Macroscale multimodal imaging reveals ancient painting production technology and the vogue in Greco-Roman Egypt.

Macroscale multimodal chemical imaging combining hyperspectral diffuse reflectance (400-2500 nm), luminescence (400-1000 nm), and X-ray fluorescence (XRF, 2 to 25 keV) data, is uniquely equipped for noninvasive characterization of heterogeneous complex systems such as paintings. Here we present the first application of multimodal chemical imaging to analyze the production technology of an 1,800-year-old painting and one of the oldest surviving encaustic ("burned in") paintings in the world. Co-registration of the data cubes from these three hyperspectral imaging modalities enabled the comparison of reflectance, luminescence, and XRF spectra at each pixel in the image for the entire painting. By comparing the molecular and elemental spectral signatures at each pixel, this fusion of the data allowed for a more thorough identification and mapping of the painting's constituent organic and inorganic materials, revealing key information on the selection of raw materials, production sequence and the fashion aesthetics and chemical arts practiced in Egypt in the second century AD

Covering the Boundary of a Simple Polygon with Geodesic Unit Disks

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 denoting the number centers found by the algorithm

How to Guard an Art Gallery: A Simple Mathematical Problem

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph theory. Furthermore, the Art Gallery Theorem and its proof have many extensions, leading to other related theorems on guarding galleries, as well as various applications, including the use of its methods in robotics and GPS. This paper serves as a cursory introduction to the theorem, its most commonly referenced proof, and these extensions and applications, particularly for those with little familiarity with visibility problems or mathematics in general

Ozone and the deterioration of works of art

Seventeen artists' watercolor pigment samples and two Japanese woodblock prints were exposed to 0.40 ppm ozone in a controlled test chamber for three months. It was found that several artists' pigments when applied on paper will fade in the absence of light if exposed to an atmosphere containing ozone at the concentrations found in photochemical smog. Alizarin-based watercolors containing 1,2 dihydroxyanthraquinone lake pigments were shown to be particularly sensitive to ozone damage, as were the yellow pigments used in the Japanese woodblock prints tested. Indoor-outdoor ozone monitoring in a Pasadena, CA art gallery confirmed that ozone concentrations half as high as those outdoors can be found in art galleries that lack a chemically protected air conditioning system. Care should be taken to protect works of art from damage due to photochemical smog

Designing Efficient Algorithms for Sensor Placement

Sensor placement has many applications and uses that can be seen everywhere you go.These include, but not limited to, monitoring the structural health of buildings and bridgesand navigating Unmanned Aerial Vehicles(UAV).We study ways that leads to efficient algorithms that will place as few as possible sen-sors to cover an entire area. We will tackle the problem from both 2-dimensional and3-dimensional points of view. Two famous related problems are discussed: the art galleryproblem and the terrain guarding problem. From the top view an area presents a 2-D im-age which will enable us to partition polygonal shapes and use graph theoretical results incoloring. We explore this approach in details and discuss potential generalizations. Wewill also look at the area from a side view and use methods from the terrain guarding prob-lem to determine where any more sensors should be placed. We provide a simple greedyalgorithm for this.Lastly, we briefly discuss the combination of the above techniques and potential furthergeneralizations to suit specific problems where the limitation of sensors (such as range andangle) are taken into consideration