10 problems

Collapsing conjecture. Suppose that

Let $u(k,q)$ denote the size of the smallest set of uniqueness for the positive function class $\left(\mathcal{B}^{k}_{q}\right)_+$. In particular, consider the case $q=2$. Minimum…

Asymptotic-bias dichotomy. The technical condition in the unbiasedness theorem should be replaceable by $\mu \geq \mu_{\textnormal{detect}}$. Under this condition, the MLE is asymp…

Let $X\subseteq\mathbb{R}^d$ be the sample configuration, let $X'\supseteq X$ and let $\Delta'$ be the finite set and bimonotone subdivision produced by the paper's algorithm. Let…

Partial-decoupling conjecture. The kernels of the partial decouplings of $Z$ are the only critical points of $\Phi_{L^*}$.

Let a superposition be a product of mutually compatible slices, and let a slice be a component obtained by a slicing algorithm from the initial syntax of a superposition. An order-…

Let $\mathcal{C}_{\mathcal{G}}$ denote the cone associated with a graph $\mathcal{G}$. A basic open semialgebraic set is an open semialgebraic set defined by finitely many strict p…

Let $B$ denote the model matrix for the directed random graph network model with reciprocation, and let $\mathrm{cone}(B)$ be its cone. For a network on $n$ nodes, the facets conje…

Let $n\ge2$ and let $s,t$ satisfy $0<s\le t$. Let $L(P)$ be the likelihood function defined in the source by equation (newLP). Alternative likelihood conjecture. The matrix … is a…

Let $n\ge2$ and let $s,t$ satisfy $0<t<s$. For positive $u$ and positive integer block dimensions, write $(u)_{l_1\times l_2}$ for the $l_1\times l_2$ matrix all of whose entries e…