Dpto. Estadística, Informática y Matemáticas - Estatistika, Informatika eta Matematika Saila [desde mayo 2018 / 2018ko maiatzetik]

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Open Access
The impact of exact probabilistic learning algorithms in EDAs based on bayesian networks
(Springer, 2008) Echegoyen Arruti, Carlos; Santana, Roberto; Lozano, José Antonio; Larrañaga, Pedro; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
This paper discusses exact learning of Bayesian networks in estimation of distribution algorithms. The estimation of Bayesian network algorithm (EBNA) is used to analyze the impact of learning the optimal (exact) structure in the search. By applying recently introduced methods that allow learning optimal Bayesian networks, we investigate two important issues in EDAs. First, we analyze the question of whether learning more accurate (exact) models of the dependencies implies a better performance of EDAs. Secondly, we are able to study the way in which the problem structure is translated into the probabilistic model when exact learning is accomplished. The results obtained reveal that the quality of the problem information captured by the probability model can improve when the accuracy of the learning algorithm employed is increased. However, improvements in model accuracy do not always imply a more efficient search.
Open Access
Analyzing the k most probable solutions in EDAs based on bayesian networks
(Springer, 2010) Echegoyen Arruti, Carlos; Mendiburu, Alexander; Santana, Roberto; Lozano, José Antonio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Estimation of distribution algorithms (EDAs) have been successfully applied to a wide variety of problems but, for themost complex approaches, there is no clear understanding of the way these algorithms complete the search. For that reason, in this work we exploit the probabilistic models that EDAs based on Bayesian networks are able to learn in order to provide new information about their behavior. Particularly, we analyze the k solutions with the highest probability in the distributions estimated during the search. In order to study the relationship between the probabilistic model and the fitness function, we focus on calculating, for the k most probable solutions (MPSs), the probability values, the function values and the correlation between both sets of values at each step of the algorithm. Furthermore, the objective functions of the k MPSs are contrasted with the k best individuals in the population. We complete the analysis by calculating the position of the optimum in the k MPSs during the search and the genotypic diversity of these solutions. We carry out the analysis by optimizing functions of different natures such as Trap5, two variants of Ising spin glass and Max-SAT. The results not only show information about the relationship between the probabilistic model and the fitness function, but also allow us to observe characteristics of the search space, the quality of the setup of the parameters and even distinguish between successful and unsuccessful runs.
Open Access
Mateda-2.0: estimation of distribution algorithms in MATLAB
(Foundation for Open Access Statistics, 2010-07-26) Larrañaga, Pedro; Santana, Roberto; Bielza, Concha; Lozano, José Antonio; Echegoyen Arruti, Carlos; Mendiburu, Alexander; Armañanzas, Rubén; Shakya, Siddartha; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
This paper describes Mateda-2.0, a MATLAB package for estimation of distribution algorithms (EDAs). This package can be used to solve single and multi-objective discrete and continuous optimization problems using EDAs based on undirected and directed probabilistic graphical models. The implementation contains several methods commonly employed by EDAs. It is also conceived as an open package to allow users to incorporate different combinations of selection, learning, sampling, and local search procedures. Additionally, it includes methods to extract, process and visualize the structures learned by the probabilistic models. This way, it can unveil previously unknown information about the optimization problem domain. Mateda-2.0 also incorporates a module for creating and validating function models based on the probabilistic models learned by EDAs.
Open Access
On the limits of effectiveness in estimation of distribution algorithms
(IEEE, 2011) Echegoyen Arruti, Carlos; Zhang, Qingfu; Mendiburu, Alexander; Santana, Roberto; Lozano, José Antonio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Which problems a search algorithm can effectively solve is a fundamental issue that plays a key role in understanding and developing algorithms. In order to study the ability limit of estimation of distribution algorithms (EDAs), this paper experimentally tests three different EDA implementations on a sequence of additively decomposable functions (ADFs) with an increasing number of interactions among binary variables. The results show that the ability of EDAs to solve problems could be lost immediately when the degree of variable interaction is larger than a threshold. We argue that this phase-transition phenomenon is closely related with the computational restrictions imposed in the learning step of this type of algorithms. Moreover, we demonstrate how the use of unrestricted Bayesian networks rapidly becomes inefficient as the number of sub-functions in an ADF increases. The study conducted in this paper is useful in order to identify patterns of behavior in EDAs and, thus, improve their performances.
Open Access
Toward understanding EDAs based on bayesian networks through a quantitative analysis
(IEEE, 2011-06-28) Echegoyen Arruti, Carlos; Mendiburu, Alexander; Santana, Roberto; Lozano, José Antonio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The successful application of estimation of distribution algorithms (EDAs) to solve different kinds of problems has reinforced their candidature as promising black-box optimization tools. However, their internal behavior is still not completely understood and therefore it is necessary to work in this direction in order to advance their development. This paper presents a methodology of analysis which provides new information about the behavior of EDAs by quantitatively analyzing the probabilistic models learned during the search. We particularly focus on calculating the probabilities of the optimal solutions, the most probable solution given by the model and the best individual of the population at each step of the algorithm. We carry out the analysis by optimizing functions of different nature such as Trap5, two variants of Ising spin glass and Max-SAT. By using different structures in the probabilistic models, we also analyze the impact of the structural model accuracy in the quantitative behavior of EDAs. In addition, the objective function values of our analyzed key solutions are contrasted with their probability values in order to study the connection between function and probabilistic models. The results not only show information about the internal behavior of EDAs, but also about the quality of the optimization process and setup of the parameters, the relationship between the probabilistic model and the fitness function, and even about the problem itself. Furthermore, the results allow us to discover common patterns of behavior in EDAs and propose new ideas in the development of this type of algorithms.
Open Access
Avatarians: playing with your friends' data
(Association for Computing Machinery, 2012) Marzo Pérez, Asier; Ardaiz Villanueva, Óscar; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Gobierno de Navarra / Nafarroako Gobernua
This article describes a new game mechanic called Game Entity Social Mapping (GESM) based on using social networking data fetched from a remote site about the player and his contacts to create characters, items or scenarios. A preliminary evaluation consisting of applying this mechanic to three different games was conducted. A small number of users tested those games to measure the enjoyment and learning about their contacts information.
Open Access
On the taxonomy of optimization problems under estimation of distribution algorithms
(MIT Press Journals, 2013-09-13) Echegoyen Arruti, Carlos; Mendiburu, Alexander; Santana, Roberto; Lozano, José Antonio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Understanding the relationship between a search algorithm and the space of problems is a fundamental issue in the optimization field. In this paper, we lay the foundations to elaborate taxonomies of problems under estimation of distribution algorithms (EDAs). By using an infinite population model and assuming that the selection operator is based on the rank of the solutions, we group optimization problems according to the behavior of the EDA. Throughout the definition of an equivalence relation between functions it is possible to partition the space of problems in equivalence classes in which the algorithm has the same behavior. We show that only the probabilistic model is able to generate different partitions of the set of possible problems and hence, it predetermines the number of different behaviors that the algorithm can exhibit. As a natural consequence of our definitions, all the objective functions are in the same equivalence class when the algorithm does not impose restrictions to the probabilistic model. The taxonomy of problems, which is also valid for finite populations, is studied in depth for a simple EDA that considers independence among the variables of the problem. We provide the sufficient and necessary condition to decide the equivalence between functions and then we develop the operators to describe and count the members of a class. In addition, we show the intrinsic relation between univariate EDAs and the neighborhood system induced by the Hamming distance by proving that all the functions in the same class have the same number of local optima and that they are in the same ranking positions. Finally, we carry out numerical simulations in order to analyze the different behaviors that the algorithm can exhibit for the functions defined over the search space {0,1}^3
Open Access
Significados conflictivos de ecuación y función en estudiantes de profesorado de secundaria
(Universidad de Salamanca, 2014) Wilhelmi, Miguel R.; Godino, Juan D.; Lasa Oyarbide, Aitzol; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
En el marco de una acción formativa sobre reconocimiento de las características del razonamiento algebraico elemental con estudiantes del máster de secundaria, especialidad matemáticas, se detecta que las nociones de función y ecuación interfieren la una en la otra. Así, en situaciones elementales en las que es preciso movilizar una función, identificando las variables independiente, dependiente y regla de correspondencia, los estudiantes interpretan la situación en términos de incógnitas y ecuaciones. Se describen algunas respuestas prototípicas de este fenómeno, el contexto y metodología de la investigación, así como algunas implicaciones para la formación de profesores.
Open Access
Comprehensive characterization of the behaviors of estimation of distribution algorithms
(Elsevier, 2015-04-20) Echegoyen Arruti, Carlos; Santana, Roberto; Mendiburu, Alexander; Lozano, José Antonio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Estimation of distribution algorithms (EDAs) are a successful example of how to use machine learning techniques for designing robust and efficient heuristic search algorithms. Understanding the relationship between EDAs and the space of optimization problems is a fundamental issue for the successful application of this type of algorithms. A step forward in this matter is to create a taxonomy of optimization problems according to the different behaviors that an EDA can exhibit. This paper substantially extends previous work in the proposal of a taxonomy of problems for univariate EDAs, mainly by generalizing those results to EDAs that are able to deal with multivariate dependences among the variables of the problem. Through the definition of an equivalence relation between functions, it is possible to partition the space of problems into equivalence classes in which the algorithm has the same behavior. We provide a sufficient and necessary condition to determine the equivalence between functions. This condition is based on a set of matrices which provides a novel encoding of the relationship between the function and the probabilistic model used by the algorithm. The description of the equivalent functions belonging to a class is studied in depth for EDAs whose probabilistic model is given by a chordal Markov network. Assuming this class of factorization, we unveil the intrinsic connection between the behaviors of EDAs and neighborhood systems defined over the search space. In addition, we carry out numerical simulations that effectively reveal the different behaviors of EDAs for the injective functions defined over the search space {0,1}^3 . Finally, we provide a novel approach to extend the analysis of equivalence classes to non-injective functions.
Open Access
Real elements and p-nilpotence of finite groups
(Aracne, 2016) Ballester Bolinches, Adolfo; Esteban Romero, Ramón; Ezquerro Marín, Luis Miguel; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Our first main result proves that every element of order 4 of a Sylow 2-subgroup S of a minimal non-2-nilpotent group G, is a real element of S. This allows to give a character-free proof of a theorem due to Isaacs and Navarro (see [9, Theorem B]). As an application, the authors show a common extension of the p-nilpotence criteria proved in [3] and [9].
Open Access
A generalization of the gravitational search algorithm
(Springer, 2017-05-19) Bustince Sola, Humberto; Minárová, María; Fernández Fernández, Francisco Javier; Sesma Sara, Mikel; Marco Detchart, Cedric; Ruiz-Aranguren, Javier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
In this work we propose a generalization of the gravitational search algorithm where the product in the expression of the gravitational attraction force is replaced by more general functions. We study some conditions which ensure convergence of our proposal and we show that we recover a wide class of aggregation functions to replace the product.
Open Access
Some properties and construction methods for ordered directionally monotone functions
(IEEE, 2017-08-24) Sesma Sara, Mikel; Marco Detchart, Cedric; Bustince Sola, Humberto; Barrenechea Tartas, Edurne; Lafuente López, Julio; Kolesárová, Anna; Mesiar, Radko; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
In this work we propose a new generalization of the notion of monotonicity, the so-called ordered directionally monotonicity. With this new notion, the direction of increasingness or decreasingness at a given point depends on that specific point, so that it is not the same for every value on the domain of the considered function.
Open Access
Holistic architecture for music education: a proposal for empirical research in educational situations
(Universitat Politècnica de València, 2018) Ángel Alvarado, Rolando Alfredo; Wilhelmi, Miguel R.; Belletich Ruiz, Olga; Ciencias Humanas y de la Educación; Giza eta Hezkuntza Zientziak; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Holistic Architecture for Music Education (HAME) arises as a Design-Based Research, that is, it is an interdisciplinary research approach based on mixed research methods, which attempts understanding empirical phenomena from music education complexity. The HAME’ structural design poses a preliminary study of phenomena, the formulation of a research hypothesis, fieldwork in real-world situations and, finally, an analysis of data collected during the fieldwork with the intention of contrasting the hypothesis. This study aims to explore the technical suitability of the HAME in music education’s empirical research. Results demonstrate consistency between four phases of the structural design, in addition to prove the empirical complexity of organisational structures in music classrooms. In conclusion, the HAME is understood as an interdisciplinary educational research approach, which is holistically described as it connects theoretical currents of the social sciences and humanities with actual educational situations of music education. As a consequence, the HAME provides theoretical and practical knowledge about music education.
Open Access
A survey on the mathematical foundations of axiomatic entropy: representability and orderings
(MDPI, 2018) Campión Arrastia, María Jesús; Gómez Polo, Cristina; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Zientziak; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Ciencias
Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations.
Open Access
Acoustic lock: position and orientation trapping of non-spherical sub-wavelength particles in mid-air using a single-axis acoustic levitator
(American Institute of Physics, 2018) Cox, L; Croxford, A; Drinkwater, Bruce W.; Marzo Pérez, Asier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
We demonstrate acoustic trapping in both position and orientation of a non-spherical particle of sub-wavelength size in mid-air. To do so, we multiplex in time a pseudo-one-dimensional vertical standing wave and a twin-trap; the vertical standing wave provides converging forces that trap in position, whereas the twin-trap applies a stabilising torque that locks the orientation. The device operates at 40 kHz, and the employed multiplexing ratio of the 2 acoustic fields is 100:50 (standing:twin) periods. This ratio can be changed to provide tunability of the relative trapping strength and converging torque. The torsional spring stiffness of the trap is measured through simulations and experiments with good agreement. Cubes from k/5.56 (1.5 mm) to k/2.5 (3.4 mm) side length were stably locked. We also apply this technique to lock different non-spherical particles in midair: cubes, pyramids, cylinders, and insects such as flies and crickets. This technique adds significant functionality to mid-air acoustic levitation and will enable applications in micro-scale manufacturing as well as containment of specimens for examination and 3D-scanning.
Open Access
Impacto en el personal sanitario de urgencias extrahospitalarias de las cargas elevadas en la movilización de pacientes con silla de transporte
(Asociación de Especialistas en Enfermería del Trabajo, 2018) Arenal Gota, Tania; Viana Gárriz, Juan Luis; Millor Muruzábal, Nora; Martínez Ramírez, Alicia; Gómez Fernández, Marisol; Belzunegui Otano, Tomás; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Ciencias de la Salud; Osasun Zientziak
Introducción. El objetivo del estudio es valorar el esfuerzo físico realizado por el personal de la urgencia extrahospitalaria al trasladar pacientes de su domicilio a la ambulancia. Material y métodos. Estudio observacional transversal con un muestreo no probabilístico de conveniencia. Se comparan tres grupos: bomberos, mujeres y hombres técnicos en emergencias sanitarias (TES), utilizando sensores inerciales con los que obtenemos datos relativos del movimiento que ejecutan 10 profesionales sanitarios del ámbito extrahospitalario (4 bomberos y 6 TES) al bajar un paciente por las escaleras en condiciones similares a una urgencia. Resultados. Los sujetos que se encuentran en la posición de arriba en el desplazamiento de la carga presentan mayor aceleración en el plano suelo-techo y en la pierna izquierda. Las mujeres presentaron mayor aceleración en piernas y brazos que el resto, sin embargo, es en los brazos donde es significativamente superior. Cuando el sujeto que está en la posición de abajo en el desplazamiento de la carga, bajando la silla de espaldas, la aceleración de las piernas es superior que al bajarla en sentido de la marcha. Conclusiones. Los sujetos presentan mayor aceleración en piernas, siendo el lugar del cuerpo que sufre la suma del peso del paciente y del trabajador. Las mujeres presentan una mayor aceleración por lo que su esfuerzo físico es más acusado. Bajar la silla en sentido de la marcha, disminuye la aceleración en las piernas por lo que está posición es ergonómicamente mejor. Cuanto mayor es la estabilidad al bajar la silla y mayor seguridad del trabajador al desempeñar este trabajo, disminuye su aceleración y por lo tanto el esfuerzo físico que realiza.
Open Access
Outcomes and features of the inspection of receiver tubes (ITR) system for improved O&M in parabolic trough plants
(American Institute of Physics, 2018) Olano, Xabier; García de Jalón, Alberto; Pérez, David; García Barberena, Javier; López, Javier; Gastón Romeo, Martín; Estadística e Investigación Operativa; Estatistika eta Ikerketa Operatiboa
Concentrated solar power (CSP) plants based on parabolic trough (PT), after several years since their commissioning, demand new operation and maintenance (O&M) developments. Particularly, the receiver tube´s potential degradation over time is a real challenge. In this paper, the current version of the ITR System's last developments and advanced features are presented together with the main outcomes provided by the system for a real, complete solar field inspection in a commercial PT power plant. Exemplarily, this commercial ITR inspection showed that 0.8% of the tubes were underperforming and thus classified as outliers, while the average relative power of the tubes from the solar field resulted in about 97% of the ideal tubes' power. This paper shows that, thanks to the ITR Inspection System, plant operators can more easily develop and adopt improved O&M strategies, such as corrective and preventive actions in the solar field and even predictive actions in case of periodic inspections.
Open Access
An axiomatic approach to finite means
(Elsevier, 2018) Campión Arrastia, María Jesús; Candeal, Juan Carlos; García Catalán, Olga Raquel; Giarlotta, Alfio; Induráin Eraso, Esteban; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications.
Open Access
Geometrical aggregation of finite fuzzy sets
(Elsevier, 2018) Campión Arrastia, María Jesús; García Catalán, Olga Raquel; Induráin Eraso, Esteban; Lizasoain Iriso, María Inmaculada; Raventós Pujol, Armajac; Valero, Óscar; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE; Estadística, Informática y Matemáticas
A fuzzy set on a finite universe can be interpreted as a vector in a unit cube. This gives rise to a huge variety of approaches in order to aggregate finite fuzzy sets or to modify a given one. We analyze several geometrical methods and discuss possible applications in a multidisciplinary setting.
Open Access
Outcomes for design and learning when teenagers with autism codesign a serious game: a pilot study
(Wiley, 2018) Bossavit, Benoît; Parsons, Sarah; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Digital educational games research tends to lack ecological validity by not adequately taking into account the views and perspectives of children and young people with autism spectrum disorders (ASD). This paper is a pilot study that explores and analyses an academic‐based educational game that was co‐designed with and for young people with ASD. The serious game aims to help the players learn Geography‐specific knowledge and integrates several strategic features so that users can collaborate together against the computer or compete against each other. The educational game was evaluated over 5 sessions by 3 peer teams from 2 different special educational institutions, involving a total of 6 students with ASD. The participants were positive about their enjoyment, motivation, and social engagement. The results showed that the players' level of competitiveness not only influenced the experience within the game but also the interaction within the peer teams. The game mechanisms did help the participants with ASD increase their knowledge in Geography content. The main conclusion is that there are considerable benefits of including children with ASD in the design process and future research should explore more fully on how their involvement can enhance curriculum‐based learning as well as social engagement within the classroom.