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 multiple-input-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(More)
This work introduces the empirical cross-gramian for multiple-input-multiple-output systems. The cross-gramian is a tool for reducing the state space of control systems, by conjoining controllability and observability information into a single matrix and does not require balancing. Its empirical gramian variant extends the applicability of the cross-gramian(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)
The cross gramian matrix can be used for model order reduction as well as system identification of linear control systems, which are frequently used in the sciences. The empirical cross gramian is solely computed from trajectories and hence extends beyond linear state-space systems to nonlinear systems. In this work the applicability of the empirical cross(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)