The mathematical part of the project is centered on the development of the theories of unimodular random graphs, point processes, and stochastic geometry, with an emphasis on dynamics on such random structures. Instances of mathematical tools involved, beyond unimodularity, are ergodic theory, mean-field techniques, spectral analysis, coupling techniques, and Palm calculus. The mathematical work on unimodular random networks is meant to analyze networks which are not necessarily embedded in the Euclidean space: how to define such random objects? how to evaluate their dimensions? what type of computational tools can one rely on to analyze them quantitatively? what classes of dynamics can they harbor? Instances of dynamics considered are navigations on graphs, optimizations on graphs, random walks and migrations on graphs, epidemics on graphs, scheduling and queuing on graphs, interference on graphs.
The application part of the project has a central component in communication networks. The mastering of the complexity of this class of systems is a major challenge worldwide. NEMO focused on the mastering of this complexity by stochastic geometry and random graph theory. It was based on a strong collaboration with Nokia Bell Laboratories Paris (NBLP). The first class of problems considered with NBLP concerned the interplay between beam management and user motion. The second class was the analysis of 5/6G cellular networks enhanced with Reconfigurable Intelligent Surfaces. A third class of questions concerned resource sharing with real-time constraints, which is of central importance for both the industrial applications of 5/6G networks and of WiFi type networks. The fourth set of questions concerned the analysis of non-terrestrial and in particular low Earth orbit satellite communication networks.
Another broad application domain investigated is that of biological networks. Three main directions of research were selected: neural network dynamics, epidemics on networks, and classification of phylogenetic networks.
The dissemination effort was thorough: 8 workshops were organized. 52 research papers were published, with a good equilibrium between math journal publications and IEEE type publications. One book on point processes was posted and another one on unimodularity is under preparation. 72 dissemination events (from poster to keynote lectures to radio interviews) were organized. The research achievements of the project members were recognized through two international and one national award, with, again, a good equilibrium between mathematics and communications. The work in NEMO also had an impact on the scientific policy concerning communication networks both in France (through two reports of the French Academy of Sciences) and at the European level. (through contributions to the SRIA).
