Related papers: Configurations of skew lines
The aim of this paper is state of conditions that ensure the convexity of a Chebyshev sets in Hilbert spaces .
In this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. We also generalize some known results for sublinear correspondences.
Sketching is used as a ubiquitous tool of expression by novices and experts alike. In this thesis I explore two methods that help a system provide a geometric machine-understanding of sketches, and in-turn help a user accomplish a…
Over the past thirty-seven years, the study of linear and quadratic skein modules has produced a rich and far-reaching skein theory, intricately connected to diverse areas of mathematics and physics, including algebraic geometry, hyperbolic…
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
A generalization of highly symmetric frames is presented by considering also projective stabilizers of frame vectors. This allows construction of highly symmetric line systems and study of highly symmetric frames in a more unified manner.…
We consider the problem of stretching pseudolines in a planar straight-line drawing to straight lines while preserving the straightness and the combinatorial embedding of the drawing. We answer open questions by Mchedlidze et al. by showing…
Karasev conjectured that for any set of $3k$ lines in general position in the plane, which is partitioned into $3$ color classes of equal size $k$, the set can be partitioned into $k$ colorful 3-subsets such that all the triangles formed by…
This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on…
Railroad diagrams (also called "syntax diagrams") are a common, intuitive visualization of grammars, but limited tooling and a lack of formal attention to their layout mostly confines them to hand-drawn documentation. We present the first…
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
While the general question of whether every closed embedding of an affine line in affine $3$-space can be rectified remains open, there have been several partial results proved by several different means. We provide a new approach, namely…
Inspired by the work of L. Drewnowski in [Studia Math. 77 (1984) 373--391], our research reveals new insights and characterizes the notion of spaceability in the context of complements of subspaces (not necessarily closed) within the…
We study a theoretical and algorithmic framework for structured prediction in the online learning setting. The problem of structured prediction, i.e. estimating function where the output space lacks a vectorial structure, is well studied in…
In this paper, we address the problem of estimating the positions of human joints, i.e., articulated pose estimation. Recent state-of-the-art solutions model two key issues, joint detection and spatial configuration refinement, together…
Metro or transit maps, are schematic representations of transit networks to facilitate effective route-finding. These maps are often advertised on a web page or pamphlet highlighting routes from source to destination stations. To visually…
Multilayer perceptrons (MLPs) have been successfully used to represent 3D shapes implicitly and compactly, by mapping 3D coordinates to the corresponding signed distance values or occupancy values. In this paper, we propose a novel…
We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.
In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…
A general framework for oblique projections of nonhermitian matrices onto rational Krylov subspaces is developed. To obtain this framework we revisit the classical rational Krylov subspace algorithm and prove that the projected matrix can…