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Creators/Authors contains: "Liu Haoran"

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  1. Free, publicly-accessible full text available February 1, 2025
  2. We construct and analyze a CutFEM discretization for the Stokes problem based on the Scott–Vogelius pair. The discrete piecewise polynomial spaces are defined on macro-element triangulations which are not fitted to the smooth physical domain. Boundary conditions are imposed via penalization through the help of a Nitsche-type discretization, whereas stability with respect to small and anisotropic cuts of the bulk elements is ensured by adding local ghost penalty stabilization terms. We show stability of the scheme as well as a divergence–free property of the discrete velocity outside an O ( h ) neighborhood of the boundary. To mitigate the error caused by the violation of the divergence–free condition, we introduce local grad–div stabilization. The error analysis shows that the grad–div parameter can scale like O ( h −1 ), allowing a rather heavy penalty for the violation of mass conservation, while still ensuring optimal order error estimates. 
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  3. Abstract This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott–Vogelius pair on Clough–Tocher splits. The velocity space consists of continuous piecewise polynomials of degree k , and the pressure space consists of piecewise polynomials of degree ( k – 1) without continuity constraints. A Lagrange multiplier space that consists of continuous piecewise polynomials with respect to the boundary partition is introduced to enforce boundary conditions and to mitigate the lack of pressure-robustness. We prove several inf-sup conditions, leading to the well-posedness of the method. In addition, we show that the method converges with optimal order and the velocity approximation is divergence-free. 
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  4. ABSTRACT Although Wnt signaling is clearly important for the intestinal epithelial homeostasis, the relevance of various sources of Wnt ligands themselves remains incompletely understood. Blocking the release of Wnt in distinct stromal cell types suggests obligatory functions of several stromal cell sources and yields different observations. The physiological contribution of epithelial Wnt to tissue homeostasis remains unclear. We show here that blocking epithelial Wnts affects colonic Reg4+ epithelial cell differentiation and impairs colonic epithelial regeneration after injury in mice. Single-cell RNA analysis of intestinal stroma showed that the majority of Wnt-producing cells were contained in transgelin (Tagln+) and smooth muscle actin α2 (Acta2+) expressing populations. We genetically attenuated Wnt production from these stromal cells using Tagln-Cre and Acta2-CreER drivers, and found that blockage of Wnt release from either epithelium or Tagln+ and Acta2+ stromal cells impaired colonic epithelial healing after chemical-induced injury. Aggregated blockage of Wnt release from both epithelium and Tagln+ or Acta2+ stromal cells drastically diminished epithelial repair, increasing morbidity and mortality. These results from two uncharacterized stromal populations suggested that colonic recovery from colitis-like injury depends on multiple Wnt-producing sources. 
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  5. Abstract

    Paneth cells (PCs), a specialized secretory cell type in the small intestine, are increasingly recognized as having an essential role in host responses to microbiome and environmental stresses. Whether and how commensal and pathogenic microbes modify PC composition to modulate inflammation remain unclear. Using newly developed PC‐reporter mice under conventional and gnotobiotic conditions, we determined PC transcriptomic heterogeneity in response to commensal and invasive microbes at single cell level. Infection expands the pool of CD74+PCs, whose number correlates with auto or allogeneic inflammatory disease progressions in mice. Similar correlation was found in human inflammatory disease tissues. Infection‐stimulated cytokines increase production of reactive oxygen species (ROS) and expression of a PC‐specific mucosal pentraxin (Mptx2) in activated PCs. A PC‐specific ablation ofMyD88reduced CD74+PC population, thus ameliorating pathogen‐induced systemic disease. A similar phenotype was also observed in mice lacking Mptx2. Thus, infection stimulates expansion of a PC subset that influences disease progression.

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