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Publications

Publications by Alberto Pinto

2015

Approximate equilibria for a T cell and treg model

Authors
Oliveira, BMPM; Figueiredo, IP; Burroughs, NJ; Pinto, AA;

Publication
Applied Mathematics and Information Sciences

Abstract
We analyse a model of immune response by T cells (CD4), where regulatory T cells (Tregs) act by inhibiting IL-2 secretion. We introduced an asymmetry reflecting that the difference between the growth and death rates can be higher for the active T cells and the active Tregs than for the inactive T cells and inactive Tregs. This asymmetry mimics the presence of memory T cells. In this paper we start by analysing the model in the absence of Tregs. We obtain an explicit formula that gives approximately the antigenic stimulation of T cells from the concentration of Tregs. Afterwards, we present an explicit formula that describes approximately the balance between the concentration of T cells and the concentration of Tregs; and an explicit formula that relates approximately the antigenic stimulation of T cells, the concentration of T cells and the concentration of Tregs. For our parameter values, the relation between the antigenic stimulation of T cells and the concentration of T cells is an hysteresis that is unfold when some of the parameters are changed. We also consider a linear tuning between the antigenic stimulation of T cells and the antigenic stimulation of Tregs. Again, we have obtained an explicit formula relating approximately the antigenic stimulation of T cells, the concentration of T cells and the concentration of Tregs. With it, we can explain the appearance of an isola and a transcritical bifurcation. © 2015 NSP Natural Sciences Publishing Cor.

2016

LOCAL MARKET STRUCTURE IN A HOTELLING TOWN

Authors
Pinto, AA; Almeida, JP; Parreira, T;

Publication
JOURNAL OF DYNAMICS AND GAMES

Abstract
We develop a theoretical framework to study the location-price competition in a Hotelling-type network game, extending the Hotelling model, with linear transportation costs, from a line (city) to a network (town). We show the existence of a pure Nash equilibrium price if, and only if, some explicit conditions on the production costs and on the network structure hold. Furthermore, we prove that the local optimal localization of the firms are at the cross-roads of the town.

2016

Localization and prices in the quadratic Hotelling model with uncertainty

Authors
Pinto, AA; Parreira, T;

Publication
Journal of Dynamics and Games

Abstract

2015

Price competition in the Hotelling model with uncertainty on costs

Authors
Pinto, AA; Parreira, T;

Publication
OPTIMIZATION

Abstract
For the linear Hotelling model with firms located at the boundaries of the segment line, we study the price competition in a scenario of incomplete information in the production costs of both firms. We introduce the bounded uncertain costs (BUC) condition in the production costs and we prove that there is a local optimum price strategy if and only if the BUC condition holds. We compute explicitly the local optimum price strategy and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We prove that the ex-post profit of a firm is smaller than its ex-ante profit if and only if the production cost of the other firm is greater than its expected cost.

2016

R&D dynamics with asymmetric efficiency

Authors
Ferreira, M; Almeida, JP; Oliveira, BMPM; Pinto, AA;

Publication
Springer Proceedings in Mathematics and Statistics

Abstract
We consider an R&D investment function in a Cournot duopoly competitionmodel inspired in the logistic equation. We study the economical effects resulting from the firms having different R&D efficiencies. We present three cases: (1) both firms are efficient and have the same degree of efficiency; (2) both firms are less efficient and have the same degree of efficiency; (3) firms are asymmetric in terms of the efficiency of their R&D investment programs.We study the myopic dynamics on the production costs obtained from investing the Nash investment equilibria. © Springer-Verlag Berlin Heidelberg 2016.

2014

BHP universality in energy sources

Authors
Ferreira, H; Goncalves, R; Pinto, AA;

Publication
Springer Proceedings in Mathematics and Statistics

Abstract

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