Related papers: Image sets of perfectly nonlinear maps
This work is devoted to the investigation of the problem about inverse mapping systems expansions of ultrauniform spaces $X$ using polyhedra over non-Archimedean locally compact fields $\bf L$. Theorems about expansions of complete…
In an undirected graph $G=(V,E)$, we say $(A,B)$ is a pair of perfectly matched sets if $A$ and $B$ are disjoint subsets of $V$ and every vertex in $A$ (resp. $B$) has exactly one neighbor in $B$ (resp. $A$). The size of a pair of perfectly…
Past studies on the local limit of maximal weight matchings in edge-weighted large random graphs rely fundamentally on the assumption that the weights are atomless, which ensures that the maximal weight matching is unique. This excludes de…
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays. The size of the smallest bounded…
In this paper we will consider an unknown binary image, of which the length of the boundary and the area of the image are given. These two values together contain some information about the general shape of the image. We will study two…
Let $F$ be an algebraically closed field of characteristic zero. We consider the question which subsets of $M_n(F)$ can be images of noncommutative polynomials. We prove that a noncommutative polynomial $f$ has only finitely many similarity…
We establish a cutting lemma for definable families of sets in distal structures, as well as the optimality of the distal cell decomposition for definable families of sets on the plane in $o$-minimal expansions of fields. Using it, we…
Autonomous navigation in unstructured off-road environments is greatly improved by semantic scene understanding. Conventional image processing algorithms are difficult to implement and lack robustness due to a lack of structure and high…
A. Ya. Zaslavskii's results on the existence of a linear (affine) selection for a linear (affine) or superlinear (convex) map $\Phi : K \to 2^Y$ defined on a convex cone (convex set) $K$ having the interpolation property are extended. We…
The unconditional generation of high fidelity images is a longstanding benchmark for testing the performance of image decoders. Autoregressive image models have been able to generate small images unconditionally, but the extension of these…
In the Minimum $d$-Dimensional Arrangement Problem (d-dimAP) we are given a graph with edge weights, and the goal is to find a 1-1 map of the vertices into $\mathbb{Z}^d$ (for some fixed dimension $d\geq 1$) minimizing the total weighted…
In applications involving matching of image sets, the information from multiple images must be effectively exploited to represent each set. State-of-the-art methods use probabilistic distribution or subspace to model a set and use specific…
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
We study the 1-planar, quasi-planar, and fan-planar crossing number in comparison to the (unrestricted) crossing number of graphs. We prove that there are $n$-vertex 1-planar (quasi-planar, fan-planar) graphs such that any 1-planar…
One primary technical challenge in photoacoustic microscopy (PAM) is the necessary compromise between spatial resolution and imaging speed. In this study, we propose a novel application of deep learning principles to reconstruct…
We prove that a large family of pairs of graphs satisfy a polynomial dependence in asymmetric graph removal lemmas. In particular, we give an unexpected answer to a question of Gishboliner, Shapira, and Wigderson by showing that for every…
Poisson distribution is used for modeling noise in photon-limited imaging. While canonical examples include relatively exotic types of sensing like spectral imaging or astronomy, the problem is relevant to regular photography now more than…
We consider the range of random analytic functions with finite radius of convergence. We show that any unbounded random Taylor series with rotationally invariant coefficients has dense image in the plane. We moreover show that if in…