a b s t r a c tTwo designs are geometrically isomorphic if one design can be obtained from the other by reordering the runs, relabeling the factors and/or reversing the level order of one or more factors. In this paper, some new necessary and sufficient conditions for identifying geometric isomorphism of symmetric designs with prime levels are provided. A new algorithm for checking geometric isomorphism is proposed and a searching result for geometrically non-isomorphic 3-level orthogonal arrays of 18 runs is presented.

No abstract

Background It is unclear whether the long non-coding RNA (lncRNA) OTX2 antisense RNA 1 (OTX2-AS1) plays a pivotal role in gastric cancer (GC). An analysis of The Cancer Genome Atlas (TCGA) database data and bioinformatics was used to explore the relationship between OTX2-AS1 and GC in the current study. Methods We evaluated the relationship between clinical features and OTX2-AS1 expression, prognostic factors, and the significant involvement of OTX2-AS1 in function using various statistical methods, such as Kaplan–Meier method, Cox regression analysis, Gene Set Enrichment Analysis (GSEA), and immune infiltration analysis. GC cell lines were tested for OTX2-AS1 expression using qRT-PCR. Results A high level of OTX2-AS1 expression was significantly and negatively associated with Helicobacter pylori ( H pylori) infection in GC patients ( P = .006) and predicted a poorer overall survival (OS) (HR: 1.54; 95% CI: 1.10-2.14; P = .011), progression-free interval (PFI) (HR: 1.75; 95% CI: 1.22-2.51; P = .002) and disease-specific survival (DSS) (HR: 1.85; 95% CI: 1.21-2.85; P = .005) in GC patients. There was an independent correlation between OTX2-AS1 expression (HR: 1.771; 95% CI: 1.164-2.696; P = .008) and OS in patients with GC. There were differential enrichments for the OTX2-AS1 high expression phenotype in the olfactory transduction, G alpha (s) signaling events, keratinization, olfactory signaling pathway, and preimplantation embryo. OTX2-AS1 expression may be related to certain immune-infiltrating cells. Compared to gastric epithelial cells (GES-1), GC cell lines showed a significant increase in OTX2-AS1 expression. Conclusion There was a significant association between OTX2-AS1 expression in GC patients and poor survival, suggesting that it may be a useful biomarker for prognosis and immunotherapy outcome of stomach adenocarcinoma (STAD) in GC.

No abstract