Related papers: Configurations of skew lines
Most recent approaches to bilingual dictionary induction find a linear alignment between the word vector spaces of two languages. We show that projecting the two languages onto a third, latent space, rather than directly onto each other,…
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
In this revised version, we add some expository material and references and make some minor corrections.
We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…
Self-supervised learning (SSL) has made enormous progress and largely narrowed the gap with the supervised ones, where the representation learning is mainly guided by a projection into an embedding space. During the projection, current…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line…
Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.
This survey of some of the more topological aspects of the placement problem for complex curves in complex surfaces was originally published in L'Enseignement Mathematique 29 (1983). The present LaTeXed redaction corrects several…
The purpose of this paper is to provide a both comprehensive and summarizing account on recent results about analysis and geometry on configuration spaces $\Gamma_X$ over Riemannian manifolds $X$. Particular emphasis is given to a complete…
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…
Translation of the paper "Interpolation of linear spaces and maximum estimates for solutions to parabolic equations" published in Russian in the collected volume "Partial differential equations", Akad. Nauk SSSR, Sibirsk. Otdel., Inst.…
In recent years two Krylov subspace methods have been proposed for solving skew symmetric linear systems, one based on the minimum residual condition, the other on the Galerkin condition. We give new, algorithm-independent proofs that in…
Predicting 3D room layout from single image is a challenging task with many applications. In this paper, we propose a new training and post-processing method for 3D room layout estimation, built on a recent state-of-the-art 3D room layout…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…
For the past few decades, structured light has been gaining popularity across various research fields. Its fascinating properties have been exploited for both previously unforeseen and established applications from new perspectives. Crucial…
After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is…
The configuration space of a non-linear sigma model is the space of maps from one manifold to another. This paper reviews the authors' work on non-linear sigma models with target a homogeneous space. It begins with a description of the…
We provide a classification result on nearly free arrangements of lines in the complex projective plane with nodes and triple points.