Related papers: A Lighthouse Illumination Problem
Spiral Galaxies is a pencil-and-paper puzzle played on a grid of unit squares: given a set of points called centers, the goal is to partition the grid into polyominoes such that each polyomino contains exactly one center and is 180{\deg}…
In a recent investigation, the initial value problem of light propagation in the gravitational field of a body at rest with monopole and quadrupole structure has been determined in the second post-Newtonian (2PN) approximation. In reality,…
Visible light positioning (VLP) is an accurate indoor positioning technology that uses luminaires as transmitters. In particular, circular luminaires are a common source type for VLP, that are typically treated only as point sources for…
Gravitational lensing deflects light. A single lens deflector can only shear images, but cannot induce rotations. Multiple lens planes can induce rotations. Such rotations can be observed in quadruply imaged sources, and can be used to…
Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio of circles, but some configurations have fewer than eight…
Let $C_1, \dots, C_n$ denote the $1/n-$neighborhood of $n$ great circles on $\mathbb{S}^2$. We are interested in how much these areas have to overlap and prove the sharp bounds $$ \sum_{i, j = 1 \atop i \neq j}^{n}{|C_i \cap C_j|^s}…
We present a systematic search for potential dark matter clumps in our Galaxy among the 630 unassociated sources included in the LAT 1-year Point Source Catalog. Assuming a dark matter particle that generates observable gamma-ray photons…
We investigate the shadow of an exact black hole solution of Einstein's equations recently proposed by Cardoso et al., to describe a supermassive black hole immersed in a dark matter halo. We analyze and discuss the light rings and the…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…
The concept of illumination bodies studied in convex geometry is used to amend the halfspace depth for multivariate data. The proposed notion of illumination enables finer resolution of the sample points, naturally breaks ties in the…
We propose a general theoretical scheme for the investigation of light emitted from nano- and micrometric structures of arbitrary shape and composition. More specifically, the proposed fully three-dimensional approach allows to derive the…
Generically, a laser is composed of an optical resonator coupled to a gain medium. If the light amplification via stimulated emission dominates the mirror losses, the emitted light is coherent. Recent studies have shown that sub-wavelength…
Lights Out is a game played on a graph $G$ where every vertex has a light bulb that is either on or off, and pressing a vertex $v$ toggles the state of every vertex in the closed neighborhood of $v$. The goal is to find a subset of vertices…
{\it Chandra} Galactic Center Survey detected $\sim 800$ X-ray point-like sources in the $2^{\circ} \times 0.8^{\circ}$ sky region around the Galactic Center. In this paper, we study the spatial and luminosity distributions of these sources…
In the past years a wealth of observations has unraveled the structural properties of the Dark and Luminous mass distribution in spirals. These have pointed out to an intriguing scenario not easily explained by present theories of galaxy…
We consider the classical problem of making mobile processes gather or converge at a same position (as performed by swarms of animals in Nature). Existing works assume that each process can see all other processes, or all processes within a…
The origin of light is a unsolved mystery in nature. Recently, it was suggested that light may originate from a new kind of order - quantum order. To test this idea in experiments, we study systems of screened magnetic/electric dipoles in…
The blocking number of a manifold is the minimal number of points needed to block out lights between any two given points in the manifold. It has been conjectured that if the blocking number of a manifold is finite, then the manifold must…
We present the first results from our HST Brightest Cluster Galaxy (BCG) survey of seven central supergiant cluster galaxies and their globular cluster (GC) systems. We measure a total of 48000 GCs in all seven galaxies, representing the…
We carried out a systematic search for new star clusters in a field of 5$^{\circ} \times5^{\circ}$ centred close to the Galactic Nucleus using the infrared JHK$_s$ 2MASS Survey archive. In addition we searched for embedded clusters in the…