31 problems

Let $G(n,d,p)$ be the spherical random geometric graph and let $G(n,p)$ be the Erdős–Rényi random graph. For probability distributions on a finite set, define total variation dista…

Strong dualizability conjecture. Every measurable equivalence relation on a standard Borel space is strongly dualizable.

Proposed functional's Gamma-convergence conjecture. The proposed functional converges, in the $\Gamma$-convergence sense, to a total variation type functional on graphs as…

Let $P$ and $Q$ be probability measures, let $V(P,Q)$ denote their total variation distance, and define … For $v$ in the relevant small-distance regime, Sixth-order surplus asympto…

Let $S^{n-1}=\{x\in\mathbb{R}^n:\lVert x\rVert_2=1\}$ be the Euclidean unit sphere, let $\sigma_{n-1}$ be Haar probability measure on $S^{n-1}$, and let $P_{n-1}$ be the transition…

Let $\Omega\subset\mathbb{R}^N$ satisfy the bounded-feature-space assumption, let $\mu\in\mathcal{P}(\Omega\times\{0,1\})$ have conditional distributions…

Total variation separation conjecture. For every such pair,

Carlier and Poon's minimum-principle conjecture. The minimum principle holds for the TV-JKO scheme in every dimension $d$.

HMC convergence conjecture. Theorem should hold for the HMC algorithm as well. The conjecture proposes that the paper's main non-asymptotic convergence result in total variation ex…

Let $\beta=k-\frac{1}{n_m}$, $p=n^{-\frac{1}{\beta}}$, and $q=n^{-\frac{km}{\beta}}$, with $n=n_m$. Let $\Gamma_{n,m,p}$ and $Y_{n,k,q}$ denote the two distributions defined in the…

Let $n\geq 2$, let $\Omega=(0,1)^n$, and consider functions with bounded Hessian--Schatten variation, together with the class $\operatorname{CPWL}(\Omega)$ of continuous piecewise-…

Linear-size approximation conjecture. As $n\in 2\mathbb{N}$ tends to infinity,

In the total variation model, the measurement operator is constructed from four blocks of measurements derived from an operator $\mathcal{A}$, contributing $4m_1$ measurements. Nee…

Strong sub-conjecture. There exists a total ordering $precsim$ on $C^i$ with minimum and maximum elements $PL, PU$ such that

Minimal sub-conjecture. There exists a simple parametrization for $C^i$ with respect to the total variation metric.

Let ${{\normalfont\textsc{rgg}}}(n,p,d)$ be the random geometric graph obtained by sampling points $X_i$ uniformly from ${\mathbb{S}}^{d-1}$ and including $(i,j)$ when…

Let ${sf TDLA}0(n,{ sf Torus}(n^c))$ denote the finite-graph DLA tree with $n$ vertices rooted at $0$, and let ${bf dla}n$ denote the standard DLA tree with $n$ vertices. **The fin…

Let $m$ be the number of measurements, $s$ the sparsity or complexity parameter, and $n$ the ambient signal dimension. Write $\operatorname{PolyLog}(n,s)$ for a factor polynomial i…

Consider the discrete analogue of the total variation prior for the normal vector field, with the surface connectivity allowed to vary as part of the design. The paper notes that t…

Let $\Gamma$ be a smooth surface with principal curvatures $k_1$ and $k_2$, and let $\Gamma_h$ be a sequence of successively refined triangular meshes approximating $\Gamma$. The d…

Let $C\subset\mathbb{R}^2$ be a bounded ellipse whose indicator function is an eigenfunction in the sense of the adaptive anisotropic total variation eigenfunction equation, and le…

Let $G=(V,E)$ be a graph, let $(V)_k$ denote the ordered $k$-tuples of distinct vertices, and let $\mathrm{IP}(k)$ and $\mathrm{RW}(k)$ denote, respectively, the $k$-particle inter…

A graph MBO scheme alternates a diffusion step with a threshold step; the graph total variation functional is the graph analogue of total variation, and graph mean curvature flow i…

The centered maximal function is considered in the setting of total variation inequalities, whose best constant is the quantity being optimized. Centered variation conjecture. The…

Let $\pi$ be a uniformly chosen parking function in $\mathcal{PF}_n$, and let $f$ be a uniformly chosen element of $\mathcal{F}_n$. For fixed $k$, consider the joint distributions…