Multidimensional analysis of complex networks

Complex Networks analysis turn out to be a very promising field of research, testified by many research projects and works that span different fields. Those analysis have been usually focused on characterize a single aspect of the system and a study that considers many informative axes along with a network evolve is lacking. We propose a new multidimensional analysis that is able to inspect networks in the two most important dimensions, space and time. To achieve this goal, we studied them singularly and investigated how the variation of the constituting parameters drives changes to the network as a whole. By focusing on space dimension, we characterized spatial alteration in terms of abstraction levels. We proposed a novel algorithm that, by applying a fuzziness function, can reconstruct networks under different level of details. We verified that statistical indicators depend strongly on the granularity with which a system is described and on the class of networks. We keep fixed the space axes and we isolated the dynamics behind networks evolution process. We detected new instincts that trigger social networks utilization and spread the adoption of novel communities. We formalized this enhanced social network evolution by adopting special nodes (called sirens) that, thanks to their ability to attract new links, were able to construct efficient connection patterns. We simulated the dynamics of the system by considering three well-known growth models. Applying this framework to real and synthetic networks, we showed that the sirens, even when used for a limited time span, effectively shrink the time needed to get a network in mature state. In order to provide a concrete context of our findings, we formalized the cost of setting up such enhancement and provided the best combinations of system's parameters, such as number of sirens, time span of utilization and attractiveness.

Design, realization, and characterization of complex reaction networks in dynamic mechanically interlocked molecules

The experimental projects discussed in this thesis are all related to the field of artificial molecular machines, specifically to systems composed of pseudorotaxane and rotaxane architectures. The characterization of the peculiar properties of these mechano-molecules is frequently associated with the analysis and elucidation of complex reaction networks; this latter aspect represents the main focus and central thread tying my thesis work. In each chapter, a specific project is described as summarized below: the focus of the first chapter is the realization and characterization of a prototype model of a photoactivated molecular transporter based on a pseudorotaxane architecture; in the second chapter is reported the design, synthesis, and characterization of a [2]rotaxane endowed with a dibenzylammonium station and a novel photochromic unit that acts as a recognition site for a DB24C8 crown ether macrocycle; in the last chapter is described the synthesis and characterization of a [3]rotaxane in which the relative number of rings and stations can be changed on command.