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© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., In the present, there are different indices that measure the difficulty level of reading a text, i.e. the readability of a text. Different studies have been made on the frequency of occurrence of letters in several languages, but as we know there are not thorough studies on the occurrence of letters according to the readability of a text. The main objective of the present work is to study the frequency of occurrence of letters in a text according to its legibility. This occurrence will be approached from two points of view. First, through the so-called power indices of game theory. To the best of our knowledge, it is the first time that a game is associated with a text and the influence or power of each letter will be analysed by means of the so-called power indices of the game theory. Thus, we present a new application of game theory. Second, by means of basic statistics to study relative frequency of letters in a text., Peer Reviewed, Postprint (author's final draft)

We study from a numerical point of view a multidimensional problem involving a vis- coelastic body with two porous structures. The mechanical problem leads to a linear system of three coupled hyperbolic partial differential equations. Its corresponding varia- tional formulation gives rise to three coupled parabolic linear equations. An existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approx- imations are introduced using the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are performed in one and two dimensions to show the accuracy of the approximation and the behaviour of the solution., Peer Reviewed, Postprint (author's final draft)

In this paper, we consider several problems arising in the theory of thermoelastic bodies with voids. Four particular cases are considered depending on the choice of the constitutive tensors, assuming different dissipation mechanisms determined by Moore-Gibson-Thompson-type viscosity. For all of them, the existence and uniqueness of solutions are shown by using semigroup arguments. The energy decay of the solutions is also analyzed for each case., Peer Reviewed, Postprint (author's final draft)

In this work, we consider, from the numerical point of view, a boundary-initial value problem for non-simple porous elastic materials. The mechanical problem is written as a coupled hyperbolic linear system in terms of the displacement and porosity fields. The resulting variational formulation is used to approximate the solution by the finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the numerical scheme is deduced under adequate regularity conditions. Finally, some numerical simulations are presented to show the accuracy of the finite element scheme studied previously, the evolution of the discrete energy and the behavior of the solution., Peer Reviewed, Postprint (author's final draft)

An influence game is a simple game represented over an influence graph (i.e., a labeled, weighted graph) on which the influence spread phenomenon is exerted. Influence games allow applying different properties and parameters coming from cooperative game theory to the contexts of social network analysis, decision-systems, voting systems, and collective behavior. The exact calculation of several of these properties and parameters is computationally hard, even for a small number of players. Two examples of these parameters are the length and the width of a game. The length of a game is the size of its smaller winning coalition, while the width of a game is the size of its larger losing coalition. Both parameters are relevant to know the levels of difficulty in reaching agreements in collective decision-making systems. Despite the above, new bio-inspired metaheuristic algorithms have recently been developed to solve the NP-hard influence maximization problem in an efficient and approximate way, being able to find small winning coalitions that maximize the influence spread within an influence graph. In this article, we apply some variations of this solution to find extreme winning and losing coalitions, and thus efficient approximate solutions for the length and the width of influence games. As a case study, we consider two real social networks, one formed by the 58 members of the European Union Council under nice voting rules, and the other formed by the 705 members of the European Parliament, connected by political affinity. Results are promising and show that it is feasible to generate approximate solutions for the length and width parameters of influence games, in reduced solving time, "Funding Statement: F. Riquelme has been partially supported by Fondecyt de Iniciación 11200113, Chile, and by the SEGIB scholarship of Fundación Carolina, Spain; X. Molinero under grants PID2019-104987GB-I00 (JUVOCO); M. Serna under grants PID2020-112581GB-C21 (MOTION) and 2017-SGR-786 (ALBCOM)", Peer Reviewed, Postprint (published version)

In this paper, we analyze the frequency distributions of weights and quotas in weighted majority voting games (WMVG) up to eight players. We also show different procedures that allow us to obtain some minimum or minimum sum representations of WMVG, for any desired number of players, starting from a minimum or minimum sum representation. We also provide closed formulas for the number of WMVG with n players having a minimum representation with quota up to three, and some subclasses of this family of games. Finally, we complement these results with some upper bounds related to weights and quotas., Peer Reviewed, Postprint (published version)

In this paper we discuss on several ways to extend power indices defined on simple games to the context of (j, 2)-games, i.e., games with 2 possible outputs and j possible input levels. The purpose of this paper is more conceptual than technical, and shows that different power indices can be obtained in (j, 2)-games depending on how the criticality of a player is measured. Some power indices for simple games, regarded as measures of power as payment, can be obtained from the selection of two items: (1) a probabilistic model, and (2) a collection of winning coalitions. The combination of two particular probabilistic models and three collections of winning coalitions lead to six well-known power indices for simple games. The Banzhaf and the Johnston power indices are among them. The main goal of the paper is to discuss the generalizations of these six power indices from (2, 2)-games to (j, 2)-games for j=3. The probabilistic model and the collection of winning coalitions are trivially extendable to (j, 2)-games. However, at least four possible ways of measuring the criticality of a player can be considered in this new context, and lead to different possible extensions of the six power indices to (j, 2)-games. We highlight two of them as being the most interesting under our point of view. The first one would be suitable for assessing sensitivity, because it measures the player’s ability to modify the output by a small change in his input level. The second one would be adequate to evaluate strength, because it measures the voter’s ability to modify the output by any change in his voting. The main conclusion is that different extensions of the considered power indices, as the Banzhaf and the Jonnston indices, are possible for j=3 and that they should be taken into account when working in a multiple input context., This research was partially supported by funds from the Spanish Ministry of Economy and Competitiveness (MINECO) and from the European Union (FEDER funds) under grant MTM2015-66818-P(MINECO/FEDER)., Peer Reviewed, Postprint (author's final draft)

We focus on bicooperative games, a variation of the classic cooperative games and, in particular, on the Banzhaf and the Shapley bisemivalues defined on these games. We consider three special classes of players: weak null, necessary defender and necessary detractor players. By introducing new properties related to this kind of players, we provide new axiomatic characterizations of the Banzhaf and the Shapley bisemivalues giving, in both cases, a set of independent properties that univocally determine them. We also provide a computational procedure to calculate the allocations given by the Shapley bisemivalue in terms of the generalized multilinear extension of the game., This research project was partially supported by funds from the Spanish Ministry of Science and Innovation grant PID2019-104987GB-I00., Peer Reviewed, Postprint (author's final draft)

We study the behavior in time of the solutions to several systems of equations for porous-thermo-elastic problems when one of the variables is considered to be quasi-static or, in other words, whose second time derivative can be neglected. We analyze three different situations using the classical Fourier law and also the type II or type III Green–Naghdi heat conduction models, Peer Reviewed, Postprint (author's final draft)

In this paper, we study, from the numerical point of view, a dynamic problem involving a mixture of two viscoelastic solids. The mechanical problem is written as a system of two coupled partial differential equations. Its variational formulation is derived and an existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced by using the classical finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown, from which we deduce the linear convergence of the algorithm. Finally, some numerical simulations, including examples in one and two dimensions, are presented to show the accuracy of the approximation and the behaviour of the solution., Peer Reviewed, Postprint (author's final draft)

Dropping out of first-year college students is a very common problem in universities in general, but especially in engineering and degrees in the STEM field. As a public university, we are committed to use resources as efficiently as possible, so it’s important to avoid dropouts as much as possible and improve student learning and performance. In particular, there are schools where the dropout rate is significant and it is absolutely necessary to carry out a project to study the problem, find the causes and apply tools to reduce it. Dropping out can be due to various causes related to, for example, lack of motivation of students, entrance marks, previous studies, etc. But the search for strategies to solve the problem can only be done after a systematic analysis of these causes. To go even further, the goal is to quantify the probability of college drop-out in advance by means of indicators so that preventive measures can be implemented to reduce it. A study was carried out in pilot groups of several degrees at the Polytechnic School of Engineering of Manresa, a college of Universitat Politècnica de Catalunya · BarcelonaTech (UPC), in the framework of a teaching improvement project promoted by the UPC. Statistical research tools and new technologies were used to classify the causes, typify them and determine good parameters that allow to transform causes in quantitative variables. The main result is the construction of a mathematical model leading to the definition of risk indices. An experimental model was tested on former data, and the aim is to be tested again next academic year. As additional result, student support and student cooperation were proven to be critical to the analysis and possibly also play a key role for resolution strategies. Also, specific apps could be implemented to help students to evaluate their personal risk in order to make their own decisions. In particular, given the restrictions and incidences dues to covid, it is even more important to, This work has been carried out within the framework of the Teaching Improvement program at UPCBarcelonaTech, under grant agreement No. 741128. The views and opinions expressed herein are those of the authors and do not necessarily reflect the official point of view of the UPC-BarcelonaTech nor the European Commission., Peer Reviewed, Postprint (published version)

Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely used voting systems of this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained., This research was partially supported by funds from the Spanish Ministry of Science and Innovation grant PID2019-I04987GB-I00. We are grateful to the associate editor and two anonymous referees whose interesting comments allowed us to improve the paper., Peer Reviewed, Postprint (author's final draft)

The coalitional multinomial probabilistic values extend the notion of multinomial probabilistic value to games with a coalition structure, in such a way that they generalize the symmetric coalitional binomial semivalues and link and combine the Shapley value and the multinomial probabilistic values. By considering the property of balanced contributions within unions, a new axiomatic characterization is stated for each one of these coalitional values, provided that it is defined by a positive tendency profile, by means of a set of logically independent properties that univocally determine the value. Two applications are also shown: (a) to the Madrid Assembly in Legislature 2015–2019 and (b) to the Parliament of Andalucía in Legislature 2018–2022., This research project was partially supported by funds from the Spanish Ministry of Science and Innovation under grant PID2019-104987GB-I00., Peer Reviewed, Postprint (published version)

Cooperative game theory considers simple games and influence games as essential classes of games. A simple game can be viewed as a model of voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. An influence game is a cooperative game in which a team of players (or coalition) succeeds if it is able to convince sufficiently many agents to participate in a task. Furthermore, influence decision models allow to represent discrete system dynamics as graphs whose nodes are activated according to an influence spread model. It let us to depth in the social network analysis. All these concepts are applied to a wide variety of disciplines, such as social sciences, economics, marketing, cognitive sciences, political science, biology, computer science, among others. In this survey we present different advances in these topics, joint work with M. Serna. These advances include representations of simple games, the definition of influence games, and how to characterize different problems on influence games (measures, values, properties and problems for particular cases with respect to both the spread of influence and the structure of the graph). Moreover, we also present equivalent models to the simple games, the computation of satisfaction and power in collective decision-making models, and the definition of new centrality measures used for social network analysis. In addition, several interesting computational complexity results have been found., Peer Reviewed, Postprint (author's final draft)

This is a post-peer-review, pre-copyedit version of an article published in Group decision and negotiation. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10726-020-09718-7., The Banzhaf power index for games admits several extensions if the players have more than two ordered voting options. In this paper we prove that the most intu-itive and recognized extension of the index fails to preserve the desirability rela-tion for games with more than three ordered input levels of approval, a failure that undermines the index to be a good measure of power. This leads us to think of an alternative to the Banzhaf index for several input levels of approval. We propose a candidate for which it is proved that: (1) coincides with the Banzhaf index for sim-ple games, (2) it is proportional to its known extension for three levels of approval, and (3) preserves the desirability relation regardless of the number of input levels of approval. This new index is based on measuring the total capacity the player has to alter the outcome. In addition, it can be expressed through a very appropriate mathematical formulation that greatly facilitates its computation. Defining exten-sions of well-established notions in a wider context requires a careful analysis. Dif-ferent extensions can provide complementary nuances and, when this occurs, none of them can be considered to be ‘the’ extension. As shown in this paper, this situa-tion applies when trying to extend the Banzhaf power index from simple games to the broader context of games with several ordered input levels of approval., This research was partially supported by funds from: the Spanish Ministry of Economy and Competitiveness (MINECO) and from the European Union (FEDER funds) under grant MTM2015-66818-P (MINECO/FEDER), and the Spanish Ministry of Science and Innovation grant PID2019-I04987GB-I00., Peer Reviewed, Postprint (author's final draft)

This is a post-peer-review, pre-copyedit version of an article published in Annals of Operations Research. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10479-021-04044-w., The context of this work is a voting scenario in which each voter expresses his/her level of affinity about a proposal, by choosing a value in the set J={-j,…,-1,0,1,…,j}, and these individual votes produce a collective result, in the same set J, through a decision function. The simple majority, defined for j=1, is a widely used example of such a decision function. In this paper, a set of independent axioms is proved to uniquely characterize the j-majority decision function. The j-majority decision is defined for any positive integer j, and it coincides with the simple majority decision when j=1. In this way, this axiomatic characterization meets two goals: it gives a new characterization of the simple majority decision when j=1 and it extends May’s theorem to this broader context., This research has been partially supported by funds from the Ministry of Science and Innovation grant PID2019-104987GB-I00., Peer Reviewed, Postprint (author's final draft)

© 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0, This paper provides a classification of all monotonic bipartite simple games. The problem we deal with is very versatile since simple games are inequivalent monotonic Boolean functions, functions that are used in many fields such as game theory, neural networks, artificial intelligence, reliability or multiple-criteria decision-making. The obtained classification can be implemented in an algorithm able to enumerate bipartite simple games. These numbers provide some light on enumerations of several subclasses of bipartite simple games, for which we find formulas. Complete simple games, a subclass of all simple games for which the desirability relation is a complete preordering, were already classified by means of two parameters: a vector and a matrix fulfilling some conditions. Complete simple games are inequivalent monotonic regular Boolean functions. In this paper, we deduce a procedure for bipartite non-complete games, which allows enumerating the number of bipartite simple games. Several formulas are obtained, in particular polynomial expressions for the number of bicameral meet games and the number of bicameral join games, two types of voting systems widely used in practice., This research has been partially supported by funds from the Ministry of Science, Innovation and Universities grant PID2019-104987GB-I00., Peer Reviewed, Postprint (author's final draft)

In this paper we consider the theory of thermoelasticity with a double porosity structure in the context of the Green-Naghdi types II and III heat conduction models. For the type II, the problem is given by four hyperbolic equations and it is conservative (there is no energy dissipation). We introduce in the system a couple of dissipation mechanisms in order to obtain the exponential de- cay of the solutions. To be precise, we introduce a pair of the following damping mechanisms: viscoelasticity, viscoporosities and thermal dissipation. We prove that the system is exponentially stable in three different scenarios: viscoporosity in one structure jointly with thermal dissipation, viscoporosity in each structure, and viscoporosity in one structure jointly with viscoelasticity. However, if viscoelasticity and thermal dissipation are considered together, undamped solutions can be obtained., Peer Reviewed, Postprint (author's final draft)

This is a post-peer-review, pre-copyedit version of an article published in Soft computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00500-020-05422-5, Boolean functions have a fundamental role in neural networks and machine learning. Enumerating these functions and significant subclasses is a highly complex problem. Therefore, it is of interest to study subclasses that escape this limitation and can be enumerated by means of sequences depending on the number of variables. In this article, we obtain seven new formulas corresponding to enumerations of some subclasses of Boolean functions. The versatility of these functions does the problem interesting to several different fields as game theory, hypergraphs, reliability, cryptography or logic gates., Peer Reviewed, Postprint (author's final draft)

In this work, we study from the mathematical and numerical points of view a poro-thermoelastic problem. A long-term memory is assumed on the heat equation. Under some assumptions on the constitutive tensors, the resulting linear system is composed of hyperbolic partial differential equations with a dissipative mechanism in the temperature equation. An existence and uniqueness result is proved using the theory of contractive semigroups. Then, a fully discrete approximation is introduced applying the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is obtained. A priori error estimates are also shown, from which the linear convergence of the approximation is derived under suitable additional regularity conditions. Finally, one- and two-numerical simulations are presented to demonstrate the accuracy of the algorithm and the behavior of the solution., Peer Reviewed, Postprint (author's final draft)

In this note we study the problem proposed by the one-dimensional thermo-porous-elasticity of type II with quasi-static microvoids or, in mathematical terms, when the second time derivative of the volume fraction is so small that it can be negligible. It is known that the isothermal deformations decay in a slow way. Here we prove that the introduction of a conservative mechanism, as it is the type II heat conduction, makes the deformations damp generically in an exponential way, which is a striking fact., Peer Reviewed, Postprint (author's final draft)

This is a post-peer-review, pre-copyedit version of an article published in Journal of Optimization Theory and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007%2Fs10957-020-01640-x., In this work, we focus on bicooperative games, a variation of the classic cooperative games, and investigate the conditions for the coefficients of the bisemivalues—a generalization of semivalues for cooperative games—necessary and / or sufficient in order to satisfy some properties, including among others, desirability relation, balanced contributions, null player exclusion property and block property. Moreover, a computational procedure to calculate bisemivalues in terms of the multilinear extension of the game is given., This research project was partially supported by funds from the Spanish Ministry of Economy and Competitiveness (MINECO) and from the European Union (FEDER funds) under grant MTM2015-66818-P (MINECO/FEDER) and Grant SGR 2017–758 of the Catalonia Government (Generalitat de Catalunya)., Peer Reviewed, Postprint (author's final draft)

We describe voting mechanisms to study voting systems as well as electoral systems and parliamentary organizations. These mechanisms are base on the so-called power indices of simple games with alternatives. The classical power indices applied to simple games just consider two options, yes/agree or not/reject. Here we also consider the abstention option, whose condition is allowed in most voting rules. In fact, we consider the extended Shapley–Shubik and Banzhaf indices to measure the power of the player/voter or the coalition in real voting systems., Peer Reviewed, Postprint (author's final draft)

We study the time decay of the solutions for the type III thermoelastic theory with microtemperatures and voids. We prove that, under suitable conditions for the constitutive tensors, the solutions decay exponentially. This fact is in somehow striking because it differs from the behaviour of the solutions in the classical model of thermoelasticity with microtemperatures and voids, where the exponential decay is not expected in the general case., Peer Reviewed, Postprint (author's final draft)

This is a post-peer-review, pre-copyedit version of an article published in Optimization letters. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11590-020-01647-3, The paper provides a new characterization of weighted games within the class of simple games. It is based on a stronger form of the point-set-additive pseudoweighting property of simple games. The characterization obtained is of interest in various research fields such as game theory, coherent structures, logic gates, operations research and Boolean algebra. A (monotonic) simple game corresponds to an inequivalent (monotonic) function in Boolean algebra and a weighted game corresponds to a threshold function. The characterization obtained provides a better understanding of these mathematical structures while opening new prospects for solving numerous open problems in these areas., This research was partially supported by funds from the Spanish Ministry of Economy and Competitiveness (MINECO) and from the European Union (FEDER funds) under grant MTM2015–66818-P(MINECO/FEDER)., Peer Reviewed, Postprint (author's final draft)

Typically, the test type exams with binary answers (true / false) are corrected by adding a +1 to the correct answers, a -1 to the incorrect ones and 0 to non-answered questions. This mainly obeys to a purely statistic criterion which incentives answering questions randomly when the student has the impression that she will not pass the exam with what she knows. From our point of view this method of qualification is not suitable and therefore should be amended as soon as possible. Unfortunately, it is still now massively used in many Faculties worldwide. The objective of the work is to provide an alternative method to accurately qualify such exams., Peer Reviewed, Postprint (published version)

We describe voting mechanisms to study voting systems. The classical power indices applied to simple games just consider parties, players or voters. Here, we also consider games with a priori unions, i.e., coalitions among parties, players or voters. We measure the power of each party, player or voter when there are coalitions among them. In particular, we study real situations of voting systems using extended Shapley–Shubik and Banzhaf indices, the so-called coalitional power indices. We also introduce a dynamic programming to compute them., Peer Reviewed, Postprint (published version)

In this paper, we numerically analyse a phase-lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one-dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution., Peer Reviewed, Postprint (author's final draft)

This is a post-peer-review, pre-copyedit version of an article published in Group Decision and Negotiation. The final authenticated version is available online at: https://doi.org/10.1007/s10726-019-09651-4., This article proposes a value which can be considered an extension of the Banzhaf value for cooperative games. The proposed value is defined on the class of j-cooperative games, i.e., games in which players choose among a finite set of ordered actions and the result depends only on these elections. If the output is binary, only two options are available, then j-cooperative games become j-simple games. The restriction of the value to j-simple games leads to a power index that can be considered an extension of the Banzhaf power index for simple games. The paper provides an axiomatic characterization for the value and the index which is closely related to the first axiomatization of the Banzhaf value and Banzhaf power index in the respective contexts of cooperative and simple games., Peer Reviewed, Postprint (author's final draft)

This is an Accepted Manuscript of a book chapter published by Routledge/CRC Press in Handbook of the Shapley value on December 6, 2019, available online: https://www.crcpress.com/Handbook-of-the-Shapley-Value/Algaba-Fragnelli-Sanchez-Soriano/p/book/9780815374688, A value that has all the ingredients to be a generalization of the Shapley value is proposed for a large class of games called j-cooperative games which are closely related to multi-choice games. When it is restricted to cooperative games, i.e. when j equals 2, it coincides with the Shapley value. An explicit formula in terms of some marginal contributions of the characteristic function is provided for the proposed value. Different arguments support it: (1) The value can be inferred from a natural probabilistic model. (2) An axiomatic characterization uniquely determines it. (3) The value is consistent in its particularization from j-cooperative games to j-simple games. This chapter also proposes various ways of calculating the value by giving an alternative expression that does not depend on the marginal contributions. This chapter shows how the technique of generating functions can be applied to determine such a value when the game is a weighted j-simple game. The chapter concludes by presenting several applications, among them the computation of the value for a proposed reform of the UNSC voting system., Peer Reviewed, Postprint (author's final draft)

The final publication is available at Springer via https://doi.org/10.1007/978-3-662-60555-4_11, Many power indices on simple games have been defined trying to measure, under different points of view, the “a priori” importance of a voter in a collective binary voting scenario. A unified probabilistic way to define some of these power indices is considered in this paper. We show that six well-known power indices are obtained under such a probabilistic approach. Moreover, some new power indices can naturally be obtained in this way., Peer Reviewed, Postprint (author's final draft)

The aim of this paper is to study the time decay of the solutions for two models of the one-dimensional phase-lag thermoelasticity with two temperatures. The first one is obtained when the heat flux vector and the inductive temperature are approximated by a second-order and first-order Taylor polynomial, respectively. In this case, the solutions decay in a slow way. The second model that we consider is obtained taking first-order Taylor approximations for the inductive thermal displacement, the inductive temperature and the heat flux. The decay is, therefore, of exponential type., Peer Reviewed, Postprint (published version)

In this work we analyze, from the numerical point of view, a dynamic problem involving a thermoelastic rod. Two porosities are considered: the first one is the macro-porosity, connected with the pores of the material, and the other one is the micro-porosity, linked with the fissures of the skeleton. The mechanical problem is written as a set of hyperbolic and parabolic partial differential equations. An existence and uniqueness result and an energy decay property are stated. Then, a fully discrete approximation is introduced using the finite element method and the backward Euler scheme. A discrete stability property and a priori error estimates are proved, from which the linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the behaviour of the approximation, Peer Reviewed, Postprint (author's final draft)

Centrality and influence spread are two of the most studied concepts in social network analysis. Several centrality measures, most of them, based on topological criteria, have been proposed and studied. In recent years new centrality measures have been defined inspired by the two main influence spread models, namely, the Independent Cascade Model (IC-model) and the Linear Threshold Model (LT-model). The Linear Threshold Rank (LTR) is defined as the total number of influenced nodes when the initial activation set is formed by a node and its immediate neighbors. It has been shown that LTR allows to rank influential actors in a more distinguishable way than other measures like the PageRank, the Katz centrality, or the Independent Cascade Rank. In this paper we propose a generalized LTR measure that explore the sensitivity of the original LTR, with respect to the distance of the neighbors included in the initial activation set. We appraise the viability of the approach through different case studies. Our results show that by using neighbors at larger distance, we obtain rankings that distinguish better the influential actors. However, the best differentiating ranks correspond to medium distances. Our experiments also show that the rankings obtained for the different levels of neighborhood are not highly correlated, which validates the measure generalization, Peer Reviewed, Postprint (author's final draft)

Electronic version of an article published as International Game Theory Review, Vol. 21, Issue 1, 1940001, 2019, p. 1-24. DOI: 10.1142/S0219198919400012] © World Scientific Publishing Company https://www.worldscientific.com/doi/10.1142/S0219198919400012, The aim of this work is to give a characterization of the Shapley–Shubik and the Banzhaf power indices for (3,2)-simple games. We generalize to the set of (3,2)-simple games the classical axioms for power indices on simple games: transfer, anonymity, null player property and efficiency. However, these four axioms are not enough to uniquely characterize the Shapley–Shubik index for (3,2)-simple games. Thus, we introduce a new axiom to prove the uniqueness of the extension of the Shapley–Shubik power index in this context. Moreover, we provide an analogous characterization for the Banzhaf index for (3,2)-simple games, generalizing the four axioms for simple games and adding another property., Peer Reviewed, Postprint (author's final draft)

In this paper we analyze the system of equations that models the behaviour of materials with a double porous structure. We introduce dissipation mechanisms in both structures. We show existence, uniqueness and analyticity for the solutions of the system. As consequences, exponential stability and impossibility of localization for the solutions are obtained., Peer Reviewed, Postprint (author's final draft)

This work focuses on the Owen value and the Owen-Banzhaf value, two classical concepts of solution defined on games with structure of coalition blocks. We provide a computation procedure for these solutions based on a method of double-level work obtained from the multilinear extension of the original game. Moreover, two applications to several possible political situations in the Madrid Assembly and the Andalusian Parliament (legislatures 2015-2019) are also given., Peer Reviewed, Postprint (published version)

In this paper, we analyse a model involving a strain gradient thermoelastic rod with voids. Existence and uniqueness, as well as an energy decay property, are proved by means of the semigroup arguments. The variational formulation is derived and then, a fully discrete approximation is introduced by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A stability result and a priori error estimates are obtained, from which the linear convergence of the algorithm is deduced under suitable additional regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the algorithm and the behaviour of the solution., Peer Reviewed, Postprint (author's final draft)

In this paper we consider the one-dimensional version of thermoelasticity with two porous structures and porous dissipation on one or both of them. We first give an existence and uniqueness result by means of semigroup theory. Exponential decay of the solutions is obtained when porous dissipation is assumed for each porous structure. Later, we consider dissipation only on one of the porous structures and we prove that, under appropriate conditions on the coefficients, there exists undamped solutions. Therefore, asymptotic stability cannot be expected in general. However, we are able to give suitable sufficient conditions for the constitutive coefficients to guarantee the exponential decay of the solutions., Peer Reviewed, Postprint (author's final draft)

The final publication is available at link.springer.com via https://doi.org/10.1007/s00245-017-9439-8, In this paper we analyze an homogeneous and isotropic mixture of viscoelastic solids. We propose conditions to guarantee the coercivity of the internal energy and also of the dissipation, first in dimension two and later in dimension three. We obtain an uniqueness result for the solutions when the dissipation is positive and without any hypothesis over the internal energy. When the internal energy and the dissipation are both positive, we prove the existence of solutions as well as their analyticity. Exponential stability and impossibility of localization of the solutions are immediate consequences., Peer Reviewed, Postprint (author's final draft)

In the last years, a big interest has been developed to understand the time decay of solutions for the porous thermoelasticity with different thermal mechanisms. We here want to consider the problem of the one-dimensional porous thermoelasticity when the heat conduction is given by means of the dual-phase-lag theory. We want to give suitable conditions in order to guarantee that the decay of solutions is controlled by a negative exponential. We also want to provide conditions for the slow decay of the solutions., Peer Reviewed, Postprint (published version)

This is a post-peer-review, pre-copyedit version of an article published in Social choice and welfare. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00355-018-1164-y., The Nakamura number is an appropriate invariant of a simple game to study the existence of social equilibria and the possibility of cycles. For symmetric (quota) games its number can be obtained by an easy formula. For some subclasses of simple games the corresponding Nakamura number has also been characterized. However, in general, not much is known about lower and upper bounds depending on invariants of simple, complete or weighted games. Here, we survey such results and highlight connections with other game theoretic concepts. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature., Peer Reviewed, Postprint (author's final draft)

We introduce collective decision-making models associated with influence spread under the linear threshold model in social networks. We define the oblivious and the non-oblivious influence models. We also introduce the generalized opinion leader–follower model (gOLF) as an extension of the opinion leader–follower model (OLF) proposed by van den Brink et al. (2011). In our model we allow rules for the final decision different from the simple majority used in OLF. We show that gOLF models are non-oblivious influence models on a two-layered bipartite influence digraph. Together with OLF models, the satisfaction and the power measures were introduced and studied. We analyze the computational complexity of those measures for the decision models introduced in the paper. We show that the problem of computing the satisfaction or the power measure is #P-hard in all the introduced models even when the subjacent social network is a bipartite graph. Complementing this result, we provide two subfamilies of decision models in which both measures can be computed in polynomial time. We show that the collective decision functions are monotone and therefore they define an associated simple game. We relate the satisfaction and the power measures with the Rae index and the Banzhaf value of an associated simple game. This will allow the use of known approximation methods for computing the Banzhaf value, or the Rae index to their practical computation., Peer Reviewed, Postprint (author's final draft)

Voting games with abstention are voting systems in which players can cast not only yes and no vote, but are allowed to abstain. This paper centers on the structure of a class of complete games with abstention. We obtain, a parameterization that can be useful for enumerating these games, up to isomorphism. Indeed, any I-complete game is determined by a vector of matrices with non-negative integers entries. It also allows us determining whether a complete game with abstention is a strongly weighted (3, 2) game or not, and for other purposes of interest in game theory., Peer Reviewed, Postprint (author's final draft)

The final authenticated version is available online at: https://doi.org/10.1007/978-3-662-58464-4_1., An equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game., Peer Reviewed, Postprint (published version)

We study qualitative properties of the solutions of the system of partial differential equations modeling thermomechanical deformations for mixtures of thermoelastic solids when the theory of Green and Lindsay for the heat conduction is considered. Three dissipation mechanisms are proposed in the system: thermal dissipation, viscosity e ects on one constituent of the mixture and damping in the relative velocity of the two displacements of both constituents. First, we prove the existence and uniqueness of the solutions. Later we prove the exponential stability of the solutions over the time. We use the semigroup arguments to establish our results, Peer Reviewed, Postprint (author's final draft)

In this paper we consider the type III thermoelastic theory with microtemperatures. We study the time decay of the solutions and we prove that under suitable conditions for the constitutive tensors, the solutions decay exponentially. This fact is in somehow shocking because it differs from the behavior of the solutions in the classical model of thermoelasticity with microtemperatures, Peer Reviewed, Postprint (author's final draft)

This paper aims to develop, for any cooperative game, a solution notion that enjoys stability and consists of a coalition structure and an associated payoff vector derived from the Shapley value. To this end, two concepts are combined: those of strong Nash equilibrium and Aumann--Dr\`{e}ze coalitional value. In particular, we are interested in conditions ensuring that the grand coalition is the best preference for all players. Monotonicity, convexity, cohesiveness and other conditions are used to provide several theoretical results that we apply to numerical examples including real--world economic situations., Peer Reviewed, Postprint (author's final draft)

Centrality and influence spread are two of the most studied concepts in social network analysis. In recent years, centrality measures have attracted the attention of many researchers, generating a large and varied number of new studies about social network analysis and its applications. However, as far as we know, traditional models of influence spread have not yet been exhaustively used to define centrality measures according to the influence criteria. Most of the considered work in this topic is based on the independent cascade model. In this paper we explore the possibilities of the linear threshold model for the definition of centrality measures to be used on weighted and labeled social networks. We propose a new centrality measure to rank the users of the network, the Linear Threshold Rank (LTR), and a centralization measure to determine to what extent the entire network has a centralized structure, the Linear Threshold Centralization (LTC). We appraise the viability of the approach through several case studies. We consider four different social networks to compare our new measures with two centrality measures based on relevance criteria and another centrality measure based on the independent cascade model. Our results show that our measures are useful for ranking actors and networks in a distinguishable way., Peer Reviewed, Postprint (author's final draft)

We consider decision models associated with cooperative influence games, the oblivious and the non-oblivious influence models. In those models the satisfaction and the power measures were introduced and studied. We analyze the computational complexity of those measures when the in uence level is set to unanimity and the rule of decision is simple majority. We show that computing the satisfaction and the power measure in those systems are #P-hard., Peer Reviewed, Postprint (author's final draft)