Related papers: Global Positioning on Earth
Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lema\^{\i}tre (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (``open'') FL universe is {\em…
Worldwide geolocalization aims to locate the precise location at the coordinate level of photos taken anywhere on the Earth. It is very challenging due to 1) the difficulty of capturing subtle location-aware visual semantics, and 2) the…
Private space companies are increasingly commercializing near-earth space. Some estimates show that more than 100,000 satellites may orbit the Earth by 2030. This increase in the number of satellites has many consequences for science,…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
In the Euclidean plane ${\bf{E}}^2$, fix four pairwise distinct points \begin{equation*} \label{eqA} \begin{array}{ccc} A=(a_1,a_2),\ B=(b_1,b_2),\ C=(c_1,c_2),\ D=(d_1,d_2), \end{array} \end{equation*} together with four non-zero real…
We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time,we…
We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a line segment, a…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat…
Motivated by secure wireless networking, we consider the problem of placing fixed localizers that enable mobile communication devices to prove they belong to a secure region that is defined by the interior of a polygon. Each localizer views…
The general position problem is to find the cardinality of a largest vertex subset S such that no triple of vertices of S lie on a common geodesic. For a connected graph G, the cardinality of S is denoted by gp(G) and called gp-number (or…
We consider the sound ranging problem, which is to find the position of the source-point from the moments when the wave-sphere of linearly, with time, increasing radius reaches the sensor-points, in the infinite-dimensional separable…
This paper is concerned with parabolic gradient systems of the form \[ u_t=-\nabla V (u) + \mathcal{D} u_{xx}\,, \] where the spatial domain is the whole real line, the state variable $u$ is multidimensional, $\mathcal{D}$ denotes a fixed…
Offering space-based Internet services with mega-constellations of low Earth orbit (LEO) satellites is a promising solution to connecting the unconnected. It can complement the coverage of terrestrial networks to help bridge the digital…
We suggest that a satellite with a stable atomic clock on board be sent through the Earth-Sun gravitational saddle point to experimentally determine whether Nature prefers static solutions of the field equations of General Relativity, such…
Mobile devices equipped with a multi-camera system and an inertial measurement unit (IMU) are widely used nowadays, such as self-driving cars. The task of relative pose estimation using visual and inertial information has important…
For dealing with the equal sphere packing problem, we propose a serial symmetrical relocation algorithm, which is effective in terms of the quality of the numerical results. We have densely packed up to 200 equal spheres in spherical…
Small satellites have proven to be viable Earth observation platforms. These satellites operate in regimes of increased trajectory uncertainty where traditional planning approaches can lead to sub-optimal task plans, limiting science…
We propose a search for sources of directed energy systems such as those now becoming technologically feasible on Earth. Recent advances in our own abilities allow us to foresee our own capability that will radically change our ability to…
Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…