Related papers: Indistinguishable sceneries on the Boolean hypercu…

Feature learning on point clouds has shown great promise, with the introduction of effective and generalizable deep learning frameworks such as pointnet++. Thus far, however, point features have been abstracted in an independent and…

This is a treatise on finite point configurations spanning a fixed volume to be found in a single color-class of an arbitrary finite (measurable) coloring of the Euclidean space $\mathbb{R}^n$, or in a single large measurable subset…

In a balanced graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various other types of local balance conditions in graph decompositions.…

We present a method to edit complex indoor lighting from a single image with its predicted depth and light source segmentation masks. This is an extremely challenging problem that requires modeling complex light transport, and disentangling…

We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided…

We study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied. Hypergraph coloring is a constraint satisfaction problem where…

We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree p. We show that the discrete minimizers in the spaces of piecewise…

The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random $d$-uniform hypergraph from its…

The reconfiguration graph of the $k$-colorings, denoted $R_k(G)$, is the graph whose vertices are the $k$-colorings of $G$ and two colorings are adjacent in $R_k(G)$ if they differ in color on exactly one vertex. A graph $G$ is said to be…

We study polynomials with no zeros on the unit ball in complex Euclidean space with a view toward characterizing when a rational function is bounded on the ball. We give a complete local description of such polynomials in two variables near…

We prove a vertex isoperimetric inequality for the $n$-dimensional Hamming ball $\mathcal{B}_n(R)$ of radius $R$. The isoperimetric inequality is sharp up to a constant factor for sets that are comparable to $\mathcal{B}_n(R)$ in size. A…

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

An $n\times n\times\dots\times n$ hypercube is made from $n^d$ unit hypercubes. Two unit hypercubes are neighbours if they share a $(d-1)$-dimensional face. In each step of a dismantling process, we remove a unit hypercube that has…

We study colorings of the Euclidean space constrained by \emph{hypersphere forcing conditions}: if an admissible hypersphere, $S_r(p)$, centered at a point $p$ and of radius $r$ contains a monochromatic set of points satisfying a certain…

Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…

We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the…

We introduce SparseNeuS, a novel neural rendering based method for the task of surface reconstruction from multi-view images. This task becomes more difficult when only sparse images are provided as input, a scenario where existing neural…

Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…

Color constancy is the problem of inferring the color of the light that illuminated a scene, usually so that the illumination color can be removed. Because this problem is underconstrained, it is often solved by modeling the statistical…

Confirming a conjecture of Gy\'arf\'as, we prove that, for all natural numbers $k$ and $r$, the vertices of every $r$-edge-coloured complete $k$-uniform hypergraph can be partitioned into a bounded number (independent of the size of the…