Related papers: The cocked hat
We investigate the Vision-and-Language Navigation (VLN) problem in the context of autonomous driving in outdoor settings. We solve the problem by explicitly grounding the navigable regions corresponding to the textual command. At each…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
The article presents the detailed analysis of the watch paradox. It is shown that it arose because of unjustified, as it turned out, identification of watch readings at the moment of its return with the time read by it.
In this paper we prove that the Cauchy problem of the Muskat equation is wellposed locally in time for any initial data in $\dot C^1(\mathbb{R}^d)\cap L^2(\mathbb{R}^d)$.
We present 35 open problems on combinatorial, geometric and algebraic aspects of k-orbit abstract polytopes. We also present a theory of rooted polytopes that has appeared implicitly in previous work but has not been formalized before.
It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case we present a scheme of analysis that…
"Embodied visual navigation" problem requires an agent to navigate in a 3D environment mainly rely on its first-person observation. This problem has attracted rising attention in recent years due to its wide application in autonomous…
Proving local well-posedness for quasilinear problems in pde's presents a number of difficulties, some of which are universal and others of which are more problem specific. While a common standard, going back to Hadamard, has existed for a…
The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…
Sudoku is a popular combinatorial puzzle. A new method of solving Sudoku is presented, which involves formulating a puzzle as a special type of transportation problem. This model allows one to solve puzzles with more than one solution,…
We discuss recent progress in understanding the issues essential to the development of better cone jet algorithms.
Connected and autonomous vehicles (CAVs) can reduce human errors in traffic accidents, increase road efficiency, and execute various tasks ranging from delivery to smart city surveillance. Reaping these benefits requires CAVs to…
Let $M$ be a 3-manifold. Every knotted (embedded) surface in $M \times \R$ can be moved via an ambient isotopy in such a way that its projection into $M$ is a generic surface. A surface is generic if every point on it is either a regular,…
For a simple one dimensional lattice version of a travelling wave equation, we obtain an exact relation between the initial condition and the position of the front at any later time. This exact relation takes the form of an inverse problem:…
Navigation research is attracting renewed interest with the advent of learning-based methods. However, this new line of work is largely disconnected from well-established classic navigation approaches. In this paper, we take a step towards…
We cautiously reanalyze some easily confused notions on particle horizon problem in this paper and then we give a new answer to the particle horizon problem. This answer is independent of physics plunging into Planck time.
Twenty years ago, in an article titled "Covariance and contravariance: conflict without a cause", I argued that covariant and contravariant specialization of method parameters in object-oriented programming had different purposes and…
The arc-routing problems are known to be notoriously hard. We study here a natural arc-routing problem on trees and more generally on bounded tree-width graphs and surprisingly show that it can be solved in a polynomial time. This implies a…
We introduce the warping matrix which is a new description of oriented knots from a viewpoint of warping degree.
Nearly all spatial reasoning problems involve uncertainty of one sort or another. Uncertainty arises due to the inaccuracies of sensors used in measuring distances and angles. We refer to this as directional uncertainty. Uncertainty also…