Two-thirds simulation indexes and modal logic characterization

Two-thirds simulation provides a kind of abstract description of an implementation with respect to a specification. In order to characterize the approximate two-thirds simulation, we propose the definition of a two- thirds simulation index which expresses the degree to which a binary relation between processes is two-thirds simulation. 2-two-thirds simulation and its substitutivity laws are given in this paper. And, based on 2-two-thirds simulation, we present a measure model for describing the degree of approximation between processes. In particular, we give the modal logical characterization of 2-two-thirds simulation.

Interplay of neuropilin-1 and semaphorin 3A after partial hepatectomy in rats

AIM： To elucidate the role of neuropilin-1 （Nrp-1） and semaphorin 3A （Sema3A） in sinusoidal remodeling dur- ing liver regeneration in rats. METHODS： Male Wistar/ST rats at 7 wk of age, weigh- ing about 200 g, were used for all animal experiments. In vivo, at 24, 48, 72, 96, 144 and 192 h after two- thirds partial hepatectomy （PHx）, the remnant livers were removed. Liver tissues were immunohistochemi- cally stained for Nrp-1, Sema3A and SE-1, a liver sinu- soidal endothelial cell （SEC） marker. Total RNA of the liver tissue was extracted and reversely transcribed into cDNA. The mRNA expression of Sema3A was ana- lyzed by quantitative real-time polymerase chain reac- tion and normalized to that of ribosomal protein $18. In vitro, SECs were isolated from rat liver and cultured in endothelial growth medium containing 20 ng/mL vascular endothelial cell growth factor. Migration of SECs in primary culture was assessed by cell transwell assay with or without recombinant Sema3A. Apoptotic cells were determined by a terminal deoxynucleotidyl transferase-mediated deoxyuridine triphosphate nick end labeling method. RESULTS： In vitro, immunohistochemistry study re- vealed that Sema3A and Nrp-1 were constitutively ex- pressed in hepatocytes and SECs, respectively, in normal rat liver tissues. Nrp-1 expression in SECs was quantified by the percentage of immunostained area with anti- Nrp-1 antibody in relation to the area stained with SE-1. Between 24 h and 96 h following resection of liver, Nrp-1 expression in SECs was transiently increased. Compared with the baseline （5.2% ± 0.1%）, Nrp-1 expression in SECs significantly increased at 24 h （17.3% ± 0.7%, P 〈 0.05）, 48 h （39.1% ± 0.6%, P 〈 0.01）, 72 h （46.9% ± 4.5%, P 〈 0.01） and 96 h （29.9% ±3.8%, P 〈 0.01） after PHx, then returned to the basal level at termination of liver regeneration. Interestingly, the expression of Sema3A was inversely associated with that of Nrp-1 in liver after PHx. Sema3A mRNA expres- sion was significantly reduced by about 75% over the period 24-144 h after PHx （P 〈 0.05）, and returned to basal levels at 192 h after PHx. In vitro, SECs isolated from rats after PHx （PHx-SECs） were observed to mi- grate to the lower chamber of the cell transwell system after incubation for 24 h, but not cells from normal rats （CONT-SECs）, indicating that mobility of PHx-SECs increases as compared with that of CONT-SECs. More- over, recombinant Sema3A significantly attenuated mi- gration in PHx-SECs in primary culture （vehicle-treated 100% ± 7.9% vs Sema3A-treated 42.6% ± 5.4%, P 〈 0.01）, but not in CONT-SECs. Compared with CONT- SECs, the apoptotic rate of PHx-SECs decreased by 78.3% （P 〈 0.05）. There was no difference in apopto- sis between CONT-SECs that were treated with vehicle and Sema3A. However, in PHx-SECs, apoptosis was induced by the presence of 5 nmol Sema3A for 24 h （vehicle-treated 21.7%±7.6% vs Sema3A-treated 104.3% ± 8.9%, P 〈 0.05）. In addition, immunohisto- chemistry confirmed the increased expression of Nrp-1 in PHx-SECs, while it was noted to a lesser extent in CONT-SECs. CONCLUSION： The interplay of Nrp-1 and Sema3A shown in our results may lead to a better understand- ing of interaction between sinusoidal remodeling and SECs during liver regeneration.