Complex Dynamics on Networks
Networks and graphs
are the most general mathematical description of a set of elements connected pairwise by a relation. Therefore, it is not surprising that graph theory has been successfully applied to a wide range of very different disciplines
, from physics to biology, to social science, computing, psychology, economy and chemistry.
In recent times, physicists have been mainly interested in networks as models of complex systems
and they have used them to describe condensed matter structures such as disordered materials, glasses, polymers, biomolecules. More recently, networks have become the main language for the description of communication networks, webs, social and economic systems, power grids, statistical models of algorithms, and many others interdisciplinary frameworks.
The function of networks in physics, however, is not purely descriptive. Geometry and topology
have a deep influence on the physical properties of complex systems. The network structure can indeed affect the dynamical and thermodynamical behaviour of the system it describes, and can give rise to surprising collective effects
Synchronization on Neural Networks
In Parma, we are studying dynamical models for synchronization on neural networks
in collaboration with the University of Granada. We are investigating spatially extended stochastic bistable systems
, with the specific purpose of understanding some of the fundamental functional features of neural networks
. Our aim is to give the description of some general mechanisms, in the simplest model and subsequently progressively make this model closer and closer to the physiology of neural cortical tissues
, according to the experimental results.
Some of the topics we address are the role of inhibition
and of synaptic plasticity
as well as the function played by the structural properties of the network
. Moreover we are focusing on the aspects of criticality
that have been shown to describe some characteristics of the neural activity, aiming at specifying some important details and properties found in this framework and gaining deeper insight in the mechanisms by which the system self-organizes
to a singular point.
Epidemics on Complex Networks
In Parma, we are dealing with the modelling of epidemic spreading on complex temporal networks
. We are investigating the dynamics of human interaction networks and its effects on epidemic spreading. Some of the topics we address are the role of memory
in network evolution and in epidemic spreading.
Moreover, we are focusing on adaptive temporal networks
which model the adaptive behaviours of populations exposed to epidemics, taking into account behavioural changes
due to awareness, symptoms onset and the attempt to reduce the risk of infection. We model and compare several epidemic control and containment measures
such as quarantine, contact tracing and sick-leave, analyzing their effectiveness in reducing the impact of an epidemic. We are also applying our adaptive temporal network models to the COVID-19 pandemic
, modelling some crucial features of COVID-19 transmission and effective control interventions.
On this topic we are collaborating with national and international groups such as the EPIcx lab at INSERM - Institut national de la santé et de la recherche médicale, Sorbonne Université in Paris, the MoBS Labs at Boston Northeastern University and the Institute for Scientific Interchange in Torino.