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), genuinely high-order accurate finite volume and discontinuous Galerkin schemes satisfying a strict maximum principle for scalar conservation laws were developed. The main advantages of such schemes are their provable high-order accuracy and their easiness for generalization to multi-dimensions for arbitrarily high-order schemes on structured and unstructured meshes. The same idea can be used to construct high-order schemes preserving the positivity of certain physical quantities, such as density and pressure for compressible Euler equations, water height for shallow water equations and density for Vlasov-Boltzmann transport equations. These schemes have been applied in computational fluid dynamics, computational astronomy and astrophysics, plasma simulation, population models and traffic flow models. In this paper, we first review the main ideas of these maximum-principle-satisfying and positivity-preserving highorder schemes, then present a simpler implementation which will result in a significant reduction of computational cost especially for weighted essentially non-oscillatory finite-volume schemes.

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Dexamethasone (Dex)-induced osteoporosis has been described as the most severe side effect in long-term glucocorticoid therapy. The decreased bone mass and the increased marrow fat suggest that Dex possibly shifts the differentiation of bone marrow stromal cells (BMSCs) to favor adipocyte over osteoblast, but the underlying mechanisms are still unknown. In this paper, we established a Dex-induced osteoporotic mouse model, and found that BMSCs from Dex-treated mice are more likely to differentiate into adipocyte than those from control mice, even under the induction of bone morphogenetic protein-2 (BMP2). We also discovered both in vitro and in vivo that the expression level of adipocyte regulator CCAAT/enhancer-binding protein alpha (C/EBPalpha) is significantly upregulated in Dex-induced osteoporotic BMSCs during osteoblastogenesis by a mechanism that involves inhibited DNA hypermethylation of its promoter. Knockdown of C/EBPalpha in Dex-induced osteoporotic cells rescues their differentiation potential, suggesting that Dex shifts BMSC differentiation by inhibiting C/EBPalpha promoter methylation and upregulating its expression level. We further found that the Wnt/beta-catenin pathway is involved in Dex-induced osteoporosis and C/EBPalpha promoter methylation, and its activation by LiCl rescues the effect of Dex on C/EBPalpha promoter methylation and osteoblast/adipocyte balance. This study revealed the C/EBPalpha promoter methylation mechanism and evaluated the function of Wnt/beta-catenin pathway in Dex-induced osteoporosis, providing a useful therapeutic target for this type of osteoporosis.

The shallow water equations model flows in rivers and coastal areas and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. In [36], the authors constructed high order discontinuous Galerkin methods for the shallow water equations which can maintain the still water steady state exactly, and at the same time can preserve the nonnegativity of the water height without loss of mass conservation. In this paper, we explore the extension of these methods on unstructured triangular meshes. The simple positivitypreserving limiter is reformulated, and we prove that the resulting scheme guarantees the positivity of the water depth. Extensive numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.