no code implementations • 14 Jan 2021 • Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith, Mauricio Velasco
The relationship between nonnegative polynomials and sums of squares is one of the central questions in real algebraic geometry.
Algebraic Geometry Optimization and Control
1 code implementation • 4 May 2018 • Mateo Díaz, Adolfo J. Quiroz, Mauricio Velasco
For data living in a manifold $M\subseteq \mathbb{R}^m$ and a point $p\in M$ we consider a statistic $U_{k, n}$ which estimates the variance of the angle between pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$, near $p$, and evaluate this statistic as a tool for estimation of the intrinsic dimension of $M$ at $p$.
