Abstract
The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion is examined by mathematical modelling. We demonstrate that cytokine dependent growth exhibits a quorum T cell population threshold that determines if immune responses develop on activation. Secretion inhibition manipulates the growth dynamics and effectively increases the quorum threshold, i.e. to develop immune responses a higher number of T cells need to be activated. Thus Treg induced secretion inhibition can provide a mechanism for tissue specific regulation of the balance between suppression (control) and immune responses, a balance that can be varied at the local tissue level through the regulation of the local active Treg population size. However, nonspecific inhibition is prone to escape of initially controlled autoimmune T cells through cross reactivity to pathogens and bystander proliferation on unrelated immune responses.

Abstract
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.

Abstract
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.

Abstract
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 gam; 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 fully characterize the boundaries of these regions.

Abstract
Eating behavior adopted during adolescence may persist into adulthood. The aims of this study were to identify eating behavior patterns among Portuguese adolescents and to explore whether groups differ in terms of early life and family characteristics, severity of depressive symptoms, and body mass index (BMI) z-score. Participants were 3601 13-year-olds enrolled in the birth cohort Generation XXI. Eating behavior was assessed using the self-reported Adult Eating Behavior Questionnaire (AEBQ), validated in this sample. The severity of depressive symptoms was measured through the Beck Depression Inventory (BDI-II), and data on sociodemographic and anthropometrics were collected at birth and 13-years-old. Latent class analysis was conducted, and associations were estimated using multinomial logistic regression models. Five patterns of individuals were identified: Picky eating, Disinterest towards food, Food neophilia, Emotional eating, and Food attractiveness. The adolescents' sex, maternal education, BMI z-score, and severity of depressive symptoms were significantly associated with the identified patterns. In particular, adolescents with a higher BMI z-score were more likely in Food neophilia while individuals with more severe depressive symptoms were in the Picky eating, Emotional eating, and Food attractiveness patterns. These findings suggest a starting point for the development and planning of targeted public health interventions.

Abstract
Malnutrition is widespread among older adults, and its determinants may differ between countries. We compared Portuguese and Turkish non-institutionalized older adults regarding nutritional status, sociodemographic, health and anthropometric characteristics and studied the relationships between nutritional status and those characteristics. This cross-sectional study analyzed data from 430 Portuguese and 162 Turkish non-institutionalized older adults regarding sociodemographics, health conditions, the Mini-Nutritional Assessment (MNA-FF) and anthropometry. Turkish older adults were more likely to be malnourished or at risk of malnutrition and had lower average BMI but a higher calf circumference. A higher proportion of the Portuguese sample had tooth loss, diabetes, hypertension, oncologic diseases, kidney diseases, osteoarticular problems or eye problems, while less had anemia. A better nutritional status (higher MNA-FF score) was found among the Portuguese, males, people using dentures, those without tooth loss, hypertension, cardiovascular diseases, anemia or oncological diseases and was related to younger age, higher BMI and a higher calf circumference. Malnutrition and its risk were higher among older adults from Turkey, despite Portuguese older adults presenting a higher prevalence of chronic diseases. Being female, older age, tooth loss, hypertension, anemia, CVD or oncological disorders and having a lower BMI or CC were associated with higher rates of malnutrition among older adults from Portugal and Turkey.