The Gorenstein and complete intersection properties of associated graded rings

Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone F(I) of I as reflected in their defining ideals as homomorphic images of polynomial rings over R/I and R/m respectively. In case all the higher conormal modules of I are free over R/I, we observe that: (i) G(I) is Cohen-Macaulay iff F(I) is Cohen- Macaulay, (ii) G(I) is Gorenstein iff both F(I) and R/I are Gorenstein, and (iii) G(I) is a relative complete intersection iff F(I) is a relative complete intersection. In case R/I is Gorenstein, we give a necessary and sufficient condition for G(I) to be Gorenstein in terms of residuation of powers of I with respect to a reduction J of I with \mu(J) = dim R and the reduction number r of I with respect to J. We prove that G(I) is Gorenstein iff J:I^{r-i} = J + I^{i+1}, for i = 0, ...,r-1. If (R,m) is a Gorenstein local ring and I \subseteq m is an ideal having a reduction J with reduction number r such that \mu(J) = ht(I) = g > 0, we prove that the extended Rees algebra R[It, t^-1}] is quasi-Gorenstein with \a-invariant a if and only if J^n:I^r = I^{n+a-r+g-1} for every integer n

Biomarkers for gastric cancer: molecular classification revisited

Gastric cancer (GC) is one of the most common lethal cancer worldwide. In recent years, several new targeted therapeutic agents for the treatment of metastatic GC have been developed. These include drugs that block human epidermal growth factor receptor 2 (HER2) or epidermal growth factor receptor, ramucirumab monoclonal antibody that binds to a receptor for vascular endothelial growth factor, and other targeted agents such as sorafenib and apatinib, and immunotherapies. In this short review, we provide a summary of clinical and preclinical biomarkers (HER2, mesenchymal-epithelial transition [MET], fibroblast growth factor receptor 2 [FGFR2], ring finger protein 43 [RNF43], microsatellite instability and mismatch repair, Epstein-Barr virus, programmed cell death ligand-1, and tumor infiltrating lymphocytes) for treatment strategies and will address the molecular classification of GC revisited with an aim to select the best-precision treatment strategies for GC patients

Two-point discrimination values vary depending on test site, sex and test modality in the orofacial region: a preliminary study

The two-point discrimination (TPD) test is one of the most commonly used neurosensory tests to assess mechanoperception in the clinical settings. While there have been numerous studies of functional sensibility of the hand using TPD test, there have been relatively not enough reports on TPD in the orofacial region. Objective The aims of the present study were to determine the normal values of TPD in the six trigeminal sites (the forehead, cheek, mentum, upper lip, lower lip, and the tongue tip) and to investigate the effect of the site, sex, and test modality on the TPD perception. Material and Methods Forty healthy volunteers consisting of age-matched men (20) and women (20) with a mean age of 27.1 years were recruited. One examiner performed the TPD test using a simple hand-operated device, i.e., by drawing compass with a blunt or sharp-pointed tip. The static TPD with a blunt-pointed tip (STPDB), moving TPD with a blunt-pointed tip (MTPDB), and static TPD with a sharp-pointed tip (STPDS) were measured. The predictors were the site, sex, and test modality, and the outcome variable was the TPD value. Three-way ANOVA was used for statistics. Results The analysis showed a significant effect of the site, sex and test modality on the TPD values. Significant differences between the test sites were observed with the descending order from the forehead and cheek>;mentum>;upper lip and lower lip>;tongue tip and index finger. Women showed lower TPD values than those of men. The STPDS measurements were consistently lower than those of the STPDB and MTPDB. Conclusions The normal values of TPD in this study suggest that the cheek and forehead were less sensitive than other regions evaluated and women were more sensitive than men. The STPDS was the most sensitive test modality