8 problems

Cryo-EM sample-complexity conjecture. If $R\geq 3$ is large enough, then the minimal number of observations required for accurate recovery of the $\operatorname{O}(n)$ orbit of $f$…

Bandeira et al.'s unique-orbit conjecture. If

Let $H=\mathbb{Z}/L\mathbb{Z}\subset\mathrm{SO}(3)$ be generated by rotation through $2\pi/L$ about the $z$-axis, and consider homogeneous projected cryo-EM with $S$ shells and $F$…

Consider heterogeneous projected cryo-EM with $K$ components, $S$ shells, and $F\geq2$ frequencies. Let $U^T_d$ denote the degree-$d$ invariant moment space and let…

For frequency indices $k_1$ and $k_2$, let $\hat L^{k_1,k_2}$ be the corresponding block of $\hat L$, and write $\kappa(\hat L^{k_1,k_2})$ for its condition number. Condition-numbe…

For frequency indices $k_1$ and $k_2$, let $\hat L^{k_1,k_2}$ denote the corresponding block of the matrix $\hat L$, and let $\lambda_{\max}(\hat L^{k_1,k_2})$ be its maximal eigen…

Let $\hat L^{k_1,k_2}$ be a block of the matrix $\hat L$ arising in the covariance-based cryo-electron microscopy algorithm, with $k_1,k_2$ its associated frequency indices. Let…

In the heterogeneous cryo-electron microscopy problem, the sample may contain molecules in multiple conformational states, and the task is to reconstruct these structural states fr…