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It is well known that a positive proportion of all points in a $d$-dimensional lattice is visible from the origin, and that these visible lattice points have constant density in $\mathbb{R}^d$. In the present paper we prove an analogous…
We search for faces of the convex set consisting of all separable states, which are affinely isomorphic to simplices, to get separable states with unique decompositions. In the two-qutrit case, we found that six product vectors spanning a…
A unified neural network structure is presented for joint 3D object detection and point cloud segmentation in this paper. We leverage rich supervision from both detection and segmentation labels rather than using just one of them. In…
The $\lambda$-core vertices of a graph correspond to the non-zero entries of some eigenvector of $\lambda$ for a universal adjacency matrix $\mathbf{U}$ of the graph. We define a partition of the vertex set $V$ based on the $\lambda$-core…
The VC-dimension plays an important role for the algorithmic problem of guarding art galleries efficiently. We prove that inside a simple polygon at most $5$ points can be shattered by $L_1$-visibility polygons and give an example where 5…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
Transformers with powerful global relation modeling abilities have been introduced to fundamental computer vision tasks recently. As a typical example, the Vision Transformer (ViT) directly applies a pure transformer architecture on image…
Recent advances in 3D modeling provide us with real 3D datasets to answer queries, such as "What is the best position for a new billboard?" and "Which hotel room has the best view?" in the presence of obstacles. These applications require…
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.…
Many Standard Model extensions predict metastable massive particles that can be detected by looking for displaced decay vertices in the inner detector volume. Current approaches to search for these events in high-energy particle collisions…
We study the integral points on $\mathbb P_ n\setminus D$, where $D$ is the branch locus of a projection from an hypersurface in $\mathbb P_{n+1}$ to a hyperplane $H\simeq\mathbb P_n$. In doing that we follow the approach proposed in a…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
Non-point spatial objects (e.g., polygons, linestrings, etc.) are ubiquitous. We study the problem of indexing non-point objects in memory for range queries and spatial intersection joins. We propose a secondary partitioning technique for…
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…
We will show that in a space of dimension $m$, any family of $2^{m-1}$ distinct Hadamard vectors (where you can choose x or -x but not both) can be partitioned into Hadamard matrices if and only if $m=2^n$ for some n. We will solve this…
Classical approaches to Vanishing Point Detection (VPD) rely solely on the presence of explicit straight lines in images, while recent supervised deep learning approaches need labeled datasets for training. We propose an alternative…
We prove that every endomorphism of an infinite-dimensional vector space splits as the sum of four idempotents and as the sum of four square-zero endomorphisms, a result that is optimal in general.
Denote by Q_d the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Q_d can be partitioned into vertex disjoint smaller cubes. Among other results, we prove that the asymptotic order of…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…
We propose a novel scoring concept for visual place recognition based on nearest neighbor descriptor voting and demonstrate how the algorithm naturally emerges from the problem formulation. Based on the observation that the number of votes…