In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion equations.Then,coupling with a kind of R...In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion equations.Then,coupling with a kind of Runge-Kutta type implicit-explicit time discretization which treats the convection term explicitly and the diffusion term implicitly,we analyze the stability and error estimates of the corresponding fully discrete schemes.The fully discrete schemes are proved to be stable if the time-stepτ≤τ0,whereτ0 is a constant independent of the mesh-size h.Furthermore,by the aid of a special projection and a careful estimate for the convection term,the optimal error estimate is also obtained for the third order fully discrete scheme.Numerical experiments are displayed to verify the theoretical results.展开更多
TGF-β and Foxp3 expressions are crucial for the induction and functional activity of CD4＋Foxp3＋ regulatory T （iTreg） cells. Here, we demonstrate that although TGF-β-primed CD8＋ cells display much lower Foxp3 ex...TGF-β and Foxp3 expressions are crucial for the induction and functional activity of CD4＋Foxp3＋ regulatory T （iTreg） cells. Here, we demonstrate that although TGF-β-primed CD8＋ cells display much lower Foxp3 expression, their suppressive capacity is equivalent to that of CD4＋ iTreg cells, and both Foxp3- and Foxp3＋ CD8＋ subsets have suppressive activities in vitro and in vivo. CD8＋Foxp3- iTreg cells produce little IFN-γ but almost no IL-2, and display a typical anergic phenotype. Among phenotypic markers expressed in CD8＋Foxp3- cells, we identify CD103 expression particularly crucial for the generation and function of this subset. Moreover, IL-IO and TGF-β signals rather than cytotoxicity mediate the suppressive effect of this novel Treg population. Therefore, TGF-β can induce both CD8＋Foxp3- and CD8＋Foxp3＋ iTreg subsets, which may represent the unique immunoregulatory means to treat autoimmune and inflammatory diseases.展开更多
基金Research sponsored by NSFC grants 11871428 and 12071214Nature Science Research Program for Colleges and Universities of Jiangsu Province grant 20KJB110011+1 种基金Research is supported in part by NSFC grants U1930402the fellowship of China Postdoctoral Science Foundation(No.2020TQ0030).
文摘In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion equations.Then,coupling with a kind of Runge-Kutta type implicit-explicit time discretization which treats the convection term explicitly and the diffusion term implicitly,we analyze the stability and error estimates of the corresponding fully discrete schemes.The fully discrete schemes are proved to be stable if the time-stepτ≤τ0,whereτ0 is a constant independent of the mesh-size h.Furthermore,by the aid of a special projection and a careful estimate for the convection term,the optimal error estimate is also obtained for the third order fully discrete scheme.Numerical experiments are displayed to verify the theoretical results.
文摘TGF-β and Foxp3 expressions are crucial for the induction and functional activity of CD4＋Foxp3＋ regulatory T （iTreg） cells. Here, we demonstrate that although TGF-β-primed CD8＋ cells display much lower Foxp3 expression, their suppressive capacity is equivalent to that of CD4＋ iTreg cells, and both Foxp3- and Foxp3＋ CD8＋ subsets have suppressive activities in vitro and in vivo. CD8＋Foxp3- iTreg cells produce little IFN-γ but almost no IL-2, and display a typical anergic phenotype. Among phenotypic markers expressed in CD8＋Foxp3- cells, we identify CD103 expression particularly crucial for the generation and function of this subset. Moreover, IL-IO and TGF-β signals rather than cytotoxicity mediate the suppressive effect of this novel Treg population. Therefore, TGF-β can induce both CD8＋Foxp3- and CD8＋Foxp3＋ iTreg subsets, which may represent the unique immunoregulatory means to treat autoimmune and inflammatory diseases.
