Complex Systems and Networks (CN)
Many of the challenges in modern society require to understand the complexity of biological, economic, financial, physical, social and technological networks. Beside the traditional difficulties which are inherent to the study of the components of these systems (e.g. cells, organizations, atoms, individuals and devices), over the last decades an additional (and often dominant) level of complexity has emerged, which derives from the interactions among components. In a world that is increasingly interconnected at the cultural, digital, economic, physical and social level, the body of knowledge developed by each discipline is becoming less and less exhaustive while the need for innovative, interdisciplinary approaches emerges forcefully.
The Theory of Complex Systems and the Science of Networks are modern approaches to the study of systems characterized by a large number of components, interconnected in irregular architectures, i.e. structures that are quite different from the ones traditionally considered within the natural and social sciences: indeed, while the interactions among atoms in simple materials can be represented as regular and symmetric lattices and those among social actors, or economic agents, as homogeneous structures, real-world networks of interactions among the constituents of cells, organisms, ecosystems, economies, societies and infrastructures turn out to be extremely heterogeneous.
Examples of recurrent structures in empirical networks are: the coexistence of elements (vertices) displaying such diverse numbers of connections that the notion of "average number of neighbours per node" becomes meaningless (scale-free property), the tendency of vertices with "neighbours in common" to be also connected between them (clustering or triadic closure), a larger cohesion within certain sets of vertices (community structure), the abundance of specific substructures (motifs). Complex systems also exhibit collective properties that emerge from the interactions among their consituent elements and cannot be traced back uniquely to the intrinsic properties of the latter ones.
Beside the need to characterise the complex structure of large-scale, real-world systems, understanding the consequences of structural complexity for the dynamics of the processes that typically take place on those systems has become more and more important. For instance, recent (economic, financial and health) crises have shown how the highly irregular and inhomogeneous structure of real networks (of firms, banks and people) deeply complicates the management, as well as the prediction, of stress and disease propagation in modern economies and societies: indeed, the phenomenology of these processes crucially depends on which vertices are hit first, how many vertices are directly connected to them and so on.
Finally, in many contexts (e.g. in ecology and economics) a strong interplay is observed between the structure of networks and the dynamics of the processes taking place on them: in fact, not only the underlying structure has an impact on the dynamics but also the dynamics has an impact on the underlying structure.
Structure of the track
The PhD track in Complex Systems and Networks offers a multidisciplinary, scientific background aimed at the empirical analysis and the mathematical modelling of complex systems, as well as their application to problems of societal relevance. The program, among the few of its kind at the international level, places theoretical research in complexity science as its core, distinctive component, emphasising methodolgical innovation (such as the introduction of novel quantitative methods of analysis).
The teaching program consists in doctoral courses that cover both a wide spectrum of theoretical knowledge (graph theory, statistical physics, information theory, stochastic processes, random matrices, optimization, machine learning) and a broad range of possible applications (to financial, economic, social, biological, neural, ecological, energetic, infrastructural systems). The theoretical methods introduced in the courses include techniques of pattern detection in empirical systems, time series analysis, network inference from partial information, physical models of complex systems and networks, noise filtering in networks. The applications include problems related to financial regulation, economic resilience, sustainability, ecological stability, (mis)information diffusion, health.
Beside the institutional courses, the program offers seminars held by international experts, visiting research and training periods abroad, co-tutorships and a constant supervision from the PhD advisor(s), the professors contributing to the track and their international collaborators.
Input and output profiles
Candidate PhD students willing to carry out research oriented towards theoretical modelling and methodological innovation should have a background in computer science, engineering, mathematics, physics, statistics or a related field while those who have more applied interests (to biology, economics, finance, social sciences, sustainability, etc.) should have a strong, quatitative background in the corresponding field.
The PhD track trains towards an academic career (e.g. in university departments or research centers), the public sector (e.g. in governmental institutions or statistical offices), the private environment (e.g. as data scientists).
For more information regarding the activities and the research personnel linked to the PhD track, please visit NETWORKS@IMT.