17 citations · 41 across the 6 of their papers we have counts for
8 papers
Paramotopy: Parameter homotopies in parallel
Daniel J. Bates, Danielle Brake, Matthew Niemerg
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an ex…
Investigating the Maximum Number of Real Solutions to the Power Flow Equations: Analysis of Lossless Four-Bus Systems
Daniel K. Molzahn, Matthew Niemerg, Dhagash Mehta +1
The power flow equations model the steady-state relationship between the power injections and voltage phasors in an electric power system. By separating the real and imaginary comp…
Three Formulations of the Kuramoto Model as a System of Polynomial Equations
Tianran Chen, Jakub Marecek, Dhagash Mehta +1
We compare three formulations of stationary equations of the Kuramoto model as systems of polynomial equations. In the comparison, we present bounds on the numbers of real equilibr…
Toward Topologically Based Upper Bounds on the Number of Power Flow Solutions
Daniel K Molzahn, Dhagash Mehta, Matthew Niemerg
The power flow equations, which relate power injections and voltage phasors, are at the heart of many electric power system computations. While Newton-based methods typically find…
Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials
Daniel J. Bates, Jonathan D. Hauenstein, Matthew E. Niemerg +1
We give a Descartes'-like bound on the number of positive solutions to a system of fewnomials that holds when its exponent vectors are not in convex position and a sign condition i…
Statistics of Stationary Points of Random Finite Polynomial Potentials
Dhagash Mehta, Matthew Niemerg, Chuang Sun
The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and M…