Asymptotic theory of time varying networks with memory and heterogeneous activation pattern

In this thesis work we develop a new generative model of social networks belonging to the family of Time Varying Networks. The importance of correctly modelling the mechanisms shaping the growth of a network and the dynamics of the edges activation and inactivation are of central importance in network science. Indeed, by means of generative models that mimic the real-world dynamics of contacts in social networks it is possible to forecast the outcome of an epidemic process, optimize the immunization campaign or optimally spread an information among individuals. This task can now be tackled taking advantage of the recent availability of large-scale, high-quality and time-resolved datasets. This wealth of digital data has allowed to deepen our understanding of the structure and properties of many real-world networks. Moreover, the empirical evidence of a temporal dimension in networks prompted the switch of paradigm from a static representation of graphs to a time varying one. In this work we exploit the Activity-Driven paradigm (a modeling tool belonging to the family of Time-Varying-Networks) to develop a general dynamical model that encodes fundamental mechanism shaping the social networks' topology and its temporal structure: social capital allocation and burstiness. The former accounts for the fact that individuals does not randomly invest their time and social interactions but they rather allocate it toward already known nodes of the network. The latter accounts for the heavy-tailed distributions of the inter-event time in social networks. We then empirically measure the properties of these two mechanisms from seven real-world datasets and develop a data-driven model, analytically solving it. We then check the results against numerical simulations and test our predictions with real-world datasets, finding a good agreement between the two. Moreover, we find and characterize a non-trivial interplay between burstiness and social capital allocation in the parameters phase space. Finally, we present a novel approach to the development of a complete generative model of Time-Varying-Networks. This model is inspired by the Kaufman's adjacent possible theory and is based on a generalized version of the Polya's urn. Remarkably, most of the complex and heterogeneous feature of real-world social networks are naturally reproduced by this dynamical model, together with many high-order topological properties (clustering coefficient, community structure etc.).

Interactions within heterogeneous systems of uncontrolled rectifiers for aircraft electrical power systems

There is an increase in the use of multi-pulse, rectifier-fed motor-drive equipment on board more-electric aircraft. Motor drives with feedback control appear as constant power loads to the rectifiers, which can cause instability of the DC filter capacitor voltage at the output of the rectifier. This problem can be exacerbated by interactions between rectifiers that share a common source impedance. In order that such a system can be analysed, there is a need for average, dynamic models of systems of rectifiers. In this study, an efficient, compact method for deriving the approximate, linear, large-signal, average models of two heterogeneous systems of rectifiers, which are fed from a common source impedance, is presented. The models give insight into significant interaction effects that occur between the converters, and that arise through the shared source impedance. First, a 6-pulse and doubly wound, transformer-fed, 12-pulse rectifier system is considered, followed by a 6-pulse and autotransformer-fed, 12-pulse rectifier system. The system models are validated against detailed simulations and laboratory prototypes, and key characteristics of the two system types are compared.

Synthesis and expression of a gene encoding a 48-residue repeat in the Pseudomonas syringae ice nucleation protein

The aim of this work was to construct short analogues of the repetitive water-binding domain of the Pseudomonas syringae ice nucleation protein, InaZ. Structural analysis of these analogues might provide data pertaining to the protein-water contacts that underlie ice nucleation. An artificial gene coding for a 48-mer repeat sequence from InaZ was synthesized from four oligodeoxyribonucleotides and ligated into the expression vector, pGEX2T. The recombinant vector was cloned in Escherichia coli and a glutathione S-transferase fusion protein obtained. This fusion protein displayed a low level of ice-nucleating activity when tested by a droplet freezing assay. The fusion protein could be cleaved with thrombin, providing a means for future recovery of the 48-mer peptide in amounts suitable for structural analysis by nuclear magnetic resonance spectroscopy.