4 problems

Let $\mathcal{G}$ be a graph on $n$ vertices with non-abelian automorphism group $G=\operatorname{Aut}(\mathcal{G})$ of order $n$, and let $\mathbf{x}$ be a single observation of a…

Blind group selection consistency conjecture. The spectral-concentration selector is consistent at high signal-to-noise ratio:

Let $Z(x,t)$ satisfy Condition B and the previous assumptions, and let $F_q({\Greekmath 0115}_m)$ and $\widehat{F}_q({\Greekmath 0115}_m)$ be the corresponding population and sampl…

Let $\mathfrak{H}_{+,m}$ denote the cone of positive semidefinite Hermitian $m\times m$ matrices, let $\mathbb T^d$ be the $d$-dimensional torus, and let $\mathrm{d}M$ be a nonnega…