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Publications

Publications by LIAAD

2017

Who controls the controller? A dynamical model of corruption

Authors
Accinelli, E; Martins, F; Oviedo, J; Pinto, A; Quintas, L;

Publication
JOURNAL OF MATHEMATICAL SOCIOLOGY

Abstract
The aim of this article is to give at least a partial answer to the question made in the title. Several works analyze the evolution of the corruption in different societies. Most of such papers show the necessity of several controls displayed by a central authority to deter the expansion of the corruption. However there is not much literature that addresses the issue of who controls the controller. This article aims to approach an answer to this question. Indeed, as it is well known, in democratic societies an important role should be played by citizens. We show that politically active citizens can prevent the spread of corruption. More precisely, we introduce a game between government and officials where both can choose between a corrupt or honest behavior. Citizens have a political influence that results in the prospects of a corrupt and a non-corrupt government be re-elected or not. This results in an index of intolerance to corruption. We build an evolutionary version of the game by means of the replicator dynamics and we analyze and fully characterize the possible trajectories of the system according to the index of intolerance to corruption and other relevant quantities of the model.

2017

A bifurcation theorem for evolutionary matrix models with multiple traits

Authors
Cushing, JM; Martins, F; Pinto, AA; Veprauskas, A;

Publication
JOURNAL OF MATHEMATICAL BIOLOGY

Abstract
One fundamental question in biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of non-extinction equilibria. In the case of nonlinear matrix models for structured populations, a bifurcation theorem answers this question when the projection matrix is primitive by showing the existence of a continuum of positive equilibria that bifurcates from the extinction equilibrium as the inherent population growth rate passes through 1. This theorem also characterizes the stability properties of the bifurcating equilibria by relating them to the direction of bifurcation, which is forward (backward) if, near the bifurcation point, the positive equilibria exist for inherent growth rates greater (less) than 1. In this paper we consider an evolutionary game theoretic version of a general nonlinear matrix model that includes the dynamics of a vector of mean phenotypic traits subject to natural selection. We extend the fundamental bifurcation theorem to this evolutionary model. We apply the results to an evolutionary version of a Ricker model with an added Allee component. This application illustrates the theoretical results and, in addition, several other interesting dynamic phenomena, such as backward bifurcation induced strong Allee effects.

2017

Modeling, Dynamics, Optimization and Bioeconomics II

Authors
Pinto, AA; Zilberman, D;

Publication
Springer Proceedings in Mathematics and Statistics

Abstract

2017

Geometric Approaches and Bifurcations in the Dichotomous Decision Model = ????? ???????? ?????????? ?? ????? ?????? ?? ??????

Authors
Mousa, AS; Pinto, AA;

Publication
Journal of the Arab American University

Abstract

2017

Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions

Authors
Figueiredo, A;

Publication
The Open Statistics & Probability Journal

Abstract

2017

Bootstrap and permutation tests in ANOVA for directional data

Authors
Figueiredo, A;

Publication
COMPUTATIONAL STATISTICS

Abstract
The problem of testing the null hypothesis of a common direction across several populations defined on the hypersphere arises frequently when we deal with directional data. We may consider the Analysis of Variance (ANOVA) for testing such hypotheses. However, for the Watson distribution, a commonly used distribution for modeling axial data, the ANOVA test is only valid for large concentrations. So we suggest to use alternative tests, such as bootstrap and permutation tests in ANOVA. Then, we investigate the performance of these tests for data from Watson populations defined on the hypersphere.

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