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Theory of Multi-Scale Neuronal Networks

The focus of this group is the investigation of mechanisms that shape the activity in neuronal networks on multiple spatial scales. The group builds theoretical descriptions from the microscopic level of single cells and synapses to effective equations capturing interacting brain areas. This allows the discovery of the mechanisms that underly and shape the observed phenomena of correlated and oscillatory neuronal activity.

Theory of multi-scale neuronal networksTeam members from left to right: Dr. David Dahmen, Jonas Stapmanns, Prof. Dr. Moritz Helias, Dr. Jannis Schücker, Tobias Kühn, Christian Keup

The organization of the cerebral cortex extends over a wide range of spatial scales, from the specificity of single synapses to hierarchically organized networks of entire cortical areas. Focusing on each of these scales separately may miss out important properties of neuronal networks that only emerge from the interplay of different scales. Understanding and identifying the fundamental and experimentally testable mechanisms by which these phenomena interact requires theoretical abstractions and reductions; reproducing experimental observations by a simulation model of identical complexity as the original biological system is not sufficient.

The group of Moritz Helias aims at theoretical descriptions that integrate different spatial scales to provide a set of powerful analytical tools. Their predictions, in quantitative agreement with full numerical simulations of neural networks, allow the identification of underlying mechanisms shaping the correlated and oscillatory activity in cortical networks.

This requires the application, extension, and adaptation of methods from theoretical physics and mathematics, such as static and dynamic mean-field theory, Fokker-Planck equations, stochastic differential equations and the path integral formalism.

multiscale theory


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