[info per studenti]


Link alla p
agina del corso

Fondamenti di automatica

(Ing. Matematica, L, 10 cfu, 2 sem)

Link alla pagina del corso
Complessità nei sistemi e nelle reti

(LM, 5 cfu, 1 sem, 2 emisem)


Link alla pagina del corso
Dinamica dei sistemi complessi

(LM, corso integrato, 5+5 cfu, 1 sem)



[info per studenti delle lauree magistrali]

Se siete interessati a studi di carattere generale riguardanti la dinamica dei sistemi complessi e le loro applicazioni, in particolare a temi quali la dinamica non lineare, il caos, le reti complesse, i sistemi adattativi, potete considerare di inserire nel vostro piano di studi qualcuno di questi corsi, attivi presso il Campus Leonardo:

Teoria dei sistemi (Dinamica non lineare) (5 cfu, 1 sem, 1 emisem), docente Sergio Rinaldi
Systems theory (Nonlinear dynamics) (5 cfu, 1 sem, 1 emisem), docente Fabio Dercole
Complessità nei sistemi e nelle reti
(5 cfu, 1 sem, 2 emisem), docente Carlo Piccardi

Dinamica dei sistemi complessi
(5+5 cfu, 1 sem),
corso integrato

Per qualunque informazione in merito a questi corsi sieti invitati a rivolgervi ai rispettivi docenti.


Last update: April 2, 2019


Carlo Piccardi

DEIB - Dipartimento di Elettronica, Informazione e Bioingegneria
Politecnico di Milano
Piazza Leonardo da Vinci 32
20133 Milano, Italy

tel (++39) 02 2399 3566
fax (++39) 02 2399 3412
e-mail carlo.piccardi@polimi.it
web page http://home.deib.polimi.it/piccardi/




    [research]
Click here for details on recent research activities (some with codes and data available).

    [publications]
Check the list of my publications on peer reviewed journals (or visit my Google Scholar page).

    [research highlights]
F. Dercole, F. Della Rossa, C. Piccardi, Direct reciprocity and model-predictive rationality explain network reciprocity over social ties, Scientific Reports, 9, 5367, 2019. [doi]



Since M. A. Nowak & R. May’s (1992) influential paper, limiting each agent’s interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments—reciprocal cooperation and unconditional defection—in a networked prisoner’s dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.
C. Piccardi and L. Tajoli, Complexity, centralization, and fragility in economic networks, PLoS One, 13(11), e0208265, 2018. [doi]





















Trade networks, across which countries distribute their products, are crucial components of the globalized world economy. Their structure affects the mechanism of propagation of shocks from country to country, as observed in a very sharp way in the past decade, characterized by economic uncertainty in many parts of the world. Such trade structures are strongly heterogeneous across products, given the different features of the countries which buy and sell goods. By using a diversified pool of indicators from network science and product complexity theory, we quantitatively demonstrate that, overall, products with higher complexity—i.e., with larger technological content and/or number of components—are traded through more centralized networks—i.e., with a smaller number of countries concentrating most of the export flow. Since centralized networks are known to be more vulnerable, we argue that the current composition of production and trading is associated to high fragility at the level of the most complex—thus strategic—products.
M. Bastos, C. Piccardi, M. Levy, N. McRoberts, and M. Lubell, Core-periphery or decentralized? Topological shifts of specialized information on Twitter, Social Networks, 52, 282-293, 2018. [doi]




















In this paper we investigate shifts in Twitter network topology resulting from the type of information being shared. We identified communities matching areas of agricultural expertise and measured the core-periphery centralization of network formations resulting from users sharing generic versus specialized information. We found that centralization increases when specialized information is shared and that the network adopts decentralized formations as conversations become more generic. The results are consistent with classical diffusion models positing that specialized information comes with greater centralization, but they also show that users favor decentralized formations, which can foster community cohesion, when spreading specialized information is secondary.


   [cv]

I am Full Professor at Politecnico di Milano. My teaching activity is in the area of complex systems and networks, dynamical systems and automatic control, both to undergraduate and graduate students of the Politecnico schools of engineering. I also teach in the PhD program of my Department (DEIB), mostly in the area of complex systems.

My research interests are focused on several topics concerning complex systems. Some recent areas of research are:

  • Structural properties of networks, with applications in economics, finance, and social sciences;
  • Spreading processes on complex networks;
  • Synchronization of networks of dynamical systems;
  • Reduced models for nonlinear systems, and their use for solving control and parameter estimation problems; 
  • Application of optimal control techniques to nonlinear systems; 
  • The use of numerical methods for bifurcation analysis of nonlinear systems, including continuation methods and harmonic-balance techniques; 
  • The analysis of structural properties of cooperative systems.