6 problems

Let $C_{PF}(\mathbf{N},P_T)$ denote the proportional fair capacity of a Gaussian broadcast channel with noise vector $\mathbf{N}$ and total power $P_T$. Let $\preceq$ denote the co…

Consider the two-colored PAM with $m_1=m_2=m$, attachment kernel … and minority-vertex probability $\mu_1$. PageRank fairness conjecture. For every sufficiently small $c>0$, there…

Let $k$ be the number of segments in the piecewise-linear functions, let $A$ be the number of protected groups, and let $C$ be the number of labels. Segment-count conjecture. The c…

Let $m^{(n)}$ be a sequence of weight distributions with corresponding probability distributions $(P^{(n)})_{n \in \mathbb{N}}$, where $P^{(n)}=(p_i^{(n)})_{i \in \mathbb{N}}$ is a…

Let $S$, $X$, and $Y$ denote sensitive features, non-sensitive features, and labels, respectively. Suppose the predictor is constructed from the remaining observations using the st…

Flow-scalability conjecture. A network is flow scalable if and only if it maximizes a weighted $\alpha$-fair utility function.