Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Prof. Dr. Gabriel Wittum, Goethe Center for Scientific Computing (G-CSC), Goethe University Frankfurt, am Thu, Feb. 23, 2006 um 15:30 Uhr im HS 9 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Towards Simulation of Neuronal Signal Processing" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

hiermit herzlich einladen.

Series A - General Colloquium:

The intention is to present general information not only to experts, but also to students and guests from outside the mathematical institutes.

Towards Simulation of Neuronal Signal Processing

The crucial feature of neuronal ensembles is their high complexity and variability. This makes modelling and computation very difficult, in particular for detailed models based on first principles. The problem starts with modelling geometry, which has to extract the essential features from those highly complex and variable phenotypes and at the same time has to take in to account the stochastic variability. Moreover, models of the highly complex processes which are living on these geometries are far from being well established, since those are highly complex too and couple on a hierarchy of scales in space and time. Simulating such systems always puts the whole approach to test, including modeling, numerical methods and software implementations. In combination with validation based on experimental data, all components have to be enhanced to reach a reliable solving strategy.

To handle problems of this complexity, new mathematical methods and software tools are required. In recent years, new approaches such as parallel adaptive multigrid methods and corresponding software tools have been developed allowing to treat problems of huge complexity. In the lecture we present an approach for the simulation of signal processing in neurons. This is an outline of work to be done in this highly complex field. Part of this approach is a method to reconstruct the geometric structure of neurons from data measured by 2-photon microscopy in vivo. Being able to reconstruct neural geometries and network connectivities from in vivo measured data is the basis of understanding coding of motoric perceptions and long term plasticity which is one of the main topics of neuroscience. Other issues are compartment models and upscaling.