Results and Publications

Nash equilibria for load balancing in networked power systems

Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics

Benjamin Schäfer, Christian Beck, Kazuyuki Aihara, Dirk Witthaut & Marc Timme, Nature Energy (2018).

The effect of energy trading is strong and comparable in size to the effect of renewables on the frequency fluctuations of a power grid, according to our new study published with collaborators from Goettingen, Juelich and Tokyo in Nature Energy (link).

We also found that splitting a large grid into small microgrids - as a way of integrating additional renewable power generation or creating smaller, mostly independent grids - will lead to larger frequency deviations which can potentially damage sensitive electronic devices.


Multiple types of fluctuations impact the collective dynamics of power grids and thus challenge their robust operation. Fluctuations result from processes as different as dynamically changing demands, energy trading and an increasing share of renewable power feed-in. Here we analyse principles underlying the dynamics and statistics of power grid frequency fluctuations. Considering frequency time series for a range of power grids, including grids in North America, Japan and Europe, we find a strong deviation from Gaussianity best described as Lévy-stable and q-Gaussian distributions. We present a coarse framework to analytically characterize the impact of arbitrary noise distributions, as well as a superstatistical approach that systematically interprets heavy tails and skewed distributions. We identify energy trading as a substantial contribution to today’s frequency fluctuations and effective damping of the grid as a controlling factor enabling reduction of fluctuation risks, with enhanced effects for small power grids.


Network dynamics of innovation processes

Iacopo Iacopini, Staša Milojević & Vito Latora, Physical Review Letters (2018).

The emergence of innovation can be modelled by using edge-reinfoced random walks over a complex network of concepts and ideas, according to our new study published with our collaborator Staša Milojević from Indiana University in Physical Review Letters (link).


Creativity and innovation are the underlying forces driving the growth of our society and economy. The dynamics of innovation has been modeled in different contexts as an evolutionary process or by using the Polya urn framework. We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks (RW) on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The network is co-evolving with the dynamical process taking place over it. In particular, i) biased random walkers move over a network with assigned topology, whose edge weights represent the strength of concept associations, and the transition matrix of the RW depends on the network weights (see Fig); ii) the network evolves in time through a reinforcement mechanism, in which the weight of an edge is increased by a quantity δw every time the edge is traversed by a walker. The presence of the network naturally accounts for the mechanism of the “adjacent possible”, and the model reproduces both the rate at which novelties emerge (Heaps’ law) and the correlations among them observed empirically. We show this by testing our model on synthetic small-world networks and on a real case, in which we consider the growth of knowledge in different scientific disciplines as a discovery process on an underlying network of relations among concepts that can be directly accessed and used from the datasets of 20 years of scientific articles. Edge-reinforced random walks on complex topologies offer a new modeling framework for the dynamics of correlated novelties and another example of co-evolution of processes and networks.


Simplicial models of social contagion

Iacopo Iacopini, Giovanni Petri, Alain Barrat & Vito Latora, arXiv preprint (2018).

New model of social contagion on simplicial complexes (link).


Complex networks have been successfully used to describe the spreading of a disease between the individuals of a population. Conversely, pairwise interactions are often not enough to characterize processes of social contagion, such as opinion formation or the adoption of novelties, where a more complex dynamics of peer influence and reinforcement mechanisms is at work. We introduce here a high-order model of social contagion in which a social system is represented by a simplicial complex and the contagion can occur, with different transmission rates, over the links or through interactions in groups of different sizes. Numerical simulations of the model on synthetic simplicial complexes and analytical results highlight the emergence of novel phenomena, such as the appearance of an explosive transition induced by the high-order interactions.