11 problems

Let $\mathcal{M}$ be the polling-system Markov chain, let $\ell$ be the boundary level, and let $\pi(x,y,s)$ denote its stationary probability at state $(x,y,s)$. In the spiral-spi…

The two approaches are scenario generation and rare-event sampling with Fleming–Viot biasing for robust stochastic programming; let the number of scenarios tend to infinity, and co…

Proof-artifact conjecture. The restriction that $d/\lambda$ be sufficiently small can be dropped using a different proof technique. The conjecture asserts that the stated remainder…

Let $g\in\{7,8\}$, let $p$ be the percentile used by the $p$-quantile algorithm to construct the set of penultimate histograms, and let efficiency mean the fraction of most likely…

Let $\zeta=100$ be the discretization level, let $g$ be the number of genotypes, and let $p(g)$ denote the smallest percentile that enables full efficiency of the $p$-quantile algo…

Let $g=3$, let $H$ and $G$ be histograms, and let $\Omega^+(H,G)$ denote the set of interior paths from $H$ to $G$. For a path $\mathbf{H}^\star\in\Omega^+(H,G)$, write $Z^\star$ f…

Finite-step optimality conjecture. A finite optimal number of steps $T^\star$ always exists such that

Carrillo et al.'s convergence conjecture. Convergence of the process also holds for $d>1$.

Apparent-bias conjecture. The observed apparent-bias phenomenon for AMS could be explained by analogy with the corresponding studies for fixed multilevel splitting.

Error-bound conjecture. A similar error bound to the one established in the paper's error bound theorem should also hold in the case of pathwise ellipticity.

Ultrametricity is a property of a metric space in which the strong triangle inequality holds. The paper considers complex systems with extremal sparse statistics and rare-event sta…