Application of the interacting particle system method to piecewise deterministic Markov processes used in reliability.

Variance reduction methods are often needed for the reliability assessment of complex industrial systems, we focus on one variance reduction method in a given context, that is, the interacting particle system (IPS) method used on piecewise deterministic Markov processes (PDMPs) for reliability assessment. The PDMPs are a very large class of processes which benefit from high modeling capacities, they can model almost any Markovian phenomenon that does not include diffusion. In reliability assessment, the PDMPs modeling industrial systems generally involve low jump rates and jump kernels favoring one safe arrival, we call such model a "concentrated PDMP." Used on such concentrated PDMPs, the IPS is inefficient and does not always provide a variance reduction. Indeed, the efficiency of the IPS method relies on simulating many different trajectories during its propagation steps, but unfortunately, concentrated PDMPs are likely to generate the same deterministic trajectories over and over. We propose an adaptation of the IPS method called IPS+M that reduces this phenomenon. The IPS+M consists in modifying the propagation steps of the IPS, by conditioning the propagation to avoid generating the same trajectories multiple times. We prove that, compared to the IPS, the IPS+M method always provides an estimator with a lower variance. We also carry out simulations on two-components systems that confirm these results.

Endothelial protein C receptor gene 6936A/G single-nucleotide polymorphism as a possible biomarker of thrombotic risk in acute myeloid leukemia.

Protein C (PC) is a natural anticoagulant, which interacts with the endothelial PC receptor (EPCR). EPCR single-nucleotide polymorphism (SNP) 6936A/G results in high levels of a free soluble form of EPCR (sEPCR) and may affect the risk of coagulation. The objective of this study was to assess whether the 6936A/G SNP of the EPCR gene is involved in the procoagulant activity displayed by hematological malignancies. EPCR 6936A/G polymorphism analysis was performed in 205 patients with hematological malignancies and in 63 healthy controls. All the subjects were genotyped for the EPCR 6936A/G SNP (AA, AG and GG genotypes). The 6936A/G polymorphism distribution was similar between healthy donors and patients. The association between EPCR 6936A/G SNP and thrombosis was investigated in 110 patients. The disease-wise break-up revealed that 55 of the patients suffered from acute myeloid leukemia (AML). In AML patients, the incidence of thrombosis was 28.3% and significantly higher in the 6936AG compared with that in the 6936AA genotype (50 vs. 22%, respectively). In conclusion, this study revealed a significant association of the 6936AG genotype of EPCR with thrombotic events in AML. Therefore, the presence of the 6936AG genotype in AML patients may be considered as a risk indicator of thrombosis.