The concept of α-ideals in posets is introduced. Several properties of α-ideals in 0-distributive posets are studied. Characterization of prime ideals to be α-ideals in 0- distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal I of a 0-distributive poset is non-dense, then I is an α-ideal. Moreover, it is shown that the set of all α-ideals α Id(P) of a poset P with 0 forms a complete lattice. A result analogous to separation theorem for finite 0-distributive posets is obtained with respect to prime α-ideals. Some counterexamples are also given.
In vitro produced β-like cells can provide promising cell therapy for curing the epidemic of diabetes. In this context, we aimed to investigate the effects of different concentrations of γ-aminobutyric acid (GABA) on the differentiation of rat pancreatic ductal epithelial-like stem cells (PDESCs) into β-like cells. The PDESC line cells were cultured in the basal media (DMEM/F12 + 10% FBS + 1% penicillinstreptomycin) supplemented with 0 µM, 5 µM, 50 µM, 500 µM, and 5 mM of GABA for 28 days to induce their differentiation. The differentiated cells were detected by cell morphology, dithizone (DTZ) staining, immunofluorescence staining, real-time polymerase chain reaction (qPCR), and glucose-stimulated insulin secretion (GSIS) assay to validate their identity. At the end of 28 days, compared with the control group, enrichment of induced cells was high among the 5 μM, 50 μM, 500 μM, and 5 mM GABA induction groups. The formation of islet-like cell clusters (ICCs) began at 14 days, and the cell clusters showed a growth trend with the culture time. The induced ICCs were positive for DTZ staining, while the control group showed negative results for DTZ staining and the differentiated cells were also positive for β-cell-specific markers (Ins1 and Pdx1). GSIS assay of 50 μM induction group cells at 28 days showed significantly higher levels of C-peptide and insulin secretion than the control, 5 μM, 500 μM, and 5 mM GABA-treated groups (P < 0.01). At the same time, the 50 μM induction group cells also showed significantly higher levels of Ins1, Pdx1 and Nkx6.1 mRNA as compared to the 5 μM, 500 μM and 5 mM GABA groups (P < 0.01). Thus, the addition of GABA to the basal medium effectively induced differentiation of adult rat PDESCs into insulin-secreting β-like cells, and 50 μM was the most effective concentration for the induction.
\vspace{-1.6cm} The paper studies the relations between ϕ-divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam's deficiency. A new and considerably simplified approach is given to the spectral representation of ϕ-divergences already established in Österreicher and Feldman \cite{OestFeld} under restrictive conditions and in Liese and Vajda \cite{LiV06}, \cite{LiV08} in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary convex functions which are strictly convex at one point only. Bayes sufficiency is characterized with the help of a binary model that consists of the joint distribution and the product of the marginal distributions of the observation and the parameter, respectively. LeCam's deficiency is expressed in terms of ϕ-divergences where ϕ belongs to a class of convex functions whose curvature measures are finite and satisfy a normalization condition.