The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements

For both the Poisson model problem and the Stokes problem in any dimension, this paper proves that the enriched Crouzeix-Raviart elements are actually identical to the first order Raviart-Thomas elements in the sense that they produce the same discrete stresses. This result improves the previous result in literature which, for two dimensions, states that the piecewise constant projection of the stress by the first order Raviart-Thomas element is equal to that by the Crouzeix-Raviart element. For the eigenvalue problem of Laplace operator, this paper proves that the error of the enriched Crouzeix-Raviart element is equivalent to that of the Raviart-Thomas element up to higher order terms

Optimized Data Representation for Interactive Multiview Navigation

In contrary to traditional media streaming services where a unique media content is delivered to different users, interactive multiview navigation applications enable users to choose their own viewpoints and freely navigate in a 3-D scene. The interactivity brings new challenges in addition to the classical rate-distortion trade-off, which considers only the compression performance and viewing quality. On the one hand, interactivity necessitates sufficient viewpoints for richer navigation; on the other hand, it requires to provide low bandwidth and delay costs for smooth navigation during view transitions. In this paper, we formally describe the novel trade-offs posed by the navigation interactivity and classical rate-distortion criterion. Based on an original formulation, we look for the optimal design of the data representation by introducing novel rate and distortion models and practical solving algorithms. Experiments show that the proposed data representation method outperforms the baseline solution by providing lower resource consumptions and higher visual quality in all navigation configurations, which certainly confirms the potential of the proposed data representation in practical interactive navigation systems

The roles of endoglin gene in cerebrovascular diseases.

Endoglin (ENG, also known as CD105) is a transforming growth factor β (TGFβ) associated receptor and is required for both vasculogenesis and angiogenesis. Angiogenesis is important in the development of cerebral vasculature and in the pathogenesis of cerebral vascular diseases. ENG is an essential component of the endothelial nitric oxide synthase activation complex. Animal studies showed that ENG deficiency impairs stroke recovery. ENG deficiency also impairs the regulation of vascular tone, which contributes to the pathogenesis of brain arteriovenous malformation (bAVM) and vasospasm. In human, functional haploinsufficiency of ENG gene causes type I hereditary hemorrhagic telangiectasia (HHT1), an autosomal dominant disorder. Compared to normal population, HHT1 patients have a higher prevalence of AVM in multiple organs including the brain. Vessels in bAVM are fragile and tend to rupture, causing hemorrhagic stroke. High prevalence of pulmonary AVM in HHT1 patients are associated with a higher incidence of paradoxical embolism in the cerebral circulation causing ischemic brain injury. Therefore, HHT1 patients are at risk for both hemorrhagic and ischemic stroke. This review summarizes the possible mechanism of ENG in the pathogenesis of cerebrovascular diseases in experimental animal models and in patients