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In this paper, we investigate the dynamics of a discrete commensal symbiosis model with Holling type functional response and density dependent birth rate. Sufficient conditions are obtained for the permanence, partial extinction, and global attractivity of the system. Our analysis presents that the density dependent birth rate plays a crucial role on the dynamic behaviors of the system. Finally, numerical simulations and graphical illustrations are given to indicate the analytical results. [ABSTRACT FROM AUTHOR]

We study A two species discrete competitive system with Beddington-DeAngelis functional response in this paper. Sufficient conditions which guarantee the extinction of a species and the global attractivity of the other one are obtained. Our results supplement some existing ones. [ABSTRACT FROM AUTHOR]

Programmed death 1 ligand 1 (PD-L1) is a negative co-stimulatory molecule in immune responses. Previous reports have indicated that inflammatory cytokines can upregulate the expression of PD-L1 in tumor cells, which in turn suppresses host immune responses. Periodontitis is characterized by persistent inflammation of the periodontium, which is initiated by infection with oral bacteria and results in damage to cells and the matrices of the periodontal connective tissues. In the present study, the expression and function of PD-L1 in periodontal tissue destruction were examined. Periodontal ligament cells (PDLCs) were stimulated by inflammatory cytokines and periodontal pathogens. The expression and function of PD-L1 on the surface of PDLCs was investigated using flow cytometry in vitro. Periodontal disease was induced by the injection of Porphyromonas gingivalis in mouse models. The expression levels of PD-L1 in the periodontal tissues of the mice were analyzed using flow cytometry and immunohistochemistry. PD-L1 was inducibly expressed on the PDLCs by the inflammatory cytokines and periodontal pathogens. The inflammation-induced expression of PD-L1 was shown to cause the apoptosis of activated T lymphocytes and improve the survival of PDLCs. Furthermore, in the mouse model of experimental periodontitis, the expression of PD-L1 in severe cases of periodontitis was significantly lower, compared with that in mild cases. By contrast, no significant differences were observed between the healthy control and severe periodontitis groups. The results of the present study showed that the expression of PD-L1 may inhibit the destruction of periodontal tissues, indicating the involvement of a possible protective feedback mechanism against periodontal infection. [ABSTRACT FROM AUTHOR]

Using the Leggett-Williams fixed point theorem in cones, we prove the existence of at least three positive solutions to the nonlinear n-th order m-point boundary-value problem Δnu(k) + a(k)f(k, u) = 0, k ∈ {0,N}, u(0) = 0, Δu(0) = 0, . . . ,Δn-2u(0) = 0, u(N + n) = ∑m-2i=1 αiu(ξi). [ABSTRACT FROM AUTHOR]

The article establishes the existence of three positive solutions for second-order discrete boundary value problems. Some background materials and definitions that will be needed in the discussion are presented, which include the definitions of an operator and a nonnegative continuous concave functional on a cone. This paper depends on an application of a fixed-point theorem which deals with fixed points of a cone-preserving operator defined on an ordered Branach space to obtain results. An example is also given to illustrate the main results.