On the topology of conformally compact Einstein 4-manifolds

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally compact Einstein 4-manifold is diffeomorphic to $B^4$ and its conformal infinity is diffeomorphic to $S^3$.Comment: 16 page

Alternatively Assessing Conceptual Learning in an Emergency Clinical Environment—A Mixed Methods Design

Modeling cognitive processes in clinical learning environments is a necessary first step towards improving learning assessment and medical practice by using an alternative assessment model. Verbal protocol and cognitive content analyses are effective methods of exploring such cognitive processes. For the purpose of simplifying the discussion, we have labeled these processes as Identification of Information, Advanced Cognition, and Medical Cognitive Action. Exploring problem solving processes with Bayesian network techniques can characterize students\u27 dynamic learning processes quantitatively, identify differences in cognitive components at different stages of learning and better represent clinical problem solving features. We develop a hierarchical cognitive model as a cognitive assessment tool to describe the complex cognitive network relations, which can be applied to various clinical cognitive situations. The study concludes that the cognitive model was useful in identifying students\u27 learning trajectories by representing the different cognitive feature