Análises estatísticas em redes complexas: propriedades topológicas, críticas e dinâmicas

In this thesis, we address two issues of broad conceptual and practical relevance in the study of complex networks. The first is associated with the topological characterization of networks while the second relates to dynamical processes that occur on top of them. Regarding the first line of study, we initially designed a model for networks growth where preferential attachment includes: (i) connectivity and (ii) homophily (links between sites with similar characteristics are more likely). From this, we observe that the competition between these two aspects leads to a heterogeneous pattern of connections with the topological properties of the network showing quite interesting results. In particular, we emphasize that there is a region where the characteristics of sites play an important role not only for the rate at which they get links, but also for the number of connections which occur between sites with similar and dissimilar characteristics. Finally, we investigate the spread of epidemics on the network topology developed, whereas its dissemination follows the rules of the contact process. Using Monte Carlo simulations, we show that the competition between states (infected/healthy) sites, induces a transition between an active phase (presence of sick) and an inactive (no sick). In this context, we estimate the critical point of the transition phase through the cumulant Binder and ratio between moments of the order parameter. Then, using finite size scaling analysis, we determine the critical exponents associated with this transition

Avaliação da concentração de vitamina A materna e de neonatos prematuros e a termo

Vitamin A is an essential nutrient for many physiological processes such as growth and development, so that their adequate nutritional state is essential during pregnancy and lactation. Lactating women and children in breastfeeding are considered risk groups for vitamin A deficiency and some factors may increase the risk of vitamin A deficiency, such as prematurity. The aim of this work was to evaluate the vitamin A concentration in preterm and term lactating women and newborns by determination of retinol in maternal serum, umbilical cord serum and breast milk collected until 72 hours postpartum. 182 mothers were recruited and divided into preterm group (GPT; n = 118) and term group (GT, n = 64). In preterm group were also analyzed transition milk (7th-15th day; n = 68) and mature milk (30th-55th day; n = 46) samples. Retinol was analyzed by high-performance liquid chromatography (HPLC). Maternal retinol concentration in serum was 48.6 ± 12.3 µg/dL in GPT and 42.8 ± 16.3 µg/dL in the GT (p <0.01). Cord serum retinol was 20.4 ± 7.4 µg/dL in GPT and 23.2 ± 7.6 µg/dL in GT (p> 0.05). Among newborns, 43% of premature and 36% of term had low levels of serum retinol in umbilical cord (<20 µg/dL). In colostrum, the retinol in preterm and term groups had an average of 100.8 ± 49.0 µg/dL and 127.5 ± 65.1 µg/dL, respectively (p <0.05). The retinol average in preterm milk increased to 112.5 ± 49.7 µg/dL in transition phase and decreased to 57.2 ± 23.4 µg/dL in mature milk, differing significantly in all stages (p <0.05). When comparing with the recommendation of vitamin A intake (400 µg/day) GT colostrum reached the recommendation for infants, but in GPT the recommendation was not achieved at any stage. Mothers of premature infants had higher serum retinol than mothers at term; however, this was not reflected in serum retinol of umbilical cord, since premature had lower concentration of retinol. Such condition can be explained due to lower maternal physiological hemodilution and placental transfer of retinol to the fetus during preterm gestation. Comparison of retinol in colostrum showed lower concentrations in GPT; however the transition phase there was a significant increase of retinol content released by the mammary gland of preterm mothers. This situation highlights a specific physiological adaptation of prematurity, likely to more contribute to formation of hepatic reserves of retinol in premature infants.