Berlin 2018 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 13: Networks: From Topology to Dynamics (joint session SOE/CPP/BP/DY)
SOE 13.8: Vortrag
Mittwoch, 14. März 2018, 11:15–11:30, MA 001
Probabilistic Quantifiers for Deterministic Spreading — •Justine Wolter1,2, Benedict Lünsmann3, Xiaozhu Zhang1,2, Malte Schröder1,2, and Marc Timme1,2,3 — 1Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), TU Dresden, Dresden, Germany — 2Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen — 3Max Planck Institute for the Physics of Complex Systems, 01069 Dresden
How do signals spread across dynamical systems? Spreading may be stochastic, e.g., during epidemic outbreaks or deterministic, e.g., in electrical or other supply networks. Due to mathematical challenges, it remains unknown how to robustly quantify even simple characteristics such as peak times or amplitudes of a spreading signal propagating across a network. Here we change the perspective and propose to analyze deterministic spreading dynamics employing concepts of probability theory. We characterize generic spreading dynamics by expectation values to work out a theory explicitly quantifying when and how strongly a perturbation initiated at one unit of a network impacts any other [1]. The theory provides this information as a function of the relative position of initially perturbed and responding unit as well as on the entire network topology. Furthermore, asymptotically exact approximation schemes enable to well predict previously inaccessible peak times and amplitudes. These insights may open up a new realm of quantifying characteristics of deterministic processes through probability theory. Ref.: [1] J. Wolter et al., http://arXiv.org/abs/1710.09687