Final Report Summary - NETADIS (Statistical Physics Approaches to Networks Across Disciplines) Networks are ubiquitous in our everyday life: they underpin the most advanced information and communication technologies. More generally they provide a compelling framework for addressing a wide range of complex problems, not only in the natural sciences and engineering but also in economics and the social sciences. Networks and network-related science are thus of central importance to human well-being as well as to economic, technological, and scientific competitiveness.Statistical physics offers a powerful set of concepts and methods to analyse problems of exactly the type posed by today’s key challenges in network science. While the European statistical physics community has an established tradition of coordinated cross-border research collaborations in this area, there has been so far no significant European coordination effort on the initial training side. NETADIS was designed to fill that gap and to train a cadre of future research leaders in advanced methods of analysis, inference, control and optimization of network structure and dynamics, thus maximizing the impact of statistical physics approaches across a broad range of application areas.NETADIS recruited 12 early stage researchers (ESRs), of which 7 were female; academic excellence was the primary selection criterion. The ESRs formed a distinctly international group, with home institutions being located in France, Italy, Germany, India, Armenia, Argentina and the Philippines. ESRs received training in network-wide events including a scientific kick-off meeting, an international summer school, two summer retreats and a final conference, as well as more specialized, subject-specific workshops. Training at these events covered both the relevant science as well as transferable skills, including e.g. workshops on presentation skills and entrepreneurship. The latter were delivered by the four private sector partners of NETADIS.An important part of the NETADIS network-wide training was the secondments programme, where ESRs spent two periods of around 2 months each away from their home institution. Secondments were hosted by a project partner pursuing research in the same application domain but with different methods, or deploying related methods in a different domain. Several of these secondments have resulted in joint publications, and all have contributed to strengthening scientific links between the ESRs and the project partners involved.Research for the NETADIS project was structured in a research matrix formed by and axis of three methodological areas (optimization and control; inference; dynamical processes on graphs) and a second axis of four application domains (systems biology and neurobiology; IT and communications; finance and socio-economic systems; laser physics), with ESR projects located at the relevant intersections.Highlights of results from NETADIS research include systematic methods for separating intrinsic and extrinsic noise in subnetworks of larger biological networks; new methods for modelling networks of protein interaction partners;information-theoretic limits to MicroRNA-mediated control of gene expression; perturbative and matrix product approaches to non-equilibrium steady states on networks; algorithms for minimizing message path lengths and traffic congestion in networks; quantitative predictions for the minimal number of initial targets needed to cover a network with a viral marketing campaign; exact solution of models of financial contagion incorporating liquidity dynamics; discovery of new dynamical phase transitions in random walks on networks; efficient simulation methods for networks of laser light modes, and construction of appropriate random network models; efficient approximation methods for inference of unobserved network variables from time trajectories of observed variables, and theoretical analysis of fundamental limitations to such inference.
