Foundations of Complex Systems

Information diffusion on a temporal network can be modeled by viral spreading processes such as the Susceptible-Infected (SI) spreading process. An infected node meaning that the node possesses the information could spread the information to a Susceptible node with a given spreading probability β whenever a contact happens between the two nodes. Progress has been made in the understanding of how temporal network features and the choice of the source node affect the prevalence, i.e. the percentage of nodes reached by the information.

In many complex systems, not only there are positive interactions promoting coordinated actions and activating collective behaviors but also prevalent are the negative interactions between agents suppressing and antagonizing them. For instance, in social networks people can be friends or foes. Such systems can best be modeled as “signed” networks. There had been considerable effort devoted to such signed interactions in social network literature; however, quantitative understanding of the generic impact of such signed interactions on network dynamics is still lacking.

Many complex systems are hierarchical; societies, economies, ecosystems, infrastructures, languages, they all develop hierarchies of their elements that emerge from networked interactions within the system and with the outside. These hierarchies evolve according to system-dependent mechanisms of interaction, such as selection in evolutionary biology, or rules of performance in human sports, and reflect the relevance of elements in performing a function in the system.

Many complex systems can be meaningfully coarse-grained into modules according to the pattern of interactions between the components or entities of the system. This coarse-graining provides a more interpretable view of the system. One such approach is to represent the system as a network and perform community detection. However, while many complex systems contain relevant information at multiple resolutions, most previous work on community detection has focused on discovering flat community structures, thus allowing information to be captured at a single resolution.

While compatibility of multiple contagious entities and heterogeneous adoptability of agents are omnipresent in social contagion, these factors are overlooked in traditional models of contagion processes. Here, we study, analytically and numerically, complex contagion processes in two directions. First [1], we study the competition of two spreading innovations focusing on the role of dual users. Competition with a preexisting technology Competition with a preexisting technology effectively suppresses the spread of a new innovation, but phases of coexistence are possible.

The traditional approach of physics proposes to characterize complex phenomena with simple idealized models, since this facilitates comprehension and the execution of controlled experiments. But, the emerging information era prompted statistical modeling as an important complement to the traditional approach, enabling the synthesization of useful information from large amounts of data.

We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we study the epidemic size of Susceptible-Infected-Recovered, SIR, models and the epidemic threshold of Susceptible-Infected-Susceptible, SIS, models. Interestingly, we find that while the presence of tightly connected clusters inhibits SIR processes, it speeds up SIS phenomena.

Knowledge is the keynote for innovation and economic growth. The effective management of organizational knowledge networks is the key for attaining competitive advantage. Applications of knowledge networks analysis already include several knowledge-intensive firms, such as consulting firms, manufacturing firms, telecommunications firms, healthcare and pharmaceuticals industry, biotechnology industry, banks and financial services companies, petroleum companies, etc. [1].

Spreading processes are ubiquitous in natural and artificial systems, being disease contagion and rumor spreading the most important of these processes due to their practical relevance. Most of the literature focuses on continuous-time Markov chains (CTMC), for which exponential inter-event times are imposed. Despite its mathematical elegance and soundness for the analysis of critical behavior, its computational cost is often prohibitive.

Assortative mixing is the tendency of nodes with a common attribute (also referred to node metadata) to be connected to each other in a network. It is typically measured using Newman’s assortativity coefficient [1], which is the network analogue of Pearson’s correlation. Just as correlation plays an important role in identifying relationships between pairs of variables, assortativity plays a fundamental role in understanding how a network is organised with respect to a given attribute of the nodes.