Alfred Horn's conjecture on eigenvalues of sums Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an $n$-tuple $\gamma$ in solution polytope, constructing with required spectra such that their sum has $\gamma$.

This paper formulates the inverse power flow problem which is to infer nodal admittance matrix (hence network structure of system) from voltage and current phasors measured at a number buses. We show that can be uniquely identified sequence measurements corresponding different steady states when every node in system equipped with measurement device, Kron-reduced determined even if some nodes ar...

Examples 1.1. • Y ∼= P, D a nodal cubic. • Y a complete nonsingular toric surface, D the toric boundary (i.e, the complement of the big torus orbit Gm). • Blowups: Given a Looijenga pair (Y ,D), we can take “toric blowups,” where Y is the blowup of Y at a nodal point of D and D is the inverse image of D). Note that toric blowups do not change U . “non-toric blowups,” where Ỹ is the blowup of Y ...