9 problems

Let $T\colon \mathbb{R}^k\times \mathcal{X}\to \mathcal{X}$ be a continuous action on a compact metrizable space $\mathcal{X}$, and let $\varphi\colon \mathcal{X}\to\mathbb{R}$ be…

Let $Q_A^t$ and $Q_B^t$ denote the length-$t$ sequences of semantic quotient states available to agents $A$ and $B$, respectively, and let $M^T$ be the sequence of messages sent by…

Non-singularity conjecture. The Jacobian matrix

Let $R^*(D)$ denote the infimum mutual-information rate over generalized causal reproductions $\mathsf{GCR}$ whose long-term distortion is at most $D$, and let $R(D)$ denote the ra…

MP-AMP cost conjecture. The total computation and communication cost scales as

Let $R(d_1,d_2)$ denote the rate-distortion function for lossy broadcasting in a two-way relay network, and let $R_L(d_1,d_2)$ be its cut-set lower bound, with distortion pair…

Let a Reed–Solomon code have either moderate rate or low rate, and let $\mu$ denote the decoding parameter used by an algebraic soft-decision (ASD) decoder. Rate-dependent ASD deco…

Bahadur-efficiency conjecture. The proposed test has high Bahadur efficiency in any case where it can be applied.

Berger–Tung Gaussian auxiliary-variable conjecture. Choosing the auxiliary random variables to be Gaussian should result in the optimal rate-distortion region for reconstructing bo…