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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
003
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.

2018

Operational Research

Authors
Vaz, AIF; Almeida, JP; Oliveira, JF; Pinto, AA;

Publication
Springer Proceedings in Mathematics & Statistics

Abstract

2018

Modelling the suppression of autoimmunity after pathogen infection

Authors
Oliveira, BMPM; Trinchet, R; Otero Espinar, MVO; Pinto, A; Burroughs, N;

Publication
Mathematical Methods in the Applied Sciences

Abstract
We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 (IL-2) secretion. We model the suppression of the autoimmune line of T cells after a different line of T cells responded to a pathogen infection. In this paper, we show that if the population of the pathogen responding line of T cells becomes large enough, the competition for IL-2 and the increase in the death rates may lead to a depletion in the concentration of autoimmune T cells. Provided this lasts for a sufficiently long time, the concentration of autoimmune T cells can be brought down to values inside the basin of attraction of the controlled state, and autoimmunity can be suppressed. Copyright © 2018 John Wiley & Sons, Ltd.

2018

Modeling, Dynamics, Optimization and Bioeconomics III

Authors
Pinto, AA; Zilberman, D;

Publication
Springer Proceedings in Mathematics & Statistics

Abstract

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.

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

On the Convergence to Walrasian Prices in Random Matching Edgeworthian Economies

Author
Yusuf Aliyu Ahmad

Institution
UP-FCUP

2016

Modelo de Rating

Author
António Miguel Arantes da Silva

Institution
UP-FCUP