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

Estudo comparativo da marcha de indivíduos hemiparéticos no solo e na esteira

The purpose of the study was to compare hemiparetic gait overground and on the treadmill. Seventeen chronic stroke patients were included in the study. They walked overground and on a treadmill level at the same speed. The Qualisys Medical AB motion analysis system was used to quantify the joint kinematic of the paretic lower limb and the spatio-temporal parameters on the two conditions: overground walking and treadmill walking on three samples of 5-minutes. During the first sample, the subjects walked on the treadmill with greater cadence, shorter stride length, shorter step time on the lower paretic limb, greater range of motion in the hip and knee, greater knee flexion at the initial contact, more extension of the knee and lower dorsiflexion of the ankle at the stance phase. It is important to emphasize that the maximal knee flexion and ankle dorsiflexion just occurred later on the treadmill. Comparisons between each walking sample on the treadmill hadn t revealed any changes on the gait parameters over time. Nonetheless, when analyzing the third walking sample on the treadmill and overground, some variables showed equivalence as such as the total range of motion of the hip, the knee angle at the initial contact and its maximal extension at the stance phase. In summary, walking on a treadmill, even thought having some influence on the familiarization process, haven t demonstrated a complete change in its characteristics of hemiparetic chronic patients