90 citations · 1.1k across the 68 of their papers we have counts for
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Kinetic Transition Networks for the Thomson Problem and Smale's 7th Problem
Dhagash Mehta, Jianxu Chen, Danny Z. Chen +2
The Thomson Problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology. Here we show that the energy landsc…
Fixed Points of Belief Propagation -- An Analysis via Polynomial Homotopy Continuation
Christian Knoll, Franz Pernkopf, Dhagash Mehta +1
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depe…
Decomposing the parameter space of biological networks via a numerical discriminant approach
Heather A. Harrington, Dhagash Mehta, Helen M. Byrne +1
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of the…
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…