We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood (ML) degree counts number critical points function restricted model. prove that ML generic is determined by its Newton polytopes and equals mixed volume related Lagrange equations.

An independent dominating set of a graph, also known as maximal set, is S pairwise non-adjacent vertices such that every vertex not in adjacent to some S. We prove for Δ=4 or Δ≥6, connected n-vertex graph maximum degree at most Δ has an size (1−Δ⌊Δ2/4⌋+Δ)(n−1)+1. In addition, we characterize all graphs having the equality and show other have (1−Δ⌊Δ2/4⌋+Δ)n.