10 problems

Limiting achievability-region conjecture.

Achievability-region monotonicity conjecture. For every $n\geq k$,

Universal hyperbolic bound. For any partition $s_1+s_2=k$ with $\max\{s_1,s_2\}\geq 2$,

For each strand index $j\in [N]$, noisy reads are aggregated by base-by-base majority voting over $\Sigma = \{\mathsf{A,C,G,T}\}$ to form a consensus sequence…

General-capacity conjecture. For every $K,D,M$, the general capacity of IPIR does not exceed the linear capacity, and both are given by

Linear-capacity conjecture. The linear capacity of IPIR is

Asymptotic optimality conjecture. For MDS-XSTPIR, the rate

Let $K\geq 1$, $M\geq 1$, and $D\geq 2$ satisfy $D+M\leq K$. Set $\mathcal{K}=[K]$, and let $\mathcal{I}$ and $\mathcal{J}$ be the sets of subsets $I,J\subseteq\mathcal{K}$ with…

The structured random mapping uses an expansion $u=Dx$, where $D\in\mathbb{R}^{m\times d}$ and $x$ is an input vector. An unbiased transform is one whose output does not exhibit th…

In the least information theory (LIT), a term's probability in a document is compared with its probability in the collection, which serves as the domain distribution and prior know…