We reelaborate on the basic properties of PT symmetry from a geometrical Perspective. The transfer matrix associated with these systems induces a Möbius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.

We present a new perspective of the link between QED and Maxwell's equations. We demonstrate that the interpretation of $\mathbf{D}=\varepsilon_{0} \mathbf{E}$ as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter, runs as it should.

We investigate the behavior of the solutions of the ray equation in isotropic media. We discuss local and global transversals and wavefronts and give examples of rays without wavefronts.

A reduced order model is developed to monitor aeroengines condition (defining their degradation from a baseline state) in real-time, by using data collected in specific sensors. This reduced model is constructed by applying higher order singular value decomposition plus interpolation to appropriate data, organized in tensor form. Such data are obtained using a detailed engine model that takes the engine physics into account. Thus, the method synergically combines the advantages of data-driven (fast online operation) and model-based (the engine physics is accounted for) condition monitoring methods. Using this reduced order model as surrogate of the engine model, two gradient-like condition monitoring tools are constructed. The first tool is extremely fast and able to precisely compute `on the fly’ the turbine inlet temperature, which is a paramount parameter for the engine performance, operation, and maintenance, and can only be roughly estimated by the engine instrumentation in civil aviation. The second tool is not so fast (but still reasonably inexpensive) and precisely computes both, the engine degradation and the turbine inlet temperature at which sensors data have been acquired. These tools are robust in connection with random noise added to the sensors data and can be straight forwardly applied to other mechanical systems.

In industrial environments, nesting consists in cutting or extracting pieces from a material sheet, with the purpose of minimizing the surface of the sheet used. This problem is present in different types of industries, such as shipping, aeronautics, woodworking, footwear, and so on. In this work, the aim is to find an acceptable solution to solve complex nesting problems. The research developed is oriented to sacrifice accuracy for speed so as to obtain robust solutions in less computational time. To achieve this, a greedy method and a genetic algorithm have been implemented, being the latter responsible for generating a sequence for the placement of the pieces, where each piece is placed in its current optimal position with the help of a representation system for both the pieces and the material sheet.

The development of the smart city concept and the inhabitants’ need to reduce travel time, as well as society’s awareness of the reduction of fuel consumption and respect for the environment, lead to a new approach to the classic problem of the Travelling Salesman Problem (TSP) applied to urban environments. This problem can be formulated as “Given a list of geographic points and the distances between each pair of points, what is the shortest possible route that visits each point and returns to the departure point?” Nowadays, with the development of IoT devices and the high sensoring capabilities, a large amount of data and measurements are available, allowing researchers to model accurately the routes to choose. In this work, the purpose is to give solution to the TSP in smart city environments using a modified version of the metaheuristic optimization algorithm TLBO (Teacher Learner Based Optimization). In addition, to improve performance, the solution is implemented using a parallel GPU architecture, specifically a CUDA implementation.

Suicide is a public health problem influenced by a variety of biological, psychological, social, and environmental factors. Recognizing the warning signs at each stage is crucial for prevention and helping those at risk. In this context, body awareness, especially interoceptive body awareness, emerges as a potentially relevant and underexplored factor. In this study, binary logistic regression and linear regression analyses were used to examine the relationship between interoceptive body awareness and suicidal orientation in Colombian university students. In addition, the bootstrap technique was used to resample and estimate the distribution of the data. The results support the idea that greater interoceptive awareness may protect against suicidal orientation by improving emotional regulation. An inverse relationship was found between interoceptive awareness and suicidal ideation. These findings are consistent with previous literature on the importance of body awareness for emotional well-being. Further longitudinal research is needed to explore this relationship in depth.