@article{LueckeWinkelmannHeitzigetal., author = {L{\"u}cke, Marvin and Winkelmann, Stefanie and Heitzig, Jobst and Molkenthin, Nora and Koltai, P{\´e}ter}, title = {Learning interpretable collective variables for spreading processes on networks}, series = {Physical Review E}, volume = {109}, journal = {Physical Review E}, number = {2}, doi = {10.1103/PhysRevE.109.L022301}, pages = {L022301}, abstract = {Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barab{\´a}si model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.}, language = {en} } @article{LueckeHeitzigKoltaietal., author = {L{\"u}cke, Marvin and Heitzig, Jobst and Koltai, P{\´e}ter and Molkethin, Nora and Winkelmann, Stefanie}, title = {Large population limits of Markov processes on random networks}, series = {Stochastic Processes and their Applications}, volume = {166}, journal = {Stochastic Processes and their Applications}, doi = {10.1016/j.spa.2023.09.007}, abstract = {We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called "voter model" on Erdős-R{\´e}nyi random graphs, on the stochastic block model, as well as on random regular graphs. Moreover, a heterogeneous population of agents is studied. For each of these types of interaction networks, we specify the convergence conditions in dependency on the corresponding model parameters.}, language = {en} }