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About

Alberto A. Pinto is a full professor at the Department of Mathematics, Faculty of Sciences, University of Porto (Portugal). He is a researcher at the Laboratory of Artificial Intelligence and Decision Support, Institute for Systems and Computer Engineering LIAAD, INESC TEC. He is the founder and co-editor-in-chief (with michel benaim) of the Journal of Dynamics and Games, published by the American Institute of Mathematical Sciences (AIMS). He was the President of International Center for Mathematics (CIM) from 2011 to 2016. Since 2016 he is President of the General Assembly of CIM.

Alberto A. Pinto worked with David Rand at the University of Warwick, UK, on his master's thesis (1989) that studied the work of Feigenbaum and Sullivan on scaling functions and he went on to a PhD (1991) on the universality features of other classes of maps that form the boundary between order and chaos.

During this time Alberto A. Pinto met a number of the leaders in dynamical systems, notably Dennis Sullivan and Mauricio Peixoto, and this had a great impact on his career. As a result he and his collaborators have made many important contributions to the study of the fine-scale structure of dynamical systems and this has appeared in leading journals and in his book "Fine Structures of Hyperbolic Diffeomorphisms" (2010) coauthored with Flávio Ferreira and David Rand.

While a postdoc with Dennis Sullivan at the Graduate Center of the City University of New York he met Edson de Faria and through Mauricio Peixoto he got in contact with Welington de Melo. With de Melo he proved the rigidity of smooth unimodal maps in the boundary between chaos and order extending the work of MacMullen. Furthermore, de Faria, de Melo and Alberto A. Pinto proved the conjecture raised in 1978 in the work of Feigenbaum and Coullet-Tresser which the characterizes the period-doubling boundary between chaos and order for unimodal maps. This appeared in the research article “Global Hyperbolicity of Renormalization for Smooth Unimodal Mappings” published at the journal Annals of Mathematics (2006) and was based in particular in the previous works of Sandy Davie, Dennis Sullivan, Curtis McMullen and Mikhail Lyubich.

Since then Alberto Pinto has branched out into more applied areas. He has contributed across a remarkably broad area of science including optics, game theory and mathematical economics, finance, immunology, epidemiology, and climate and energy. In these applied areas, he has published widely overpassing more than one hundred scientific articles. He edited two volumes, with Mauricio Peixoto and David Rand, untitled “Dynamics and Games I and II” (2011). These two volumes initiated the new Springer Proceedings in Mathematics series. He edited with David Zilberman the volume untitled “Optimization, Dynamics, Modeling and Bioeconomy I” (2015) that also appeared at Springer Proceedings in Mathematics & Statistics series. While President of CIM, with Jean-Pierre Bourguignon, Rolf Jeltsch and Marcelo Viana, he edited the books "Dynamics, Games and Science" and "Mathematics of Planet Earth" that initiated the "CIM Series in Mathematical Sciences", published by Springer-Verlag. He edited, with J. F. Oliveira and J. P. Almeida, the book "Operational Research", published by Springer-Verlag at the CIM Series in Mathematical Sciences". he edited, with Lluís Alsedà, Jim Cushing and Saber Elaydi, the book "Difference Equations, Discrete Dynamical Systems and Applications", published at the Springer Proceedings in Mathematics & Statistics. He published, with Elvio Accinelli Gamba, Athanasios N. Yannacopoulos and Carlos Hervés-Beloso, the book "Trends in Mathematical Economics", published by Springer-Verlag.

Alberto A. Pinto with Michel Benaim founded the Journal of Dynamics and Games (2014) of the American Institute of Mathematical Sciences (AIMS) and currently they are the editors-in-chief of the journal. He has also increasingly taken on important administrative tasks. He was a member of the steering committee of Prodyn at the European Science Foundation (1999-2001). He was the executive coordinator (2009-2010) of the Scientific Council of Exact Sciences and Engineering at the Fundação para a Ciência e Tecnologia.

Interest
Topics
Details

Details

  • Name

    Alberto Pinto
  • Cluster

    Computer Science
  • Role

    Research Coordinator
  • Since

    01st May 2011
002
Publications

2018

Cournot duopolies with investment in R&D: Regions of nash investment equilibria

Authors
Oliveira, BMPM; Becker Paulo, J; Pinto, AA;

Publication
Springer Proceedings in Mathematics and Statistics

Abstract
We study a model of a Cournot duopoly where firms invest in R&D to reduce their production costs. Depending on the parameters, we may find regions with one, two or three Nash equilibria of the investment. Here, we study the effect of the parameters in these regions, in particular, we study the effect of the possible market saturation, the maximum relative cost reduction and the product differentiation, giving special attention to regions with multiple Nash equilibria. We observed that, in general, the competitive region, where both firms invest, is reduced as we increase the possible market saturation and the differentiation of the products and is enlarged when we increase the maximum relative cost reduction. © 2018, Springer International Publishing AG, part of Springer Nature.

2017

Bistability of Evolutionary Stable Vaccination Strategies in the Reinfection SIRI Model

Authors
Martins, J; Pinto, A;

Publication
BULLETIN OF MATHEMATICAL BIOLOGY

Abstract
We use the reinfection SIRI epidemiological model to analyze the impact of education programs and vaccine scares on individuals decisions to vaccinate or not. The presence of the reinfection provokes the novelty of the existence of three Nash equilibria for the same level of the morbidity relative risk instead of a single Nash equilibrium as occurs in the SIR model studied by Bauch and Earn (PNAS 101:13391-13394, 2004). The existence of three Nash equilibria, with two of them being evolutionary stable, introduces two scenarios with relevant and opposite features for the same level of the morbidity relative risk: the low-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a low probability; and the high-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a high probability. We introduce the evolutionary vaccination dynamics for the SIRI model and we prove that it is bistable. The bistability of the evolutionary dynamics indicates that the damage provoked by false scares on the vaccination perceived morbidity risks can be much higher and much more persistent than in the SIR model. Furthermore, the vaccination education programs to be efficient they need to implement a mechanism to suddenly increase the vaccination coverage level.

2017

NASH AND SOCIAL WELFARE IMPACT IN AN INTERNATIONAL TRADE MODEL

Authors
Zubelli, JP; Pinto, AA; Martins, F;

Publication
JOURNAL OF DYNAMICS AND GAMES

Abstract
We study a classic international trade model consisting of a strategic game in the tariffs of the governments. The model is a two-stage game where, at the first stage, governments of each country use their welfare functions to choose their tariffs either (i) competitively (Nash equilibrium) or (ii) cooperatively (social optimum). In the second stage, firms choose competitively (Nash) their home and export quantities. We compare the competitive (Nash) tariffs with the cooperative (social) tariffs and we classify the game type according to the coincidence or not of these equilibria as a social equilibrium, a prisoner's dilemma or a lose-win dilemma.

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.

Supervised
thesis

2017

Social and Economic Games

Author
Renato Borges de Araújo de Moura Soeiro

Institution
UP-FCUP

2017

R&D Dynamics with uncertainty in the production cost

Author
Joana Becker Paulo

Institution
UP-FCUP

2017

Applications to dynamical systems to immunology and to random exchange economies

Author
Yusuf Aliyu Ahmad

Institution
UP-FCUP

2016

Modelo de Rating

Author
António Miguel Arantes da Silva

Institution
UP-FCUP

2016

Dynamics and Pure Nash Equilibria in Human Decisions

Author
Ricard Trinchet Arnejo

Institution
UP-FCUP