3 problems

Let $A\in\mathbb{R}_{\geq 0}^{M\times N}$ have non-negative rank $H_0$, and suppose that $A=U_0V_0$ for some strictly positive matrices $U_0\in\mathbb{R}_{>0}^{M\times H_0}$ and…

Because the outputs are constrained by $\mathbf{1}^T x=1$, let $x'=x-\frac{1}{d}\mathbf{1}$, so that $\mathbf{1}^T x'=0$, and let $W\in\mathbb{R}^{m\times d}$ act on the input. Def…

Tightness conjecture. The bound from Theorem bound-alternate is tight for all such $p$, $k$, and $r$; equivalently,