Browsing by Author "Estevan Muguerza, Asier"
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Publication Open Access An approach to distributed systems from orderings and representability(Springer, 2024) Estevan Muguerza, Asier; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, JIUPNA19-2022In the present paper, we propose a new approach on ‘distributed systems’: the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations met in various fields (such as computer science, economics and decision theory). We investigate questions associated to the numerical representability of order structures, relating concepts of economics and computing to each other. The concept of ‘quasi-finite partial orders’ is introduced as a finite family of chains with a communication between them. The representability of this kind of structure is studied, achieving a construction method for a finite (continuous) Richter–Peleg multi-utility representation.Publication Open Access Aprendizaje práctico del estudio estadístico en 3º de la ESO(2022) Ventura Rípodas, Daniel; Estevan Muguerza, Asier; Facultad de Ciencias Humanas, Sociales y de la Educación; Giza, Gizarte eta Hezkuntza Zientzien FakultateaEste Trabajo Fin de Máster tiene como objetivo estudiar el aprendizaje de un estudio estadístico en estudiantes de 3º ESO orientadas a las enseñanzas académicas. El trabajo se estructura en dos partes. En la primera parte se realiza un estudio longitudinal del currículo y en los libros de texto en el tercer ciclo de Primaria, en ESO y en Bachillerato con relación al tema indicado. En la segunda parte se propone un proceso de estudio sobre el aprendizaje de un estudio estadístico, el cual se ha puesto en marcha en un aula de 3º ESO en el marco del Prácticum II del Máster. Los resultados extraídos de esta experimentación se fundamentan en un estudio estadístico, teniendo en cuenta asimismo las restricciones institucionales. El trabajo concluye con una síntesis, unas conclusiones y unas cuestiones abiertas.Publication Open Access Continuous representations of interval orders by means of two continuous functions(Springer, 2020) Bosi, Gianni; Estevan Muguerza, Asier; Institute for Advanced Materials and Mathematics - INAMAT2In this paper, we provide a characterization of the existence of a representation of an interval order on a topological space in the general case by means of a pair of continuous functions, when neither the functions nor the topological space are required to satisfy any particular assumptions. Such a characterization is based on a suitable continuity assumption of the binary relation, called weak continuity. In this way, we generalize all the previous results on the continuous representability of interval orders, and also of total preorders, as particular cases.Publication Open Access DBHko 1. mailan aljebraren irakaskuntzan Dragon Box 12+ erabiltzeko proposamen didaktikoa(2019) Iriarte Goikoa, Asier; Estevan Muguerza, Asier; Facultad de Ciencias Humanas y Sociales; Giza eta Gizarte Zientzien FakultateaMaster Bukaerako Lan honen helburu nagusia ondoko hau da: DBHko 1. mailan aljebraren irakaskuntzan Dragon Box 12+ jokoa txertatzeko proposamen didaktikoa egitea. Lana bi ataletan antolatu da. Lehenengoan, curriculumaren eta testu-liburuen luzetarako azterketa egiten da Lehen Hezkuntzako hirugarren zikloan, DBHn eta Batxilergoan, zehazturiko gaiaren inguruan. Bigarrenean, aljebrari buruzko ikasketa prozesu bat proposatzen da, eta proposamen hori DBHko 1. ikasmailari dagokion ikasgela batean ezarri da, Masterreko Practicum II irakasgaiaren baitan. Esperimentazio horretatik lortu diren emaitzak ad hoc diseinaturiko galdetegi batean oinarritzen dira, kontuan hartuz, halaber, baldintzapen instituzionalak. Lanaren amaieran, aurkeztu egiten dira sintesia, zenbait ondorio eta erantzun gabe gelditu diren zenbait galdera.Publication Open Access Estudio de ecuaciones y su aplicación en la resolución de problemas por estudiantes de 2º de la ESO(2022) Isla Abadía, Miren Iosune; Estevan Muguerza, Asier; Facultad de Ciencias Humanas, Sociales y de la Educación; Giza, Gizarte eta Hezkuntza Zientzien FakultateaEste Trabajo Fin de Máster tiene como objetivo el análisis de un proceso de estudio de ecuaciones y su aplicación en la resolución de problemas para estudiantes de 2º E.S.O. El trabajo está constituido de dos partes principales. En una primera parte, se realiza un análisis teórico que consiste en un estudio longitudinal del currículo (contenidos, criterios de evaluación y estándares de aprendizaje) y de los libros de texto empleados en dicho proceso de estudio. Para terminar esta parte, se realiza un análisis de la relación existente entre ambos. En la segunda parte del trabajo, se desarrolla un estudio sobre el proceso de aprendizaje del tema tratado de resolución de ecuaciones y su aplicación en la resolución de problemas, en dos grupos de alumnos de 2º E.S.O, llevado a cabo en el centro de estudios Santa Teresa de Jesús en el que se ha realizado el Practicum II. Se comienza realizando un análisis de la unidad didáctica del libro de referencia del centro respecto al tema tratado, así como de las dificultades y errores previsibles que los alumnos van a encontrarse a lo largo del proceso. A continuación, se detalla el proceso llevado a cabo, presentando y analizando los resultados obtenidos en el aula. Finalmente, para concluir, se realiza una síntesis del resultado, se presentan unas conclusiones y una serie de cuestiones abiertas.Publication Open Access Librería en android para medidor de fuerza de dedos para escaladores(2023) Hamuraru, Eugen; Pérez Goya, Unai; Estevan Muguerza, Asier; Escuela Técnica Superior de Ingeniería Industrial, Informática y de Telecomunicación; Industria, Informatika eta Telekomunikazio Ingeniaritzako Goi Mailako Eskola TeknikoaEn el contexto de la escalada, la fuerza y la destreza física son elementos fundamentales que determinan el éxito de los escaladores al enfrentarse a desfiantes rutas y ascensos. La búsqueda constante de mejorar el rendimiento y superar obstáculos ha llevado al desarrollo de diversas herramientas y tecnologías que permiten a los escaladores medir y analizar su fuerza en diferentes situaciones. En este sentido, el presente Trabajo de Fin de Grado (TFG) se centra en la utilización de un dispositivo innovador diseñado para medir con precisión la fuerza ejercida por los dedos de los escaladores para la creación de una aplicación móvil capaz de almacenar, gestionar y mostrar los datos recabados por el dispositivo. Esta herramienta no solo permitirá obtener mediciones objetivas de la fuerza, sino que también capturará y analizará una serie de variables ambientales, como temperatura, humedad y geolocalización, que podrían influir en el rendimiento de los escaladores.Publication Open Access A mathematical approach to law and deal modelling: legislation and agreements(MDPI, 2021) Benito Ostolaza, Juan Miguel; Campión Arrastia, María Jesús; Estevan Muguerza, Asier; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasSocial norms are a set of rules to be followed by the people of a community in order to have a better coexistence, to which the behaviors, tasks, and activities of the human being must be adjusted. The set or system of norms, rules, or duties regulates the actions of individuals among themselves. This work presents a new and original approach to the situations of agreement as well as to the constructions of regulations. This is done by giving a mathematical formalization to the set of all possible agreements or regulations, so that, then, the proximity between them is defined by means of a premetric. Thanks to this mathematical structure that tries to capture the problematic of agreements and modifications of regulations, some currently issues related to game theory or law are now reduced to mathematical optimization problems.Publication Open Access New trends on the numerical representability of semiordered structures(EUSFLAT, 2012) Abrísqueta Usaola, Francisco Javier; Campión Arrastia, María Jesús; García Catalán, Olga Raquel; Miguel Velasco, Juan Ramón de; Estevan Muguerza, Asier; Induráin Eraso, Esteban; Zudaire Sarobe, Margarita; Agud, L.; Candeal, Juan Carlos; Díaz, S.; Martinetti, D.; Montes Rodríguez, Susana; Gutiérrez García, J.; Automática y Computación; Automatika eta KonputazioaWe introduce a survey, including the historical background, on di erent techniques that have recently been issued in the search for a characterization of the representability of semiordered structures, in the sense of Scott and Suppes, by means of a real-valued function and a strictly positive threshold of discrimination.Publication Open Access On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms(Springer, 2019) Estevan Muguerza, Asier; Miñana, Juan José; Valero, Óscar; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasThe celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An affirmative answer to the aforesaid inquiry is provided so that a characterization of those properties that a self-mapping must satisfy in order to guarantee that its set of fixed points is non-empty when no notion of completeness are assumed to be satisfied by the partially ordered set. Moreover, the case in which the partially ordered set is coming from a quasi-metric space is treated in depth. Finally, an application of the exposed theory is obtained. Concretely, a mathematical method to discuss the asymptotic complexity of those algorithms whose running time of computing fulfills a recurrence equation is presented. Moreover, the aforesaid method retrieves the fixed point based methods that appear in the literature for asymptotic complexity analysis of algorithms. However, our new method improves the aforesaid methods because it imposes fewer requirements than those that have been assumed in the literature and, in addition, it allows to state simultaneously upper and lower asymptotic bounds for the running time computing.Publication Open Access Partial representations of orderings(World Scientific, 2018) Bosi, Gianni; Estevan Muguerza, Asier; Zuanon, Magali; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaIn the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner, avoiding any unnecessary information. For this purpose, the new concept of representability is developed by means of partial functions, so that other common definitions of representability (i.e. (Richter-Peleg) multi-utility, Scott-Suppes representability, … ) are now particular cases in which the partial functions are actually functions. The paper also presents a collection of examples and propositions showing the advantages of this kind of representations, particularly in the case of partial orders and semiorders, as well as some results showing the connections between distinct kinds of representations.Publication Open Access Quasi-metrics for possibility results: intergenerational preferences and continuity(MDPI, 2023) Estevan Muguerza, Asier; Maura, Roberto; Valero, Óscar; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa JIUPNA19-2022In this paper, we provide the counterparts of a few celebrated impossibility theorems for continuous social intergenerational preferences according to P. Diamond, L.G. Svensson and T. Sakai. In particular, we give a topology that must be refined for continuous preferences to satisfy anonymity and strong monotonicity. Furthermore, we suggest quasi-pseudo-metrics as an appropriate quantitative tool for reconciling topology and social intergenerational preferences. Thus, we develop a metric-type method which is able to guarantee the possibility counterparts of the aforesaid impossibility theorems and, in addition, it is able to give numerical quantifications of the improvement of welfare. Finally, a refinement of the previous method is presented in such a way that metrics are involved.Publication Open Access Searching for a Debreu’s open gap lemma for semiorders(Springer, 2020) Estevan Muguerza, Asier; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasIn 1956 R. D. Luce introduced the notion of a semiorder to deal with indifference relations in the representation of a preference. During several years the problem of finding a utility function was studied until a representability characterization was found. However, there was almost no results on the continuity of the representation. A similar result to Debreu’s Lemma, but for semiorders was never achieved. In the present paper we propose a characterization for the existence of a continuous representation (in the sense of Scott-Suppes) for bounded semiorders. As a matter of fact, the weaker but more manageable concept of ε-continuity is properly introduced for semiorders. As a consequence of this study, a version of the Debreu’s Open Gap Lemma is presented (but now for the case of semiorders) just as a conjecture, which would allow to remove the open-closed and closed-open gaps of a subset S ⊆ R, but now keeping the constant threshold, so that x + 1 < y if and only if g(x) + 1 < g(y) (x, y ∈ S).Publication Open Access Semiorders and continuous Scott–Suppes representations. Debreu’s Open Gap Lemma with a threshold(Elsevier, 2023) Estevan Muguerza, Asier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, JIUPNA19-2022The problem of finding a utility function for a semiorder has been studied since 1956, when the notion of semiorder was introduced by Luce. But few results on continuity and no result like Debreu’s Open Gap Lemma, but for semiorders, was found. In the present paper, we characterize semiorders that accept a continuous representation (in the sense of Scott–Suppes). Two weaker theorems are also proved, which provide a programmable approach to Open Gap Lemma, yield a Debreu’s Lemma for semiorders, and enable us to remove the open-closed and closed-open gaps of a set of reals while keeping the threshold.Publication Open Access Topologies for semicontinuous Richter–Peleg multi-utilities(Springer, 2020) Bosi, Gianni; Estevan Muguerza, Asier; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y MatemáticasThe present paper gives a topological solution to representability problems related to multi-utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of a semicontinuous and finite Richter–Peleg multi-utility for a preorder are studied. It is well known that, given a preorder on a topological space, if there is a lower (upper) semicontinuous Richter–Peleg multi-utility, then the topology of the space must be finer than the Upper (resp. Lower) topology. However, this condition fails to be sufficient. Instead of search for properties that must be satisfied by the preorder, we study finer topologies which are necessary or/and sufficient for the existence of semicontinuous representations. We prove that Scott topology must be contained in the topology of the space in case there exists a finite lower semicontinuous Richter–Peleg multi-utility. However, the existence of this representation cannot be guaranteed. A sufficient condition is given by means of Alexandroff’s topology, for that, we prove that more order implies less Alexandroff’s topology, as well as the converse. Finally, the paper is implemented with a topological study of the maximal elements.