In this paper, we study the evolution of a Finitary Random Interlacement (FRI) with respect to the expected length of each fiber. In contrast to the previously proved phase transition between sufficiently large and small fiber length, for all d≥3, FRI is NOT stochastically monotone as fiber length increases. At the same time, numerical evidence still strongly supports the existence and uniqueness of a critical fiber length, which is estimated theoretically and numerically to be an inversely proportional function with respect to system intensity.

The current outbreak of coronavirus disease 2019 (COVID-19) has become a global crisis due to its quick and wide spread over the world. A good understanding of the dynamic of the disease would greatly enhance the control and prevention of COVID19. However, to the best of our knowledge, the unique features of the outbreak have limited the applications of all existing dynamic models. In this paper, a novel stochastic model was proposed aiming to account for the unique transmission dynamics of COVID-19 and capture the effects of intervention measures implemented in Mainland China. We found that: (1) instead of aberration, there was a remarkable amount of asymptomatic virus carriers, (2) a virus carrier with symptoms was approximately twice more likely to pass the disease to others than that of an asymptomatic virus carrier, (3) the transmission rate reduced significantly since the implementation of control measures in Mainland China, and (4) it was expected that the epidemic outbreak would be contained by early March in the selected provinces and cities in China.

BackgroundTrastuzumab has been prevailingly accepted as a beneficial treatment for gastric cancer (GC) by targeting human epidermal growth factor receptor 2 (HER2)-positive. However, the therapeutic resistance of trastuzumab remains a major obstacle, restricting the therapeutic efficacy. Therefore, identifying potential key genes and pathways is crucial to maximize the overall clinical benefits.MethodsThe gene expression profile GSE77346 was retrieved to identify the differentially expressed genes (DEGs) associated with the trastuzumab resistance in GC. Next, the DEGs were annotated by the gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways. The DEGs-coded protein-protein interaction (PPI) networks and the prognostic values of the 20 hub genes were determined. Correlation of the hub genes were analyzed in The Cancer Genome Atlas. The prognostic values of hub genes were further validated by Kaplan-Meier (KM) plotter.ResultsA total of 849 DEGs were identified, with 374 in upregulation and 475 in downregulation. Epithelium development was the most significantly enriched term in biological processes while membrane-bounded vesicle was in cellular compartments and cell adhesion molecular binding was in molecular functions. Pathways in cancer and ECM-receptor interaction were the most significantly enriched for all DEGs. Among the PPI networks, 20 hub genes were defined, including CD44 molecule (CD44), HER-2, and cadherin 1 (CDH1). Six hub genes were associated with favorable OS while eight were associated with poor OS. Mechanistically, 2′-5′-oligoadenylate synthetase 1, 3 (OAS1, OAS3) and CDH1 featured high degrees and strong correlations with other hub genes.ConclusionsThis bioinformatics analysis identified key genes and pathways for potential targets and survival predictors for trastuzumab treatment in GC.Electronic supplementary materialThe online version of this article (10.1186/s12957-018-1475-6) contains supplementary material, which is available to authorized users.

Due to the excellent lubricity of V2O5 and soft metals, V and Cu have been added to Mo-N based coatings to further improve the tribological properties. In this study, the Mo-V-Cu-N coatings were deposited by high power impulse magnetron sputtering (HIPIMS). The effects of V and Cu on the microstructure and mechanical properties of Mo-N coatings were investigated. With increasing V/Cu content ratio, the deposition rate decreased from 15.4 to 6.5 nm/min, and the microstructure transformed from a featureless structure into a dense columnar structure. At low Cu contents, less than 6.5 at.%, the Mo-V-Cu-N coatings exhibited a single solid solution phase of c-Mo2(V)N. When the Cu content reached 29.7 at.%, the Mo45V1Cu30N24 coating showed the lowest surface roughness of 2.0 nm, and the coating changed into a double-phase of c-Mo2(V)N and c-Cu. The adhesion strength gradually increased from 32.2 to 87.8 N with an increasing V/Cu content ratio. Due to the microstructure densification, a maximum hardness of 27.3 GPa was achieved for the Mo46V15Cu1N38 coating, which was accompanied by a high compressive residual stress.