6 problems

The “Meaning of Life” conjecture. The sequence was present in the genome of the ancestor of all vertebrates, and it has been completely conserved to the present time: none of its b…

Let $R_{m,n}^{(\operatorname{al})}$ be the number of optimality regions in the parameter space of the sequence-alignment model, with both sequences having length $n$. An optimality…

Let $H$ and $L$ denote extremal alignments, let $h_o(H,L)$ be the restricted Hausdorff distance, and let $h(H,L)$ be the full Hausdorff distance. Full Hausdorff-distance extension…

Let $H$ and $L$ denote the extremal alignments, let $h_o(H,L)$ be the restricted Hausdorff distance between them, and let $h(H,L)$ be the full Hausdorff distance. Suppose the sourc…

Let $X$ and $Y$ be two sequences, and let their optimal alignments be the alignments attaining the optimal sequence-alignment score. Optimal-alignment variation conjecture. The var…

Piecewise computability conjecture. The dynamic programming algorithm for finding the minimizer of the ${\bar R}_C$-risk, together with exponential smoothing, could be used to find…