Art gallery problem with guards whose range of vision is 180

It is shown that in any polygonal art gallery of n sides it is possible to place n/3 point guards whose range of vision is 180° so that every interior point of the gallery can be seen by at least one of them. The guards can be stationed at any point of the art gallery. This settles an open problem posed by J. Urrutia.     

Triangulating and guarding realistic polygons

We propose a new model of realistic input: k-guardable objects. An object is k-guardable if its boundary can be seen by k guards. We show that k-guardable polygons generalize two previously identified classes of realistic input. Following this, we give two simple algorithms for triangulating k-guardable polygons. One algorithm requires the guards as input while the other does not. Both take linear time assuming that k is constant and both are easily implementable.     

Trimethylsulfonium hydroxide as derivatization reagent for the chemical investigation of drying oils in works of art by gas chromatography

A procedure for the determination of fatty acids (FA) and glycerol in oils has been developed. The method includes a derivatization step of the FAs into their methyl esters or a transesterification of the triacylglycerols with trimethylsulfonium hydroxide (TMSH), respectively. The analysis is carried out by gas chromatography with parallel flame ionization and mass spectrometric detection. The parameters involved in the transesterification reaction were optimized. Only the stoichiometric ratio of TMSH:total FA amount showed a significant influence on the reaction yield. Relative standard deviations for 10 replicates were below 3% for all FAs studied and their linearity range was 0.5-50 mmol/L, when using heptadecanoic acid as an internal standard. The final procedure was rapid and required little sample handling. It was then tested on fresh oil samples and presented satisfying results, in agreement with previous works.     

Analysis of post-Byzantine icons from the Church of the Assumption in Cephalonia, Ionian Islands, Greece: a multi-method approach

A multi-method approach has been developed for the characterisation of the proteinaceous binding media, drying oils and pigments present in samples from the panel paintings of the Church of the Assumption in Cephalonia (Ionian Islands, Greece). The analytical protocol involved the use of scanning electron microscopy/energy dispersive X-ray analysis (SEM/EDX), Raman spectroscopy and gas chromatography. The identification of the pigments was achieved by SEM/EDX and Raman spectroscopy. The latter technique was also used for the detection of the binding media, while their characterisation was achieved by gas chromatographic analysis of ethyl chloroformate derivatives. The aim of this multi-method protocol was to obtain as much information as possible from the panel paintings of the Church of the Assumption, through non-destructive methods, before proceeding to gas chromatography. Little scientific information is available for the understanding of the construction technique and the materials used by the post-Byzantine artists and whatever is available comes mainly from artists’ manuals. One of the aims of this paper is to provide a scientific background to the technology of the Ionian post-Byzantine icons.     

Thermal and Raman-spectroscopic analysis of Maya Blue carrying artefacts, especially fragment IV of the Codex Huamantla

Maya Blue, a pigment composed of very low concentrations of natural indigo and the clay mineral palygorskite, is one of the most brilliant blue dyes, intensively used for more than 2000 years in Mesoamerica. It is extremely stable against environmental attacks and was applied by the Indians for inside and outside mural paintings, ceramics, textiles and for colouring their famous codices. In the present paper it was studied as a powder (compared with modern synthetic indigo) and as colour on tissues, a Maya clay head, and fragment IV of the famous Codex Huamantla. Investigations using Raman spectroscopy in the visible and near-infrared range showed a high degree of correspondence among all Maya Blue-carrying samples and a good agreement with synthetic indigo. Additional spectral lines may be explained by a transformation of the planar indigo molecule when binding to the palygorskite lattice. Thermal investigations of the original “amatl” paper of the codex and of recent paper from fig-trees showed a high similarity and thus proved that this tree was chosen for paper making by Mayas, Aztecs and other Indian tribes. This was also true for the codex.     

Move me,astonish me… delight my eyes and brain: The Vienna Integrated Model of top-down and bottom-up processes in Art Perception (VIMAP) and corresponding affective,evaluative, and neurophysiological correlates

This paper has a rather audacious purpose: to present a comprehensive theory explaining, and further providing hypotheses for the empirical study of, the multiple ways by which people respond to art. Despite common agreement that interaction with art can be based on a compelling, and occasionally profound, psychological experience, the nature of these interactions is still under debate. We propose a model, The Vienna Integrated Model of Art Perception (VIMAP), with the goal of resolving the multifarious processes that can occur when we perceive and interact with visual art. Specifically, we focus on the need to integrate bottom-up, artwork-derived processes, which have formed the bulk of previous theoretical and empirical assessments, with top-down mechanisms which can describe how individuals adapt or change within their processing experience, and thus how individuals may come to particularly moving, disturbing, transformative, as well as mundane, results. This is achieved by combining several recent lines of theoretical research into a new integrated approach built around three processing checks, which we argue can be used to systematically delineate the possible outcomes in art experience. We also connect our model's processing stages to specific hypotheses for emotional, evaluative, and physiological factors, and address main topics in psychological aesthetics including provocative reactions—chills, awe, thrills, sublime—and difference between “aesthetic” and “everyday” emotional response. Finally, we take the needed step of connecting stages to functional regions in the brain, as well as broader core networks that may coincide with the proposed cognitive checks, and which taken together can serve as a basis for future empirical and theoretical art research.     

Art gallery theorems for guarded guards

We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in and (ii) every point in is visible to some other point in We prove that a polygon with n sides always has a guarded guard set of cardinality (3n−1)/7 and that this bound is sharp (n5); our result corrects an erroneous formula in the literature. We also use a coloring argument to give an entirely new proof that the corresponding sharp function for orthogonal polygons is n/3 for n6; this result was originally established by induction by Hernández-Peñalver.