has several polymorphic variants. Several substances that have been shown to activate TAS2R14 are powerful toxic and carcinogenic agents. Methods: Using a tagging approach we investigated all the common genetic variation of the gene region in relation to colon cancer risk with a case-control study design. This is, at the best of our knowledge also the first report on the allele frequencies of the gene in the Caucasian population. Results: We found no evidence of statistically significant associations between polymorphisms in the TAS2R14 gene and colon cancer risk. Conclusion: In conclusion we can confidently exclude a major role for common polymorphisms of the TAS2R14 gene in colorectal cancer risk in this population, although in this report we had insufficient statistical power to completely exclude the possibility that rare variants of the TAS2R14 might be involved in colorectal cancer risk

Association between polymorphisms of TAS2R16 and susceptibility to colorectal cancer

Background: Genetics plays an important role in the susceptibility to sporadic colorectal cancer (CRC). In the last 10 years genome-wide association studies (GWAS) have identified over 40 independent low penetrance polymorphic variants. However, these loci only explain around 1‑4% of CRC heritability, highlighting the dire need of identifying novel risk loci. In this study, we focused our attention on the genetic variability of the TAS2R16 gene, encoding for one of the bitter taste receptors that selectively binds to salicin, a natural antipyretic that resembles aspirin. Given the importance of inflammation in CRC, we tested whether polymorphic variants in this gene could affect the risk of developing this neoplasia hypothesizing a role of TAS2R16 in modulating chronic inflammation within the gut. Methods: We performed an association study using 6 tagging SNPs, (rs860170, rs978739, rs1357949, rs1525489, rs6466849, rs10268496) that cover all TAS2R16 genetic variability. The study was carried out on 1902 CRC cases and 1532 control individuals from four European countries. Results: We did not find any statistically significant association between risk of developing CRC and selected SNPs. However, after stratification by histology (colon vs. rectum) we found that rs1525489 was associated with increased risk of rectal cancer with a (Ptrend of = 0.0071). Conclusions: Our data suggest that polymorphisms within TAS2R16 gene do not have a strong influence on colon cancer susceptibility, but a possible role in rectal cancer should be further evaluated in larger cohorts