Sculpted Muqarnas: The Five Capitals in the Alhambra as a Case Study for the Proportions of Western Profiles

In the Alhambra of the Nasrid era (1230–1492), a transformed type of capital emerged that incorporated muqarnas to materialize the transition from the column to the abacus. Although the Alhambra contains the most muqarnas compositions from the Occident (Iberian Peninsula), the present understanding of “Western” muqarnas is based upon two carpentry manuscripts from the 1630s, from different authors on each side of the Atlantic (López de Arenas and Fray Andrés de San Miguel). In this research, the proportions of the muqarnas profiles from each manuscript are studied and compared to each other to articulate the formal consequences of their differences. By sculpting four examples of muqarnas capitals in the Alhambra, this study assesses whether the results correspond to the information provided in the manuscripts. The particularities that arise from these simple muqarnas capitals shed light on the proportions of the Alhambra muqarnas, generate new profiles that are distinct from those of the manuscripts, and establish geometrical relationships that have hitherto been unclear. These observations offer a basis for future tests on other muqarnas compositions in Nasrid palaces, therefore advancing the definition of the formal language of the Alhambra muqarnas.

Geometrical Interpretation of Isomers

The present article considers isomerism, which is one of the most important topics of chemistry. A model is proposed in 2D and 3D-Euclidean geometry starting from the very fundamental concepts and has established certain geometrical relationships between the mass of a molecule and its bonds and atoms. Some crucial angles are defined. Certain mathematical analysis have been presented as well.

Active Virtual Impedance Control for Sound-Following Robots to Avoid Obstacles

A novel active virtual impedance algorithm is here proposed to help sound-following robots avoid obstacles while tracking a sound source. The tracking velocity of a mobile robot to a sound source is determined by virtual repulsive and attraction forces to avoid obstacles and to follow the sound source, respectively. Active virtual impedance is defined as a function of distances and relative velocities to the sound source and obstacles from the mobile robot, which is used to generate the tracking velocity of the mobile robot. Conventional virtual impedance methods have fixed coefficients for relative distances and velocities. However, in this research, the coefficients are dynamically adjusted to extend the obstacle avoidance performance to multiple obstacle environments. The relative distances and velocities are obtained using a microphone array consisting of three microphones in a row. The geometrical relationships of the microphones are utilized to estimate the relative position and orientation of the sound source with respect to the mobile robot, which carries the microphone array. The effectiveness of the proposed algorithm is demonstrated by experiments.

The operational concepts in the Vitruvian system of design

The study aims to contribute to understand the Vitruvian design system through the analysis of the temples described in the text leading to the three key concepts related: proportio, commensus and commodulatio. At first, it is proposed a conceptual discussion about the origin of the compositional elements, and further it is discussed the concept of proportio as an operation of sizing and scaling these elements individually. Analyzed the definition and types of elements, it is proposed to continue the discussion on the relationship that must be built as a way of associating elements in a consistent way, leading to the notion of symmetria, understood as an ideal state in which the elements maintain dimensional and/or geometrical relationships between them, creating a relational harmony. From the operational point of view, it is sought to demonstrate that the Vitruvian symmetria is fetched from two types of relations: a modular (commodulatio) and a dimensional (commensus).

Computational Assessment of Facial Expression Production in ASD Children

In this paper, a computational approach is proposed and put into practice to assess the capability of children having had diagnosed Autism Spectrum Disorders (ASD) to produce facial expressions. The proposed approach is based on computer vision components working on sequence of images acquired by an off-the-shelf camera in unconstrained conditions. Action unit intensities are estimated by analyzing local appearance and then both temporal and geometrical relationships, learned by Convolutional Neural Networks, are exploited to regularize gathered estimates. To cope with stereotyped movements and to highlight even subtle voluntary movements of facial muscles, a personalized and contextual statistical modeling of non-emotional face is formulated and used as a reference. Experimental results demonstrate how the proposed pipeline can improve the analysis of facial expressions produced by ASD children. A comparison of system’s outputs with the evaluations performed by psychologists, on the same group of ASD children, makes evident how the performed quantitative analysis of children’s abilities helps to go beyond the traditional qualitative ASD assessment/diagnosis protocols, whose outcomes are affected by human limitations in observing and understanding multi-cues behaviors such as facial expressions.

N1 component of event-related potential evoked by simple composite figures in the lateral occipital cortex

Since Sugawara and Morotomi (1991) first reported that illusory contour (IC) figures, or Kanizsa square inducers (KSI), evoked a significant N1 component, the first visually evoked negative component of event-related potentials (ERPs), in the lateral occipital cortex (LO), many ERP studies have confirmed their finding, and these studies showed that Kanizsa-type inducers alone evoked a relatively large N1 in the LO, even when the inducers are oriented to not form an IC (see Murray and Herrmann, 2013). In the present study, we used non-IC simple composite figures composed of several elementary shapes (e.g., triplet squares or quadruplet circles) as visual stimuli, and found that the composite figures evoked a significant N1 comparable to that evoked by KSI in the anterior LO, whereas solitary elementary shapes did not. Thus, it appears that the LO is activated by not only an IC but also the compositeness of figures, which implies that the LO might analyze the geometrical relationships among multiple 2D shapes that compose a single composite figure.

Classical Measurement Methods and Laser Scanning Usage in Shaft Hoist Assembly Inventory

The shaft hoist assembly is the base of underground mining plant. Its efficiency and correct operation is subject to restrictive legal regulations and is controlled on a daily visual assessment by shaft crew and energomechanics. In addition, in the regular interval, the shaft hoist assembly is subject to a thorough inventory, which includes the determination of the geometrical relationships between the hoisting machine, the headframe and the shaft with its housing. Inventory measurements for shaft and headframe are used for years of conventional geodetic methods including mechanical or laser plumbing and tachymetric surveys. Additional precision levelling is also used for measuring shafts of hoisting machines and rope pulleys. Continuous modernization of measuring technology makes it possible to implement the further methods to the above mentioned purposes. The comparison of the accuracy and the economics of performing measurements based on many years of experience with comprehensive inventory of shaft hoist assembly using various research techniques was made and detailed in the article.

MINERALOGICAL, PETROGRAPHIC AND STABLE ISOTOPIC STUDY OF ANCIENT WHITE MARBLE QUARRIES IN THESSALY, GREECE - II. CHASANBALI, TEMPI, ATRAX, TISAION MOUNTAIN

The present study focuses on the identification of marble sources from four ancient quarries in Thessaly, including Atrax, Tempi, Chasanbali and Tisaion and aims in characterizing the variations of the mineralogical and petrographic features, and the stable isotope ratios (δ13C and δ18O). The results provide additional data and complete the databases presented in previous works from Kastri, Kalochorion and Gonnoi. Microscopy was employed both to evidence the geometrical relationships among the mineral constituents, with particular reference to calcite, and to detect the accessory grains. The studied marbles demonstrate various textures, whereas the maximum grain size of calcites has been used to discriminate the marbles. The geometric relationships of carbonate grains, such as the grain boundary shape, were also evaluated. According to the stable isotope compositions, most of the samples plot in the same area, although some groupings are observed.