Related papers: A disk-covering problem with application in optica…
The $k$-cover of a point cloud $X$ in $\mathbb{R}^{d}$ at radius $r$ is the set of all points within distance $r$ of at least $k$ points of $X$. By varying $r$ and $k$ we obtain a two-parameter filtration known as the multicover…
We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union…
We count orientable small covers over cubes. We also get estimates for $O_n/R_n$, where $O_n$ is the number of orientable small covers and $R_n$ is the number of all small covers over an $n$-cube up to the Davis-Januszkiewicz equivalence.
Astronomical optical interferometers (OI) sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid atmospheric perturbations, the phases of the complex Fourier samples…
Astronomers usually need the highest angular resolution possible, but the blurring effect of diffraction imposes a fundamental limit on the image quality from any single telescope. Interferometry allows light collected at widely-separated…
We describe the use of partially overlapping galaxies to provide direct measurements of the effective absorption in galaxy disks, independent of assumptions about internal disk structure. The non-overlapping parts of the galaxies and…
We study a geometric facility location problem under imprecision. Given $n$ unit intervals in the real line, each with one of $k$ colors, the goal is to place one point in each interval such that the resulting \emph{minimum color-spanning…
Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, can be mapped into a non-uniformly illuminated exit pupil, such that the image formed from this pupil will have suppressed sidelobes, many…
The propagation of errors through the uniform disk visibility function is examined. Implications of those errors upon measures of absolute visibility through optical and near-infrared interferometers are considered within the context of…
The direct imaging and characterization of Earth-like planets is among the most sought-after prizes in contemporary astrophysics, however current optical instrumentation delivers insufficient dynamic range to overcome the vast contrast…
Nulling interferometry is a technique providing high angular resolution which is the core of the space missions Darwin and the Terrestrail Planet Finder. The first objective is to reach a deep degree of starlight cancelation in the range 6…
Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of…
In this article, we consider colorable variations of the Unit Disk Cover ({\it UDC}) problem as follows. {\it $k$-Colorable Discrete Unit Disk Cover ({\it $k$-CDUDC})}: Given a set $P$ of $n$ points, and a set $D$ of $m$ unit disks (of…
In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, compact, and totally separable packings. We discuss shortest…
Optical long baseline interferometry was recently established as a technique capable of resolving stars and their circumstellar environments at the milliarcsecond (mas) resolution level. This high-resolution opens an entire new window to…
Our goal is to study the physical properties of the circumstellar environment of young stellar objetcs (YSOs). In particular, the determination of the scattering mechanism can help to constrain the optical depth of the disk and/or envelope…
In this paper, we consider a facility location problem to find a minimum-sum coverage of n points by disks centered at a fixed line. The cost of a disk with radius r has a form of a non-decreasing function f(r) = r^a for any a >= 1. The…
Although there has yet been no undisputed discovery of a still-forming planet embedded in a gaseous protoplanetary disk, the cleared inner holes of transitional disks may be signposts of young planets. Here we show that the subset of…
We are interested in the following problem of covering the plane by a sequence of congruent circular disks with a constraint on the distance between consecutive disks. Let $(\mathcal{D}_n)_{n \in \mathbb N}$ be a sequence of closed unit…
We consider the problem of covering the boundary of a simple polygon on n vertices using the minimum number of geodesic unit disks. We present an O(n \log^2 n+k) time 2-approximation algorithm for finding the centers of the disks, with k…