The availability of information about complex networks is severely restrained by issues, such as confidentiality and privacy. This poses a problem when analysing properties of networks that are of...Show moreThe availability of information about complex networks is severely restrained by issues, such as confidentiality and privacy. This poses a problem when analysing properties of networks that are of relevance to the general public. One example is the study of the resilience of banking networks to financial distress. We discuss a random graph model that reconstructs such unavailable networks, based on information that is either node specific or specific to groups of nodes. The procedure is determined by enforcing renormalizability, i.e. consistency when modelling renormalizations of networks. Then we propose a weighted semi-renormalizable extension of this model. Both models are tested on an empirical trade network, by analysing how well they captures properties that are commonly used to characterize networks. Their performances are shown to closely resemble that of the (weighted) fitness-induced Configuration Model.Show less
Spontaneous synchronization of coupled oscillators is ubiquitous in biological and physical systems. Among the many attempts to model such behavior, the Kuramoto model has proven to be mathematical...Show moreSpontaneous synchronization of coupled oscillators is ubiquitous in biological and physical systems. Among the many attempts to model such behavior, the Kuramoto model has proven to be mathematical tractable yet sufficiently rich to capture this phenomenology. In the past three decades, numerous extensive studies have been devoted to the model. The first aim of this thesis is to review these works. In particular, we discuss the rich phenomenology of the Kuramoto model defined on complex networks, which has mainly been studied in the statistical physics literature. Moreover, we consider several rigorous results obtained in the mathematical literature concerning the synchronization behavior of the Kuramoto model with a mean-field coupling. As a second aim, we investigate a Kuramoto-like model defined on the hierarchical lattice. To this end, we provide a preliminary analysis for a renormalization program in order to rigorously describe the behavior of this model.Show less
