6 problems

Georgiou–Pavon conjecture. Given a positivity-improving completely positive trace-preserving map $\mathcal{E}$ and two density matrices $\rho$ and $\omega$, there exist invertible…

Let $p$, $n$, and $q_1,\dots,q_k$ be the dimensions governing the iPCA estimation problem, let $\Theta$ be the true precision matrix, and let $\hat{\Theta}$ be the maximum likeliho…

Polynomial-time decidability conjecture. The decision problem for $(P,Q)$-rank-nondecreasingness is in $\mathbf{P}$.

Let $X=(x_{ij})$ be a $3$-tensor with $x_{ij}\in\mathbb C^n$, and define … For $\varepsilon>0$, call $X$ an $\varepsilon$-QLS if … Starting with independent uniform points $x_{ij}$…

Let $A,\widetilde A\in\mathbb{R}^{d\times d}$ and let $\Sigma\in\mathbb{R}^{d\times m}$ and $\widetilde\Sigma\in\mathbb{R}^{d\times\widetilde m}$ have full rank $d$. Assume that th…

Let $A$ be the scaling matrix, let $\bigl(M^{(i)}_t\bigr)_{t\nin[0,T)}$ denote the martingales arising in the bridge construction, and let $operatorname{ReSpec}(A)$ be the set of…