Episode 52 “Carrier Classes & Discussing Syntax” [AtA]

The essential graph is a distinguished member of a Markov equivalence class of AMP chain graphs. However, the directed edges in the essential graph are not necessarily strong or invariant, i.e. they may not be shared by every member of the equivalence class. Likewise for the undirected edges. In this paper, we develop a procedure for identifying which edges in an essential graph are strong. We also show how this makes it possible to bound some causal effects when the true chain graph is unknown.

Extending DiNezza-Lu's approach to the setting of big cohomology classes, we prove that solutions of degenerate complex Monge-Amp{è}re equations on compact K{ä}hler manifolds are continuous on a Zariski open set. This allows us to show that singular K{ä}hler-Einstein metrics on log canonical varieties of general type have continuous potentials on the ample locus outside of the non-klt part.