The aims of the present study were analyze the fatigue process at distinct intensity efforts and to investigate its occurrence as interactions at distinct body changes during exercise, using complex network models. For this, participants were submitted to four different running intensities until exhaustion, accomplished in a non-motorized treadmill using a tethered system. The intensities were selected according to critical power model. Mechanical (force, peak power, mean power, velocity and work) and physiological related parameters (heart rate, blood lactate, time until peak blood lactate concentration (lactate time), lean mass, anaerobic and aerobic capacities) and IPAQ score were obtained during exercises and it was used to construction of four complex network models. Such models have both, theoretical and mathematical value, and enables us to perceive new insights that go beyond conventional analysis. From these, we ranked the influences of each node at the fatigue process. Our results shows that nodes, links and network metrics are sensibility according to increase of efforts intensities, been the velocity a key factor to exercise maintenance at models/intensities 1 and 2 (higher time efforts) and force and power at models 3 and 4, highlighting mechanical variables in the exhaustion occurrence and even training prescription applications.

Sports and exercise today are popular for both amateurs and athletes. However, we continue to seek the best ways to analyze best athlete performances and develop specific tools that may help scientists and people in general to analyze athletic achievement. Standard statistics and cause-and-effect research, when applied in isolation, typically do not answer most scientific questions. The human body is a complex holistic system exchanging data during activities, as has been shown in the emerging field of network physiology. However, the literature lacks studies regarding sports performance, running, exercise, and more specifically, sprinter athletes analyzed mathematically through complex network modeling. Here, we propose complex models to jointly analyze distinct tests and variables from track sprinter athletes in an untargeted manner. Through complex propositions, we have incorporated mathematical and computational modeling to analyze anthropometric, biomechanics, and physiological interactions in running exercise conditions. Exercise testing associated with complex network and mathematical outputs make it possible to identify which responses may be critical during running. The physiological basis, aerobic, and biomechanics variables together may play a crucial role in performance. Coaches, trainers, and runners can focus on improving specific outputs that together help toward individuals’ goals. Moreover, our type of analysis can inspire the study and analysis of other complex sport scenarios.

Cascading failures are very disruptive events that can damage critical infrastructure such as electrical and telecommunication networks. They start with a single-point failure and spread fast through the networks, sometimes causing the collapse of the whole system. We study and classify three containment strategies for cascading failures. Additionally, we propose a simple dynamic model for cascading failures in scale-free networks considering random failures and targeted attack scenarios. Our results allowed us to mathematically describe the behavior of the process and to test three strategies to protect the network against the cascade.

Ao Rei eterno, ao Deus único, imortal, invisível e real, seja toda honra e glória para todo o sempre. Porque dEle, por Ele e para Ele são todas as coisas.A minha amada família, pelo apoio completo em todos os momentos.A minha orientadora Profa. Dra. Fúlvia de Barros Manchado Gobatto, exemplo de pessoa e profissional, pelos preciosos ensinamentos, orientação, parceria, dedicação e amizade.Ao Prof. Dr. Cláudio Alexandre Gobatto, pelos valorosos conhecimentos compartilhados, palavras inspiradoras, ideias, amizade e profissionalismo.Ao Prof. PhD Theodore Gyle Lewis, da Naval Postgraduate School (CA), por me inspirar a sonhar além, pelo aprendizado constante, amor pela ciência, motivação e exemplo de vida.Aos professores participantes das bancas de qualificação e defesa: Prof.