Complex Systems and Networks (CN)


Many challenges in modern society require a deep understanding of systems characterized by a large number of components, arranged in structures strongly differing from the ones traditionally considered within the natural and social sciences. The difficulties concerning the study of constituents (be they atoms, cells, devices, individuals, organizations) are, thus, accompanied by those concerning the study of their interactions.

In a world that is increasingly interconnected at any level, the body of knowledge developed by each discipline is becoming less and less exhaustive with the need for innovative approaches emerging forcefully. Complex systems theory and network science represent modern attempts to overcome the too simplistic pictures provided by specific domains, such as the one depicting interactions among atoms as regular lattices or the one depicting interactions among socio-economic actors in an "all with all" fashion.

Real-world networks of interactions turn out to be extremely heterogeneous, being characterized by structures such as i) the coexistence of elements (nodes or vertices) displaying such diverse numbers of connections that the notion of "average number of neighbors per node" becomes meaningless (scale-free property); ii) the tendency of vertices sharing many neighbours to be also inter-connected (clustering or triadic closure); iii) the abundance of specific substructures (motifs); iv) a larger cohesion within certain sets of vertices (community structure).

The need of characterizing the structural complexity of large-scale, real-world systems comes along the need of understanding its impact on the dynamics of the processes taking place on them. As recent (economic, financial, health) crises have shown, the highly irregular structure of real-world networks (of firms, banks, people) deeply complicates the prediction, as well as the management, of the propagation of shocks in modern economies and societies.

Finally, in contexts like ecology and economics, a strong interplay between the structure of networks and the dynamics of processes is observed with the latter having a non negligible impact on the former as well.

 Structure of the track 

The PhD track in Complex Systems and Networks offers an interdisciplinary program embracing the theoretical and computational tools of complexity science as well as their application to real-world biological, economic, social and technological systems. The program, among the few of its kind at the international level, emphasizes methodolgical innovation, placing theoretical research as its core, distinctive component.

The study plan integrates courses covering both a wide spectrum of theoretical knowledge (graph theory, information theory, machine learning, physics of complex systems, statistical mechanics of networks, stochastic processes) and a broad range of possible applications (to biological, ecological, economic, financial, infrastructural, neural, social systems). The basket of theoretical methods includes techniques to detect patterns in empirical systems, analyze time series, infer networked structures from partial information, build physical models of complex systems; the basket of applications includes problems related to ecological stability, economic resilience, financial regulation, (mis)information diffusion.

Beside the institutional courses, the program offers seminars held by international experts, visiting periods abroad, co-tutorships.

 Input and output profiles 

Candidate students willing to carry out research oriented towards methodological innovation should have a background in computer science, engineering, mathematics, physics, statistics or a related field while those having more applied interests (e.g. in biology, economics, finance, social sciences, sustainability) should have a strong, quatitative background in the corresponding field.

The PhD track trains towards an academic career (in university departments or research centers), the public sector (in governmental institutions or statistical offices), the private environment (as data scientists).

For more information regarding the activities and the research personnel linked to the track, please visit NETWORKS@IMT.