Poincar-Einstein manifolds are a class of noncompact Riemannian manifolds with a well- defined boundary at infinity. They appear as the framework of AdS/CFT correspondence in string theory and have been studied intensively.

High dimensional partial differential equations (PDE) are challenging to compute by traditional mesh-based methods especially when their solutions have large gradients or concentrations at unknown locations.

Conductivity imaging from various observational data represents one fundamental task in medical imaging.

Stock picking and market timing are two critical skills in fund performance evaluation. Measuring these skills and examining the association often relies on a factor model.

In practice, the data  collected often systematically deviate from their actual values; a typical example is the underreporting of data in social sciences, ecology and epidemiology.