2 problems

Let $\mathcal{A}$ be a unital C-algebra, let $0<\varepsilon<1$, and let $M,N\in\mathbb{N}$ and $\mathbf{x}_1,\dots,\mathbf{x}_M\in\mathcal{A}^N$. Modular Johnson–Lindenstrauss flat…

Let $f(n,d,\varepsilon)$ denote the smallest $m$ such that every $n$-point subset of $\ell_2^d$ can be embedded into $\ell_2^m$ with distortion at most $1+\varepsilon$. Dimension-r…