joint work with E. Feliu, N. Kaihnsa, B. Sturmfels, Timo de Wolff
Parameterized ordinary differential equation systems are crucial for modeling in biochemical reaction networks under the assumption of mass-action kinetics. Various questions concerning the signs of multivariate polynomials in positive orthant arise from studying the solutions' qualitative behavior with respect to parameter values. In this work, we utilize circuit polynomials to find symbolic certificates of nonnegativity to provide further insight into the number of positive steady states of the n-site phosphorylation cycle model.
joint work with Alexander Kovacec, Mina Saee Bostanabad
In 2004, Boman et al introduced the concept of factor width of a semidefinite matrix $A$. This is the smallest $k$ for which one can write the matrix as $A=VV^T$ with each column of $V$ containing at most $k$ non-zeros. In the polynomial optimization context, these matrices can be used to check if a polynomial is a sum of squares of polynomials of support at most $k$. We will prove some results on the geometry of the cones of matrices with bounded factor widths and their
I will discuss several recent results on symmetric nonnegative polynomials and their approximations by sums of squares. I will consider several types of symmetry, but the situation is especially interesting in the limit as the number of variables tends to infinity. There are diverse applications to quantum entanglement, graph density inequalities and theoretical computer science.