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    Help to new students of ICT Systems Engineering Degree at EPSEM-UPC: Mentoring  Open access

     Gorchs Altarriba, Roser; Molinero Albareda, Xavier
    Journal of technology and science education
    Date of publication: 2014
    Journal article

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    New students at the Manresa School of Engineering (EPSEM, Escola Politècnica Superior d'Enginyeria de Manresa) of the Universitat Politècnica de Catalunya (UPC) are voluntarily provided with the mentoring service during their initial period at University. Mentoring gives academic, teaching and self-organizational support. It improves academic results and reduces the desertion of the studies. In particular, the mentor is an experimented learner which studies in the last year of his/her Degree. The goal is to expose such mentoring applied to ICT (Information, Communication and Technology) Systems Engineering Degree at EPSEM, studies of new creation which are probably unique in Spain, and to present a treatment and analysis of the performance and possible actions of continuous improvement. However, it is necessary to take into account that the mentoring has been implemented just three years because of grants finished, so it should be necessary to start again with mentoring to develop a more exhaustive paper.

    New students at the Manresa School of Engineering (EPSEM, Escola Politècnica Superior d'Enginyeria de Manresa) of the Universitat Politècnica de Catalunya (UPC) are voluntarily provided with the mentoring service during their initial period at University. Mentoring gives academic, teaching and self-organizational support. It improves academic results and reduces the desertion of the studies. In particular, the mentor is an experimented learner which studies in the last year of his/her Degree. The goal is to expose such mentoring applied to ICT (Information, Communication and Technology) Systems Engineering Degree at EPSEM, studies of new creation which are probably unique in Spain, and to present a treatment and analysis of the performance and possible actions of continuous improvement. However, it is necessary to take into account that the mentoring has been implemented just three years because of grants finished, so it should be necessary to start again with mentoring to develop a more exhaustive paper.

  • Power indices of influence games and new centrality measures for social networks

     Molinero Albareda, Xavier; Riquelme Csori, Fabián; Serna Iglesias, Maria Jose
    Date: 2013-06-28
    Report

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    In social network analysis, there is a common perception that influence is relevantto determine the global behavior of the society and thus it can be used to enforce cooperation by targeting an adequate initial set of individuals or to analyze global choice processes. Here we propose centrality measures that can be used to analyze the relevance of the actors in process related to spread of influence. In [39] it was considered a multiagent system in which the agents are eager to perform a collective task depending on the perception of the willingness to perform the task of other individuals. The setting is modeled using a notion of simple games called influence games. Those games are defined on graphs were the nodes are labeled by their influence threshold and the spread of influence between its nodes is used to determ ine whether a coalition is winning or not. Influence games provide tools to measure the importance of the actors of a social network by means of classic power indices and provide a framework to consider new centrality criteria. In this paper we consider two of the most classical power indices, i.e., Banzhaf and Shapley-Shubik indices, as centrality measures for social networks in influence games. Although there is some work related to specific scenarios of game-theoretic networks, here we use such indices as centrality measures in any social network where the spread of influence phenomenon can be applied. Further, we define new centrality measures such as satisfaction and effort that, as far as we know, have not been considered so far. Besides the definition we perform a comparison of the proposed measures with other three classic centrality measures, degree, closeness and betweenness. To perform the comparison we consider three social networks. We show that in some cases our measure ments provide centrality hierarchies similar to those of other measures, while in other cases provide different hierarchies.

  • Pasado, presente y futuro de la mentoría en la EPSEM

     Gorchs Altarriba, Roser; Molinero Albareda, Xavier; Garriga Sucarrats, Salvador
    Revista Internacional de Educación y Aprendizaje
    Date of publication: 2013
    Journal article

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    This work details the coaching (mentoring) at Manresa School of Engineering (Escola Politècnica Superior d'Enginyeria de Manresa). It considers the evolution from the beginning (course 2009-10) to the present. Each course (2009-10, 2010-11 and 2011-12) is analized with some improve- ment actions. Finally, some proposes to the future are also introduced.

  • TEORIA DE JUEGOS: FUNDAMENTOS MATEMÁTICOS Y APLICACIONES

     Amer Ramon, Rafael; Carreras Escobar, Francisco; Freixas Bosch, Josep; Giménez Pradales, José Miguel; Llongueras Arola, Maria Dolors; Magaña Nieto, Antonio; Molinero Albareda, Xavier; Pons Vallès, Montserrat; Puente Del Campo, Mª Albina; Sales Ingles, Vicente
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  • Centrality measures based on power indices for social networks

     Molinero Albareda, Xavier; Riquelme Csori, Fabián; Serna Iglesias, Maria Jose
    European Conference on Operational Research
    Presentation's date: 2013-07-04
    Presentation of work at congresses

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    In 2012 we defined influence games, simple games where a coalition wins if it is able to convince enough agents to participate in a collective task. Influence is exerted through a social network. Classic power indices such as Banzhaf or Shapley-Shubik provide measures on the relevance of the agents. Although power indices are well known in voting systems and cooperative games, they have not been used as centrality measures for social networks. We are evaluating this approach comparing these new centrality measures with other classic ones like degree or closeness in several social networks.

  • La mentoría en la EPSEM: un caso particular

     Gorchs Altarriba, Roser; Molinero Albareda, Xavier
    Congreso Universitario de Innovación Educativa en las Enseñanzas Técnicas
    Presentation's date: 2013-07
    Presentation of work at congresses

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    A los estudiantes de nuevo ingreso en la Escola Politècnica Superior d'Enginyeria de Manresa (EPSEM) de la Universitat Politècnica de Catalunya (UPC), de los diferentes Grados de Ingeniería que se imparten en dicho centro, se les proporciona ¿La mentoría¿ a modo voluntario y de acompañamiento en su fase inicial (1r curso) para favorecer y fortalecer su adaptación al nuevo ritmo de estudios, así como mejorar sus resultados académicos y reducir el abandonamiento de los estudios. La mentoria es un soporte docente, de auto-organización y muy enfocada a favorecer el auto-aprendizaje individual y en grupo, donde el mentor es un estudiante experimentado de último curso. En este artículo se expone el modo cómo se ha llevado a cabo la mentoría en el Grado en Ingeniería de Sistemas TIC, titulación de nueva creación y probablemente única en España, así como un análisis de su funcionamiento y posibles acciones de mejora continuada. New students at Escola Politènica Superior d¿Enginyeria de Manresa (EPSEM) of the Universitat Politècnica de Catalunya (UPC), for all Degrees in Engineering that are imparted, are voluntarily provided with the mentoring service for their initial period (1st course): docent support, self-organizational support, and also a teaching focused in the increasing of self-learning in group. The mentor is an experimented learner coursing the last year of the Degree. It pretend that the new ingress student in the university feel himself accompanied to favour and strengthen his adaptation at the new rhythm of the studies; also it is intended that they improve their academic results and to reduce the abandonment of the studies. Here we expose the mentoring applied to the Degree in Engineering of TIC Systems, studies of new creation which are probably unique in Spain, and also a treatment and analysis of the performance and possible actions of continuous improvement.

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    Recolzament als nous estudiants del grau d'Enginyeria de sistemes TIC en l'EPSEM¿UPC: la mentoria  Open access

     Gorchs Altarriba, Roser; Molinero Albareda, Xavier
    Congrés Internacional UNIVEST
    Presentation's date: 2013
    Presentation of work at congresses

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    Als estudiants de nou ingrés a l'Escola Politècnica Superior d'Enginyeria de Manresa (EPSEM) de la UPC se'ls proporciona voluntàriament "La mentoria" a manera d'acompanyament en la seva fase inicial (1r curs). Bàsicament se'ls proporciona suport docent, d'autoorganització i molt enfocada a afavorir l'autoaprenentatge en grup. El mentor és un estudiant experimentat, d'últim curs de grau. L'objectiu principal és afavorir i enfortir l'adaptació al nou ritme d'estudis, a més de pretendre a millorar els resultats acadèmics i evitar així l'abandonament dels estudis. S'exposa i analitza la manera com s'ha dut a terme la mentoria en el Grau en Enginyeria de Sistemes TIC, titulació singular a Espanya. New students at l'Escola Politècnica Superior d'Enginyeria de Manresa (EPSEM) of the UPC are provided with the mentoring service. They can be voluntarily assisted in their initial period. Mentoring gives academic, teaching and self-organizational support. It improves academic results and reduces the desertion of the studies. The mentor is an experimented learner which studies in the last year of his/her Degree. Here we expose such mentoring applied to the Degree in Engineering of TIC Systems, studies of new creation which are probably unique in Spain, and also a treatment and analysis of the performance and possible actions of continuous improvement.

    Als estudiants de nou ingrés a l'Escola Politècnica Superior d'Enginyeria de Manresa (EPSEM) de la UPC se'ls proporciona voluntàriament

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    Star-shaped mediation in influence games  Open access

     Molinero Albareda, Xavier; Riquelme Csori, Fabián; Serna Iglesias, Maria Jose
    Cologne-Twente Workshop on Graphs and Combinatorial Optimization
    Presentation's date: 2013-05-21
    Presentation of work at congresses

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    We are interested in analyzing the properties of multi-agent systems [13] where a set of agents have to take a decision among two possible alternatives with the help of the social environment or network of the system itself. The ways in which people in uence each other through their interactions in a social network and, in particular, the social rules that can be used for the spread of influence have been proposed in an alternative simple game model [11]. However not all individuals play the same role in the process of taking a decision. In this paper we are interested in formalizing and analyzing the simple game model that results in a mediation system. In this scenario we have a social network together with an external participant, the mediator. The mediator can interact, in dierent degrees, with the agents and thus help to reach a decision.

    We are interested in analyzing the properties of multi-agent systems [13] where a set of agents have to take a decision among two possible alternatives with the help of the social environment or network of the system itself. The ways in which people influence each other through their interactions in a social network and, in particular, the social rules that can be used for the spread of influence have been proposed in an alternative simple game model [11]. However not all individuals play the same role in the process of taking a decision. In this paper we are interested in formalizing and analyzing the simple game model that results in a mediation system. In this scenario we have a social network together with an external participant, the mediator. The mediator can interact, in different degrees, with the agents and thus help to reach a decision.

  • Complete voting systems with two types of voters: weightedness and counting

     Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
    Annals of operations research
    Date of publication: 2012
    Journal article

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    We investigate voting systems with two classes of voters, for which there is a hierarchy giving each member of the stronger class more influence or important than each member of the weaker class. We deduce for voting systems one important counting fact that allows determining how many of them are for a given number of voters. In fact, the number of these systems follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. On the other hand, we classify by means of some parameters which of these systems are weighted. This result allows us to state an asymptotic conjecture which is opposed to what occurs for symmetric games.

    We investigate voting systems with two classes of voters, for which there is a hierarchy giving each member of the stronger class more influence or important than each member of the weaker class. We deduce for voting systems one important counting fact that allows determining how many of them are for a given number of voters. In fact, the number of these systems follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. On the other hand, we classify by means of some parameters which of these systems are weighted. This result allows us to state an asymptotic conjecture which is opposed to what occurs for symmetric games.

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    Computation of several power indices by generating functions  Open access

     Alonso Meijide, José María; Freixas Bosch, Josep; Molinero Albareda, Xavier
    Applied mathematics and computation
    Date of publication: 2012
    Journal article

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    In this paper we propose methods to compute the Deegan-Packel, the Public Good, and the Shift power indices by generating functions for the particular case of weighted voting games. Furthermore, we define a new power index which combines the ideas of the Shift and the Deegan-Packel power indices and also propose a method to compute it with generating functions. We conclude by some comments about the complexity to compute these power indices.

    Postprint (author’s final draft)

  • Social influence as a voting system: a complexity analysis of parameters and properties

     Molinero Albareda, Xavier; Riquelme Csori, Fabián; Serna Iglesias, Maria Jose
    Date: 2012-08-08
    Report

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  • Pasado, presente y futuro de la mentoría en la EPSEM (Past, present and future of coaching at EPSEM)

     Gorchs Altarriba, Roser; Molinero Albareda, Xavier; Garriga, Salvador
    Congreso Internacional de Educación y Aprendizaje
    Presentation's date: 2012-08-14
    Presentation of work at congresses

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  • Variations in strict separating systems representing a linearly separable function

     Molinero Albareda, Xavier; Freixas Bosch, Josep
    International Symposium on Mathematical Programming
    Presentation's date: 2012-08-23
    Presentation of work at congresses

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  • On the complexity of problems on simple games

     Freixas Bosch, Josep; Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, Maria Jose
    RAIRO. Operations research
    Date of publication: 2011-10
    Journal article

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  • Cómo mejorar el aprendizaje de los grados en ingeniería desde la perspectiva de los estudiantes

     Molinero Albareda, Xavier; Navarro Antunez, Ramon
    Congreso Universitario de Innovación Educativa en las Enseñanzas Técnicas
    Presentation's date: 2011-10-06
    Presentation of work at congresses

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    Cómo mejorar el aprendizaje de los grados en ingeniería desde la perspectiva de los estudiantes  Open access

     Navarro Antunez, Ramon; Molinero Albareda, Xavier
    Congreso Universitario de Innovación Educativa en las Enseñanzas Técnicas
    Presentation's date: 2011-07-06
    Presentation of work at congresses

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    La implantación de las nuevas titulaciones derivadas del Espacio Europeo de Educación Superior ha supuesto para las Escuelas de Ingeniería un considerable desafío, no tanto por su contenido o metodología docente, sino por el hecho de estar enmarcados en un sistema de garantía interna de calidad que vela por la satisfacción de los grupos de interés implicados, estudiantes incluidos. El artículo presenta los resultados y conclusiones de una encuesta de satisfacción realizada en dos cursos consecutivos entre los estudiantes que han cursado el primer cuatrimestre de carrera y ofrece una línea de acción para la mejora continua deseada, especialmente en dos de las herramientas básicas de la actual educación superior: la tutoría y la mentoría para los estudiantes.

  • Efficient enumeration of complete simple games

     Molinero Albareda, Xavier; Polyméris, Andreas; Riquelme Cepeda, Francisco; Serna Iglesias, Maria Jose
    International Conference on Game Theory and Management
    Presentation's date: 2011-06-27
    Presentation of work at congresses

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    La tutoria: opcional o obligada?  Open access

     Gorchs Altarriba, Roser; Giralt Mas, M. Rosa; Molinero Albareda, Xavier
    Congrés Internacional UNIVEST
    Presentation's date: 2011-06-16
    Presentation of work at congresses

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  • Relative errors of strict separating systems

     Molinero Albareda, Xavier; Freixas Bosch, Josep
    International Conference on Operational Research
    Presentation's date: 2011-07-10
    Presentation of work at congresses

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  • Weighted games without a unique minimal representation in integers

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Optimization methods software
    Date of publication: 2010-04
    Journal article

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  • TEORÍA DE JUEGOS Y SISTEMAS DE DECISIÓN COLECTIVA CON APLICACIONES TECNOLÓGICAS, ECONÓMICAS, POLÍTICAS Y SOCIOLÓGICAS

     Freixas Bosch, Josep; Amer Ramon, Rafael; Carreras Escobar, Francisco; Giménez Pradales, José Miguel; Llongueras Arola, Maria Dolors; Molinero Albareda, Xavier; Pons Vallès, Montserrat; Puente Del Campo, Mª Albina; Sales Ingles, Vicente; Magaña Nieto, Antonio
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  • European journal of operational research

     Molinero Albareda, Xavier
    Collaboration in journals

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  • On the use of generating functions to compute power indices based on minimal winning coalitions

     Freixas Bosch, Josep; Alonso-Meijide, José María; Molinero Albareda, Xavier
    International Conference Operations Research
    Presentation's date: 2010-09-02
    Presentation of work at congresses

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    Detection of paradoxes of power indices for simple games  Open access

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Date of publication: 2010-06
    Book chapter

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  • Maximum tolerance and maximum greatest tolerance

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Date of publication: 2010
    Book chapter

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  • On maximum bounds for the tolerance and greatest tolerance of strict separating systems

     Molinero Albareda, Xavier; Freixas Bosch, Josep
    European Chapter on Combinatorial Optimization
    Presentation's date: 2010-05-28
    Presentation of work at congresses

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  • On the ordinal equivalence of power indices

     Freixas Bosch, Josep; Molinero Albareda, Xavier; Pons Vallès, Montserrat; Marciniak, Dorota
    Joint Mathematics Meetings
    Presentation's date: 2010
    Presentation of work at congresses

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  • Maximum tolerance and maximum greatest tolerance

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Second International Conference on Agents and Artificial Intelligence
    Presentation's date: 2010-01
    Presentation of work at congresses

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  • Completeness on simple games

     Molinero Albareda, Xavier; Freixas Bosch, Josep; Olsen, Martin; Serna Iglesias, Maria Jose
    International Conference on Game Theory and Management
    Presentation's date: 2010-06-29
    Presentation of work at congresses

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  • Software matemàtic lliure  Open access

     Molinero Albareda, Xavier
    Jornada de Sosteniblitat i Compromís Social
    Presentation's date: 2010-12-02
    Presentation of work at congresses

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  • Weighted games without a unique minimal representation in integers

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Date: 2009
    Report

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  • On the existence of a minimum integer representation for weighted voting systems

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Annals of operations research
    Date of publication: 2009-02
    Journal article

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    A basic problem in the theory of simple games and other fields is to study whether a simple game (Boolean function) is weighted (linearly separable). A second related problem consists in studying whether a weighted game has a minimum integer realization. In this paper we simultaneously analyze both problems by using linear programming. For less than 9 voters, we find that there are 154 weighted games without minimum integer realization, but all of them have minimum normalized realization. Isbell in 1958 was the first to find a weighted game without a minimum normalized realization, he needed to consider 12 voters to construct a game with such a property. The main result of this work proves the existence of weighted games with this property with less than 12 voters

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    A Fibonacci sequence for linear structures with two types of components  Open access

     Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
    Date: 2009-07-23
    Report

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    We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to count, up to isomorphism, the number of these voting systems for an arbitrary number of voters. We obtain a closed formula for the number of these systems, this formula follows a Fibonacci sequence with a smooth polynomial variation on the number of voters.

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    On the complexity of problems on simple games  Open access

     Freixas Bosch, Josep; Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, Maria Jose
    Date: 2009-10-08
    Report

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    Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes–no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand, each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games. This analysis as usual depends on the game representation used as input. We consider four natural explicit representations: winning, losing, minimal winning, and maximal losing. We first analyze the complexity of testing whether a game is simple and testing whether a game is weighted. We show that, for the four types of representations, both problems can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. We analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game. We finalize with some considerations on the possibility of representing a game in a more succinct representation showing a natural representation in which the recognition problem is hard.

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    Maximum tolerance and maximum greatest tolerance  Open access

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Date: 2009-09-23
    Report

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    An important consideration when applying neural networks is the sensitivity to weights and threshold in strict separating systems representing a linearly separable function. Two parameters have been introduced to measure the relative errors in weights and threshold of strict separating systems: the tolerance and the greatest tolerance. Given an arbitrary separating system we study which is the equivalent separating system that provides maximum tolerance or/and maximum greatest tolerance.

    Postprint (author’s final draft)

  • ALGORISMIA, BIOINFORMÀTICA, COMPLEXITAT I METODES FORMALS (ALBCOM)

     Orejas Valdes, Fernando; Galceran Oms, Marc; Oliva Valls, Sergi; Godoy Balil, Guillermo; Atserias Peri, Albert; Martinez Parra, Conrado; Pasarella Sanchez, Ana Edelmira; Pino Blanco, Elvira Patricia; Alvarez Faura, Maria Del Carme; Blum, Christian Clemens; Gabarro Valles, Joaquin; Cortadella Fortuny, Jordi; Molinero Albareda, Xavier; Serna Iglesias, Maria Jose; Messeguer Peypoch, Xavier; Roura Ferret, Salvador; Blesa Aguilera, Maria Jose; Valiente Feruglio, Gabriel Alejandro; Duch Brown, Amalia; Carmona Vargas, Jose; Hernandez Pibernat, Hugo; Gel Moreno, Bernat; Gascon Caro, Adrian; Petit Silvestre, Jordi; Diaz Cort, Jose Maria
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  • 4th International Computer Science Symposium in Russia

     Molinero Albareda, Xavier
    Collaboration in journals

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  • Measures of voting power: counting of power indices and paradoxes

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    International Conference Game Theory and Management
    Presentation's date: 2009-06
    Presentation of work at congresses

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  • Maximum tolerance and maximum greatest tolerance of strict separating systems

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    European Conference on Operational Research
    Presentation's date: 2009-07
    Presentation of work at congresses

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  • Weightedness for simple games with less than 9 voters

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Date of publication: 2009-06
    Book chapter

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  • Simple games and weighted games: a theoretical and computational viewpoint

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Discrete applied mathematics
    Date of publication: 2009-04
    Journal article

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    It is a well-known result in the theory of simple games that a game is weighted if and only if it is trade robust. In this paper we propose a variant of trade robustness, that we call invariant-trade robustness, which is enough to determine whether a simple game is weighted. To test whether a simple game is invariant-trade robust we do not need to consider all winning coalitions; a reduced subset of minimal winning coalitions is enough. We make a comparison between the two methods (trade robustness and invariant-trade robustness) to check whether a simple game is weighted. We also provide by means of algorithms a full classification using both methods, for simple games with less than 8 voters according to the maximum level of (invariant-)trade robustness they achieve.

  • Journal of automata, languages and combinatorics

     Molinero Albareda, Xavier
    Collaboration in journals

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  • Theoretical computer science

     Molinero Albareda, Xavier
    Collaboration in journals

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  • A new method to check whether a simple game is weighted

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    Second International Conference on Game Theory and Management
    Presentation of work at congresses

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  • Weighted integer realizations for linear simple games with two types of voters

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    International Workshop on Operational Research (IWOR 2008)
    Presentation of work at congresses

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  • Generació ordenada d'estructures combinatòries

     Molinero Albareda, Xavier
    SCM/Notícies
    Date of publication: 2008-06
    Journal article

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  • The greatest allowed error of linearly separable switching functions

     Freixas Bosch, Josep; Molinero Albareda, Xavier
    IEEE transactions on neural networks
    Date of publication: 2008-05
    Journal article

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    An important consideration when applying neural networks is the sensitivity to weights and threshold in strict separating systems representing a linearly separable function. Perturbations may affect weights and threshold so that it is important to estimate the maximal percentage error in weights and threshold, which may be allowed without altering the linearly separable function. In this paper, we provide the greatest allowed bound which can be associated to every strict separating system representing a linearly separable function. The proposed bound improves the tolerance that Hu obtained. Furthermore, it is the greatest bound for any strict separating system. This is the reason why we call it the greatest tolerance.

  • The complexity of testing properties of simple games

     Freixas Bosch, Josep; Molinero Albareda, Xavier; Serna Iglesias, Maria Jose; Olsen, M
    Date: 2008-04
    Report

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  • A Fibonacci sequence for linear structures with two types of components

     Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
    International Conference on Applied Mathematical Programming and Modeling
    Presentation of work at congresses

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    We investigate binary voting systems with two types of voter s and a hierarchy among the members in each type, so that members in one class have mor e influence or importance than members in the other class. The purpose of this paper is t o count, up to isomorphism, the number of these voting systems for an arbitrary number of voters. We obtain a closed formula for the number of these systems, this formula follow s a Fibonacci sequence with a smooth polynomial variation on the number of voters.

  • International conference on the analysis of algorithms 2007

     Molinero Albareda, Xavier
    Collaboration in journals

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