Decisiveness indices are semiindices: addendum

In the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.Peer ReviewedPostprint (author's final draft

Using the multilinear extension to study some probabilistic power indices

The final publication is available at Springer via http://dx.doi.org/10.1007/s10726-016-9514-6We consider binary voting systems modeled by a simple game, in which voters vote independently of each other, and the probability distribution over coalitions is known. The Owen’s multilinear extension of the simple game is used to improve the use and the computation of three indices defined in this model: the decisiveness index, which is an extension of the Banzhaf index, the success index, which is an extension of the Rae index, and the luckiness index. This approach leads us to prove new properties and inter-relations between these indices. In particular it is proved that the ordinal equivalence between success and decisiveness indices is achieved in any game if and only if the probability distribution is anonymous. In the anonymous case, the egalitarianism of the three indices is compared, and it is also proved that, for these distributions, decisiveness and success indices respect the strength of the seats, whereas luckiness reverses this order.Peer ReviewedPostprint (author's final draft

Decisiveness indices are semiindices

In this note we prove that any decisiveness index, defined for any voter as the probability of him/her being decisive, is a semiindex when the probability distribution over coalitions is anonymous, and it is a semiindex with binomial coefficients when the probability over coalitions is anonymous and independent.Peer ReviewedPostprint (author's final draft

Components with higher and lower risk in a reliability system

A new reliability importance measure for components in a system, that we call Representativeness measure, is introduced. It evaluates to which extent the performance of a component is representative of the erformance of the whole system. Its relationship with Birnbaum’s measure is analyzed, and the ranking of components given by both measures are compared. These rankings happen to be equal when all components have the same reliability but different in general. In contrast with Birnbaum’s, the Representativeness reliability importance measure of a component does depend on its reliability.Peer ReviewedPostprint (published version

On anonymous and weighted voting systems

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 ReviewedPostprint (author's final draft

An extension and an alternative characterization of May’s theorem

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 ReviewedPostprint (author's final draft

Similarities and differences between success and decisiveness

We consider binary voting systems in which a probability distribution over coalitions is known. In this broader context decisiveness is an extension of the Penrose-Banzhaf index and success an extension of the Rae index for simple games. Although decisiveness and success are conceptually different we analyze their numerical behavior. The main result provides necessary and sufficient conditions for the ordinal equivalence of them. Indeed, under anonymous probability distributions they become ordinally equivalent. Moreover, it is proved that for these distributions, decisiveness and success respect the strength of the seats, whereas luckiness reverses the order.Peer ReviewedPostprint (author’s final draft

All-trans-retinoic acid activates the pro-invasive Src-YAP-Interleukin 6 axis in triple-negative MDA-MB-231 breast cancer cells while cerivastatin reverses this action

All-trans-retinoic acid (RA), the active metabolite of vitamin A, can reduce the malignant phenotype in some types of cancer and paradoxically also can promote cancer growth and invasion in others. For instance, it has been reported that RA induces tumor suppression in tumor xenografts of MDA-MB-468 breast cancer cells while increasing tumor growth and metastases in xenografts of MDA-MB-231 breast cancer cells. The signaling pathways involved in the pro-invasive action of retinoic acid remain mostly unknown. We show here that RA activates the pro-invasive axis Src-YAP-Interleukin 6 (Src-YAP-IL6) in triple negative MDA-MB-231 breast cancer cells, yielding to increased invasion of these cells. On the contrary, RA inhibits the Src-YAP-IL6 axis of triple-negative MDA-MB-468 cells, which results in decreased invasion phenotype. In both types of cells, inhibition of the Src-YAP-IL6 axis by the Src inhibitor PP2 drastically reduces migration and invasion. Src inhibition also downregulates the expression of a pro-invasive isoform of VEGFR1 in MDA-MB-231 breast cancer cells. Furthermore, interference of YAP nuclear translocation using the statin cerivastatin reverses the upregulation of Interleukin 6 (IL-6) and the pro-invasive effect of RA on MDA-MB-231 breast cancer cells and also decreases invasion and viability of MDA-MB-468 breast cancer cells. These results altogether suggest that RA induces pro-invasive or anti-invasive actions in two triple-negative breast cancer cell lines due to its ability to activate or inhibit the Src-YAP-IL6 axis in different cancer cells. The pro-invasive effect of RA can be reversed by the statin cerivastatin

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