“…, x mj ∈ E. The same conclusion continues to hold if the polynomials p j are replaced by p j (Φ j,1 (x 1 ), · · · , Φ j,mj (x mj )), where Φ j,k are C 1 -diffeomorphisms of R n . Interestingly, the Hausdorff dimension bound in [14], while depending on the ambient dimension n and the maximum degree d of the polynomials, is independent of the number of input vectors m j in p j , which may continue to grow without bound. This paper uses similar ideas to present two results in a somewhat different direction.…”