Related papers: Global Positioning: the Uniqueness Question and a …
In this two-part study we develop a unified approach to the analysis of the global exactness of various penalty and augmented Lagrangian functions for finite-dimensional constrained optimization problems. This approach allows one to verify…
We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…
Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations…
The project SYPOR wishes to use the global navigation satellite system GALILEO as an autonomous relativistic positioning system for the Earth. Motivations and a sketch of the basic concepts underlying the project are presented. For non…
Erd\H{o}s asked the following question: given $n$ points in the plane in almost general position (no 4 collinear), how large a set can we guarantee to find that is in general position (no 3 collinear)? F\"uredi constructed a set of $n$…
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…
Let $X$ be a vertex subset of a graph $G$. Then $u, v\in V(G)$ are $X$-positionable if $V(P)\cap X \subseteq \{u,v\}$ holds for any shortest $u,v$-path $P$. If each two vertices from $X$ are $X$-positionable, then $X$ is a general position…
This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The vertical direction can be determined in two ways: 1- using direct physical measurement like IMU…
Worldwide image geo-localization aims to infer the geographic location of an image captured anywhere on Earth, spanning street, city, regional, national, and continental scales. Existing methods rely on visual features that are sensitive to…
Worldwide visual geo-localization aims to determine the geographic location of an image anywhere on Earth using only its visual content. Despite recent progress, learning expressive representations of geographic space remains challenging…
We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.
This paper presents a new extension of the classical Heron problem, termed the generalized $(k,m)$-Heron problem, which seeks an optimal configuration among $k$ feasible and $m$ target non-empty closed convex sets in $\mathbb{R}^n$. The…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
Global constraints proved themselves to be an efficient tool for modelling and solving large-scale real-life combinatorial problems. They encapsulate a set of binary constraints and using global reasoning about this set they filter the…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
A simple method to generate a two-dimensional binary grid pattern, which allows for absolute and accurate self-location in a finite planar region, is proposed. The pattern encodes position information in a local way so that reading a small…
This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has attracted a lot of attention in recent years, and…
We introduce several modifications of conic fitting in Geometric algebra for conics by incorporating additional conditions into the optimisation problem. Each of these extra conditions ensure additional geometric properties of a fitted…
Recently, unsupervised domain adaptation in satellite pose estimation has gained increasing attention, aiming at alleviating the annotation cost for training deep models. To this end, we propose a self-training framework based on the…
This paper describes a method of global localization based on graph-theoretic association of instances between a query and the prior map. The proposed framework employs correspondence matching based on the maximum clique problem (MCP). The…