The discovery of scientific formulae that parsimoniously explain natural phenomena and
align with existing background theory is a key goal in science. Historically, scientists have …

A fundamental challenge in learning an unknown dynamical system is to reduce model
uncertainty by making measurements while maintaining safety. In this work, we formulate a …

We prove that convex ternary quartic forms are sum-of-squares-convex (sos-convex). This
result is in a meaningful sense the``convex analogue''a celebrated theorem of Hilbert from …

We introduce a remarkable new family of norms on the space of n× nn*n complex matrices.
These norms arise from the combinatorial properties of symmetric functions, and their …

This paper is devoted to show that the flatness of tangents of $1 $-codimensional measures
in Carnot Groups implies $ C^ 1_\mathbb {G} $-rectifiability. As applications we prove that …

We propose faster methods for unconstrained optimization of\emph {structured convex
quartics}, which are convex functions of the form\begin {equation*} f (x)= c^\top x+ …

A theorem of Hunter ensures that the complete homogeneous symmetric polynomials of
even degree are positive definite functions. A probabilistic interpretation of Hunter's theorem …

High-order tensor methods for solving both convex and nonconvex optimization problems
have recently generated significant research interest, due in part to the natural way in which …

Every convex homogeneous polynomial (or form) is nonnegative. Blekherman has shown
that there exist convex forms that are not sums of squares via a nonconstructive argument …

The work is devoted to one of the variations of the Hadwiger--Nelson problem on the
chromatic number of the plane. In this formulation one needs to find for arbitrarily small …