It is shown that a large class of systems non-linear wave equations, based on the good-bad-ugly model, admit formal solutions with polyhomogeneous expansions near null infinity. A particular set variables introduced which allows us to write Einstein field equations in generalized harmonic gauge as system and functional form first few orders such an expansion found by applying aforementioned res...

The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k and their adjacent edges are removed until no vertices of degree less than k are left. Often the question is whether the remaining hypergraph, the k-core, is empty or not. In some settings, it may be possible to remove either vertices or edges from t...