Abstract: From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosophic extended triplet loop) are systematically analyzed and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is neutrosophic extended triplet group if and only if it is a completely regular semigroup; (2) an algebraic system is weak commutative neutrosophic extended triplet group if and only if it is a Clifford semigroup; (3) for any element in an AG-NET-loop, its neutral element is unique and idempotent; (4)…every AG-NET-loop is a completely regular and fully regular Abel-Grassmann groupoid (AG-groupoid), but the inverse is not true. Moreover, the constructing methods of NETGs (completely regular semigroups) are investigated, and the lists of some finite NETGs and AG-NET-loops are given.
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Abstract: BACKGROUND: Serous epithelial ovarian cancer is the most common variety of ovarian cancer and is currently diagnosed using serum CA-125 levels. HMGA1 a small 10.6-12 kDa protein, has been implicated as a potentially important tumor biomarker and may enter the urinary trace, thus potentially able to serve as a disease biomarker. OBJECTIVE: To determine if urine HMGA1 can be detected and potentially serve as a clinical diagnostic biomarkers. METHOD: Urine was collected from 20 healthy normal control patients, 20 patients with benign gynecological disease and 55 epithelial ovarian specimens of which 20 exhibited G1/2 ovarian cancer and 35 G3 ovarian…cancers. Serum was also collected from 20 healthy normal control patients and 55 serous epithelial ovarian cancers patients. HMGA1 levels were examined via enzyme-linked immunosorbent assay (ELISA) and were reported independently and normalized to urine creatinine levels. Serum CA-125 levels were examined via enzyme assay and the data was analyzed via box and ROC analysis. RESULTS: Urine HMGA1 was significantly elevated in serous epithelial ovarian cancer specimen relative to healthy control specimens with G3 specimens exhibiting higher levels than G1-G2 specimens. ROC analysis revealed a high degree of sensitivity and specificity for urine HMGA1 detection in ovarian cancer, with a higher AUC value noted for urine HMGA1 than serum CA-125. Furthermore, urine HMGA1 and serum CA-125 combined AUC indicated that urine HMGA1 is an excellent diagnostic biomarker for serous epithelial ovarian cancer. CONCLUSION: Our data indicates that measuring urine HMGA1 may serve as a useful diagnostic tool.
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