Reduction rules for reset/inhibitor nets

Reset/inhibitor nets are Petri nets extended with reset arcs and inhibitor arcs. These extensions can be used to model cancellation and blocking. A reset arc allows a transition to remove all tokens from a certain place when the transition fires. An inhibitor arc can stop a transition from being enabled if the place contains one or more tokens. While reset/inhibitor nets increase the expressive power of Petri nets, they also result in increased complexity of analysis techniques. One way of speeding up Petri net analysis is to apply reduction rules. Unfortunately, many of the rules defined for classical Petri nets do not hold in the presence of reset and/or inhibitor arcs. Moreover, new rules can be added. This is the first paper systematically presenting a comprehensive set of reduction rules for reset/inhibitor nets. These rules are liveness and boundedness preserving and are able to dramatically reduce models and their state spaces. It can be observed that most of the modeling languages used in practice have features related to cancellation and blocking. Therefore, this work is highly relevant for all kinds of application areas where analysis is currently intractable.

Brivanib alaninate, a dual inhibitor of vascular endothelial growth factor receptor and fibroblast growth factor receptor tyrosine kinases, induces growth inhibition in mouse models of human hepatocellular carcinoma

PURPOSE: Hreceptor (VEGFR) and FGF receptor (FGFR) signaling pathways. EXPERIMENTAL DESIGN: Six different s.c. patient-derived HCC xenografts were implanted into mice. Tumor growth was evaluated in mice treated with brivanib compared with control. The effects of brivanib on apoptosis and cell proliferation were evaluated by immunohistochemistry. The SK-HEP1 and HepG2 cells were used to investigate the effects of brivanib on the VEGFR-2 and FGFR-1 signaling pathways in vitro. Western blotting was used to determine changes in proteins in these xenografts and cell lines. RESULTS: Brivanib significantly suppressed tumor growth in five of six xenograft lines. Furthermore, brivanib-induced growth inhibition was associated with a decrease in phosphorylated VEGFR-2 at Tyr(1054/1059), increased apoptosis, reduced microvessel density, inhibition of cell proliferation, and down-regulation of cell cycle regulators. The levels of FGFR-1 and FGFR-2 expression in these xenograft lines were positively correlated with its sensitivity to brivanib-induced growth inhibition. In VEGF-stimulated and basic FGF stimulated SK-HEP1 cells, brivanib significantly inhibited VEGFR-2, FGFR-1, extracellular signal-regulated kinase 1/2, and Akt phosphorylation. CONCLUSION: This study provides a strong rationale for clinical investigation of brivanib in patients with HCC.