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The author recently designed, developed and implemented in Maple a package based on the use of digraphs that analyses the connectivity of an overtaking station on a double-track line. It was used to propose an alternative track layout for this kind of station, with advantages over the track layouts usually adopted. However, that package could only deal with "standard" turnouts (but neither with crossings nor with "special" turnouts, such as "single slip turnouts" or "scissors crossings"). This new article presents an improved version of the package. It uses a trick consisting in including virtual vertices in the associated digraph that are dead ends. This way it is possible to include the "special" turnouts in the track layout. It makes it possible to evaluate different alternative track layouts, including "special" turnouts; and to finally find one track layout that has advantages over the standard one and over the one proposed in the previous article. Let us observe that the design of the track layout is key for the exploitation of the infrastructure. In fact, the Spanish infrastructure administrator is nowadays remodelling the track layout of some of its main railway stations, as well as other smaller facilities. [ABSTRACT FROM AUTHOR]

Proper diagnosis and management of equine cardiac diseases require a broad experience and a specialization in the field, but acquisition of specific knowledge is difficult, due, among other reasons, to the limited literature in this field. Therefore, we have designed, developed, and implemented (on a computer algebra system) a Decision Support System (DSS) for equine cardiovascular diseases diagnosis and management based on clinical practise. At this step it is appropriate for equine science teaching, but this work paves the way for a clinical decision support system that facilitated equine clinicians the management of horses with cardiac diseases, allowing improving health care in this species. The latter would require extensive testing prior to its use. The novelty of this work relies on the organization of the equine cardiology workflow in mathematical logic form, that allowed designing, develop and implement a DSS in this new field. An innovation of this work is the part of the DSS devoted to data completion (motivated by the possible lack of specialization of the users—the veterinarians). [ABSTRACT FROM AUTHOR]

This work integrates the Kenzo system within Sagemath as an interface and an optional package. Our work makes it possible to communicate both computer algebra programs and it enhances the SageMath system with new capabilities in algebraic topology, such as the computation of homotopy groups and some kind of spectral sequences, dealing in particular with simplicial objects of an infinite nature. The new interface allows computing homotopy groups that were not known before. [ABSTRACT FROM AUTHOR]

With the particular interest of being implemented in cryptography, the recognition and analysis of image patterns based on Latin squares has recently arisen as an efficient new approach for classifying partial Latin squares into isomorphism classes. This paper shows how the use of a Computer Algebra System (CAS) becomes necessary to delve into this aspect. Thus, the recognition and analysis of image patterns based on these combinatorial structures benefits from the use of computational algebraic geometry to determine whether two given partial Latin squares describe the same affine algebraic set. This paper delves into this topic by focusing on the use of a CAS to characterize when two partial Latin squares are either partial transpose or partial isotopic. [ABSTRACT FROM AUTHOR]

The electric system scenario has been changing during the last years moving to a distributed system with a high penetration of renewables. Due to the unpredictable behavior of some renewables sources, the development of the energy management system is considered crucial to guarantee the reliability and stability of the system. At the same time, increasing the lifespan of the energy storage system is one of the most important points to take into account. In this sense, a software package implemented in the computer algebra system Maple is proposed in this work to control a grid-connected nanogrid with hybrid energy storage system (composed by batteries and supercapacitors). The energy management system considers several rules as the state of charge of the energy storage system, the photovoltaic power generation and the load profile, the nanogrid power trend and the energy prices. The improved performance of the nanogrid is proven by simulations in MATLAB/Simulink. [ABSTRACT FROM AUTHOR]

In the paradigm of Knowledge-Based Systems (KBS), the design of methods to simplify the reasoning leads to more efficient processes. A point of view that provides valuable insights is the algebraic one. In this work, a notion of basis (and dimension) for Knowledge Bases in Propositional Logic associated with knowledge forgetting is introduced. It is based on ideas that come from the translation of such logic in (Computer) Algebra, particularly from the interpretation of variable forgetting. In this paper, the concept of weak base is defined as a set of variables sufficient to decide the consistency using variable forgetting. Several applications of weak bases are presented in order to show their usefulness in KBS reasoning and to justify their study and use in solving problems within this topic. [ABSTRACT FROM AUTHOR]

Tennis is a sport with a very complex technique. Amateur tennis players have trainers and/or coaches, but are not usually accompanied by them to championships. Curiously, in this sport, the result of many matches can be changed by a small hint like 'hit the ball a little higher when serving'. However, the biomechanical of a tennis stroke is only clear to an expert. We, therefore, developed a prototype of a rule-based expert system (RBES) aimed at an amateur competition player that is not accompanied by his/her coach to a championship and is not serving as usual (the RBES is so far restricted to serving). The player has to answer a set of questions about how he/she is serving that day and his/her usual serving technique and the RBES obtains a diagnosis using logic inference about the possible reasons (according of the logic rules that have been previously given to the RBES). A certain knowledge of the tennis terminology and technique is required from the player, but that is something known at this level. The underlying logic is Boolean and the inference engine is algebraic (it uses Groebner bases). [ABSTRACT FROM AUTHOR]