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Iterative deadlock prevention strategies based on siphons have drawn increasing attention. For iterative strategies, selecting which siphon to control at each iteration has an influence on the final supervisor in structural complexity, computational complexity, and behavioral permissiveness. In this paper, we define two kinds of emptiable siphons and provide two modified mixed-integer programming (MIP) formulations to compute such siphons. On the basis of them, a three-stage iterative deadlock prevention policy that specifies the siphon control order is proposed. The experimental results show that a supervisor with a simpler structure, higher behavioral permissiveness, and lower computational complexity can be obtained by the proposed strategy since neither the exhaustive siphon enumeration nor the reachability analysis is required. INDEX TERMS Deadlock prevention, discrete event systems, mixed integer programming, Petri nets.

The present study aimed to determine the effect of microRNA (miR)‑210 on osteoarthritis (OA). The expression levels of miR‑210, type I and X collagen (COL1A1 and COL10A1) and matrix metallopeptidase 13 (MMP13) in OA and normal chondrocytes were determined using reverse transcription‑quantitative polymerase chain reaction analysis. The OA chondrocytes were transfected with an miRNA precursor for miR‑210 or a negative control. After 3, 7, 14 and 21 days, the expression levels of miR‑210 were examined, the proliferation of the OA chondrocytes were determined using an XTT assay and the protein levels of Ki67 and HIF‑3α were analyzed by Western blotting. After 21 days, the mRNA and protein levels of COL1A1, COL10A1 and MMP13 were analyzed. Th present study demonstrated that the expression levels of miR‑210 and COL1A1 were lower, and the expression levels of COL10A1 and MMP13 were higher in the OA chondrocytes, compared with the levels of expression in the normal chondrocytes. Overexpression of miR‑210 significantly promoted the proliferation of OA chondrocytes and induced the protein expression of Ki67. In addition, miR‑210 overexpression markedly increased the expression of COL1A1 expression, but decreased the expression levels of COL10A1 and MMP13. A luciferase reporter assay confirmed the direct interaction between miR‑210 and hypoxia‑inducible factor (HIF)‑3α. miR‑210 did not alter the mRNA expression of HIF‑3α, however, it suppressed the protein expression of HIF‑3α. Additionally, HIF‑3α knockdown significantly promoted OA chondrocyte proliferation and increased the mRNA levels of COL1A1, whereas it decreased the mRNA levels of COL10A1 and MMP13. The results of the present study suggested that miR‑210 may be a negative regulator of the progression of OA, which increases chondrocyte proliferation and prompts extracellular matrix deposition by directly targeting HIF‑3α.

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Osteoarthritis (OA) has long been a difficult to overcome joint disease for medical workers. However, there is still a lack of effective treatments for OA. In the present study, we aimed to evaluate the treatment effect of celecoxib (CLX) combined with diacerein (DC) on OA and delineate the underlying molecular mechanism. The OA model was established by using rats, and OA rats were treated with either CLX alone, DC alone, and CLX combined with DC. The results showed that, as compared with a single treatment of CLX or DC, CLX combined with DC markedly attenuated OA and inhibited the levels of inflammatory mediators interleukin-1β and nitric oxide, improved bone cartilage metabolism, and suppressed chondrocyte apoptosis. Most importantly, CLX combined with DC significantly inactivated the c-Jun N-terminal kinases (JNK) signaling pathway by the inhibition of MEKK1 and MKK7, as detected by Western blot analysis. Furthermore, the protein expression of downstream genes of JNK, including activating-transcription factor (Atf-2), matrix metalloproteinase-13 (MMP-13), and cyclooxygenase (COX-2), were also significantly inhibited by CLX combined with DC as compared with single treatments. Furthermore, CLX combined with DC also effectively inhibits p38 mitogen-activated protein kinase and nuclear factor-κB signaling pathways. Taken together, our study suggests that CLX combined with DC has satisfactory treatment effects on OA via a stronger inhibitory effect on inflammatory signaling pathway.