M. Ferreira

Autoimmunity arising from bystander proliferation of T cells in an immune response model

We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 secretion. The bystander proliferation to an immune response is modelled. We consider an asymmetry reflecting that the difference between the growth and death rates can be higher for the active T cells and Tregs than for the inactive. This asymmetry leads to a better understanding of the bystander proliferation. An exposure to a pathogen results in an increased proliferation rate of the bystander T cells. If the population of the bystander T cells becomes large enough, autoimmunity can arise, eventually after a long transient period.

A Transcritical Bifurcation in an Immune Response Model

The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We find a transcritical bifurcation that might explain two alternative scenarios: in one case the appearance of autoimmune responses and in another the suppression of the immune response.

Immune response dynamics

The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We determine the analytic formula that describes the fine balance between Regulatory T cells and T cells at controlled and immune response equilibrium states. We demonstrate that cytokine dependent growth exhibits a quorum T cell population threshold that determines if immune responses develop on activation. We determine the analytic formulas of T cell proliferation thresholds that allow us to study the sensibility of the quorum growth thresholds controlling immune responses.

Patents in new technologies

We present a new R&D investment function in a Cournot competition model inspired in the logistic equation. We do a full characterization of the associated game and study the short- and long-term economical effects derived from using this new R&D investment function. In particular, we find the existence of regions with multiple Nash investment equilibria. For low production costs, that can correspond to the production of old technologies, the long-term economical effects are not very sensitive to small changes in the efficiency of the R&D programmes neither to small changes in the market structure. However, for high production costs, that can correspond to the production of new technologies, the long-term economical effects are very sensitive to small changes in the efficiency of the R&D programmes and also to small changes in the market structure.

Flexibility in a Stackelberg leadership with differentiated goods

We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.

Torsion sensor based on a figure-of-eight cavity fibre laser

A figure-of-eight based fibre laser cavity is proposed for the measurement of torsion. In one of the loops a section of photonic crystal fibre is inserted, acting both as an optical filter and the sensing head. The laser emission depends on the optical filter polarization and length. A single lasing band is achieved with a full width at half maximum of 1.72 nm. The proposed sensor presents sensitivity to torsion of 7.13 pm/degree over a range of 180 . This configuration can also be used to measure optical power variations. Besides, due to the properties of the optical filter this sensor presents low sensitivity to temperature. (Some figures may appear in colour only in the online journal)

Dynamics of Immunological Models

We analyse the effect of the regulatory T cells (Tregs) in the local control of the immune responses by T cells. We obtain an explicit formula for the level of antigenic stimulation of T cells as a function of the concentration of T cells and the parameters of the model. The relation between the concentration of the T cells and the antigenic stimulation of T cells is an hysteresis, that is unfold for some parameter values. We study the appearance of autoimmunity from cross-reactivity between a pathogen and a self antigen or from bystander proliferation. We also study an asymmetry in the death rates. With this asymmetry we show that the antigenic stimulation of the Tregs is able to control locally the population size of Tregs. Other effects of this asymmetry are a faster immune response and an improvement in the simulations of the bystander proliferation. The rate of variation of the levels of antigenic stimulation determines if the outcome is an immune response or if Tregs are able to maintain control due to the presence of a transcritical bifurcation for some tuning between the antigenic stimuli of T cells and Tregs. This behavior is explained by the presence of a transcritical bifurcation.

On the convergence to Walrasian prices in random matching Edgeworthian economies

We show that for a specific class of random matching Edgeworthian economies, the expectation of the limiting equilibrium price coincides with the equilibrium price of the related Walrasian economies. This result extends to the study of economies in the presence of uncertainty within the multi-period Arrow-Debreu model, allowing to understand the dynamics of how beliefs survive and propagate through the market.

Bankruptcy Boundaries Determined by Patents

We use a new R&D investment function in a Cournot competition model inspired in the logistic equation. We present the full characterization of the associated game and study the short and long term economical effects derived from using this new R&D investment function. We observe the existence of four different Nash investment equilibria regions and do a full characterization of the boundaries of these regions.

Refractive index sensor using a Fabry-Perot cavity in polymer fiber

The possibility of using polymer fiber as a refractive index sensor is presented. The sensor is based on a Fabry-Perot interferometer formed at the tip of the polymer fiber. The interference is granted due to reflections between a fiber Bragg grating and the fiber end-face. The sensor was characterized to refractive index changes at constant temperature using a fast Fourier transform analysis of the interference signal. A sensitivity of −1.94 RIU⁻¹ was achieved with a resolution of 1 × 10⁻⁴ RIU and a cross sensitivity to temperature of 1× 10⁻⁴ RIU/T.