Research Domain
Mathematics & Foundation of Complex Systems

Research Leaders
Mario Rasetti

In general terms, a “complex system” is any system comprised of a great number of heterogeneous entities, where local interactions among entities create multiple levels of collective structure and organization. The specificity of complex systems resides in the emergence of non-trivial superstructures that often dominate the system behaviour and cannot be easily traced back to the properties of the constituent entities.

The Mathematics & Foundation of Complex Systems domain research on one hand aims at providing theoretical and analytical support to research in complex phenomena; on the other deals with a new field – for whose creation the ISI researchers gave a significant contribution – aiming at exploring new methods to extract information from data. These activities, performed by going beyond the known techniques typical of machine learning and data mining, are based mostly on topological and categorical approach. Particular areas of interest application include, e.g.:

I. neuroscience – brain and intelligence models; II. computation ‘beyond Turing’; III. relation between form and functions in living matter.

A general objective is to provide tools for systematically dealing with quantitative aspects for a complexity science theoretical framework, ranging from structure to dynamics, as well as to establish sound foundational principles for the construction of a reliable theory of multi-level, data based, complex systems.

In the context of globalization and the growing importance of long-distance interactions through a variety of networks, complex systems analysis (including direct observations and simulation experiments) can help people explore a variety of issues related to economic development, social cohesion, or the environment at different geographical scales.

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Steering Socio-technical Systems (S3)

S3 is a multipronged project thrusting a major effort to explore societal issues by complex systems, data and computational thinking science, in an integrated framework for mathematical, modelling and computational foundation of socio/econo-technical systems science, with a portfolio of case studies.

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ADnD: Algebraic-topological Detection of neurodegenerative Diseases

Deciphering the unfathomable workings of the brain is the tremendous challenge that neuroscience has been grappling over the past few decades.

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The shape of collaborations

A. Patania, G. Petri, F. Vaccarino

EPJ Data Science 20176:18 (2017)

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Insights into Brain Architectures from the Homological Scaffolds of Functional Connectivity Networks

L. Lord, P. Expert, H. M. Fernandes, G. Petri, T. J. Van Hartevelt, F. Vaccarino, G. Deco, F. Turkheimer, M. L. Kringelbach

Front. Syst. Neurosci. 10:85. doi: 10.3389/fnsys.2016.00085 (2016)