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About

About

My name is Filipe Martins. I am a Phd student of Applied Mathematics at the Department of Mathematics of the Faculty of Sciences of the University of Porto and at LIAAD-INESC. My supervisor is Professor Alberto Adrego Pinto.

My research interests are Mathematics and Applications to Biology, Economics and Social Sciences. With the goal of studying these applications I am interested in Dynamical Systems, bifurcation theory and Game theory. I also have an interest in Mathematical Finance and stochastic optimal control.

Interest
Topics
Details

Details

  • Name

    Luís Filipe Martins
  • Cluster

    Computer Science
  • Role

    External Research Collaborator
  • Since

    01st August 2013
002
Publications

2021

Firms, technology, training and government fiscal policies: An evolutionary approach

Authors
Accinelli, E; Martins, F; Muñiz, H; Oliveira, BMPM; Pinto, AA;

Publication
Discrete & Continuous Dynamical Systems - B

Abstract
<p style='text-indent:20px;'>In this paper we propose and analyze a game theoretical model regarding the dynamical interaction between government fiscal policy choices toward innovation and training (I&amp;T), firm's innovation, and worker's levels of training and education. We discuss four economic scenarios corresponding to strict pure Nash equilibria: the government and I&amp;T poverty trap, the I&amp;T poverty trap, the I&amp;T high premium niche, and the I&amp;T ideal growth. The main novelty of this model is to consider the government as one of the three interacting players in the game that also allow us to analyse the I&amp;T mixed economic scenarios with a unique strictly mixed Nash equilibrium and with I&amp;T evolutionary dynamical cycles.</p>

2021

Immune Response Model Fitting to CD4$$^+$$ T Cell Data in Lymphocytic Choriomeningitis Virus LCMV infection

Authors
Afsar, A; Martins, F; Oliveira, BMPM; Pinto, AA;

Publication
Springer Proceedings in Mathematics & Statistics - Modeling, Dynamics, Optimization and Bioeconomics IV

Abstract

2020

Evolutionary dynamics for the generalized Baliga–Maskin public good model

Authors
Accinelli, E; Martins, F; Pinto, AA;

Publication
Chaos, Solitons and Fractals

Abstract
The problem of the consumption or provision of common and public goods is a well known and well studied problem in economic sciences. The nature of the problem is the existence of non-excludable externalities which gives rise to incentives to free-riding behaviour. There are several economical frameworks trying to deal with the problem such as coalition theory or mechanism design and implementation theory to ensure a Pareto efficient consumption or provision of such good. Baliga and Maskin considered an environmental game where several communities face a problem of pollution reduction. They show that all communities except one of them have incentives to act as a free-rider, i.e. only one community is willing to face the costs that air cleaning implies, namely the one with greatest preference for the good. In this work we introduce an adaptive evolutionary dynamics for the generalization of the Baliga–Maskin model to quasi-linear utility functions. We show that the Baliga–Maskin equilibrium is the only asymptotically stable dynamical equilibrium, all others being unstable. This result reasserts the problem of free-riding and externalities for the case of a common good in a dynamically/evolutionary setting, and reiterates the relevance of mechanism design and coalition formation in the context of dynamical models. © 2019

2019

Evolutionary Game Theory: A Generalization of the ESS Definition

Authors
Accinelli, E; Martins, F; Oviedo, J;

Publication
International Game Theory Review

Abstract
In this paper, we study the concept of Evolutionarily Stable Strategies (ESSs) for symmetric games with n = 3 players. The main properties of these games and strategies are analyzed and several examples are provided. We relate the concept of ESS with previous literature and provide a proof of finiteness of ESS in the context of symmetric games with n = 3 players. We show that unlike the case of n = 2, when there are more than two populations an ESS does not have a uniform invasion barrier, or equivalently, it is not equivalent to the strategy performing better against all strategies in a neighborhood. We also construct the extended replicator dynamics for these games and we study an application to a model of strategic planning of investment. © 2019 World Scientific Publishing Company.

2019

A fit of CD4+ T cell immune response to an infection by lymphocytic choriomeningitis virus

Authors
Afsar, A; Martins, F; Oliveira, BMPM; Pinto, AA;

Publication
Mathematical Biosciences and Engineering

Abstract
We fit an immune response model to data reporting the CD4+ T cell numbers from the 28 days following the infection of mice with lymphocytic choriomeningitis virus LCMV.We used an ODE model that was previously used to describe qualitatively the behaviour of CD4+ T cells, regulatory T cells (Tregs) and interleukine-2 (IL-2) density. The model considered two clonotypes of T cells in order to fit simultaneously the two time series for the gp61 and NP309 epitopes. We observed the proliferation of T cells and, to a lower extent, Tregs during the immune activation phase following infection and subsequently, during the contraction phase, a smooth transition from faster to slower death rates. The six parameters that were optimized were: the beginning and ending times of the immune response, the growth rate of T cells, their capacity, and the two related with the homeostatic numbers of T cells that respond to each epitope. We showed that the ODE model was able to be calibrated thus providing a quantitative description of the data. © 2019 the Author(s).