Christian Himpe

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Theta oscillations are considered crucial mechanisms in neuronal communication across brain areas, required for consolidation and retrieval of fear memories. One form of inhibitory learning allowing adaptive control of fear memory is extinction, a deficit of which leads to maladaptive fear expression potentially leading to anxiety disorders. Behavioral(More)
This work introduces the empirical cross gramian for multipleinput-multiple-output systems. The cross gramian is a tool for model reduction of the state space of control systems, which conjoins controllability and observability information into a single matrix and does not require balancing. Its empirical variant extends the application of the cross gramian(More)
Over the recent years the importance of numerical experiments has gradually been more recognized. Nonetheless, sufficient documentation of how computational results have been obtained is often not available. Especially in the scientific computing and applied mathematics domain this is crucial, since numerical experiments are usually employed to verify the(More)
Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so called system Gramian matrices were developed in linear system theory for applications such as model order reduction of control systems. Empirical Gramian matrices are an extension to the system Gramians for(More)
Dynamical systems of large order appear in many applications. For an efficient simulation it can become necessary to reduce the system dimension using a reliable model order reduction method, in particular in a many-query context when the system is to be solved for varying parameters and input signals. Nowadays, it is often required that the models include(More)
In this contribution we present an accelerated optimization-based approach for combined state and parameter reduction of a parametrized forward model, which is used to construct a surrogate model in a Bayesian inverse problem setting. Following the ideas presented in Lieberman et al. (SIAM J. Sci. Comput. 32(5), 2523–2542, 2010), our approach is based on a(More)