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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)

- Christian Himpe, Mario Ohlberger
- ArXiv
- 2013

A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical Gramians not only extended this concept to nonlinear systems but also provided a uniform computational method. This work… (More)

- Christian Himpe, Mario Ohlberger
- ArXiv
- 2013

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)

- Jörg Fehr, Jan Heiland, Christian Himpe, Jens Saak
- ArXiv
- 2016

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)

- Christian Himpe
- ArXiv
- 2016

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)

- Christian Himpe, Mario Ohlberger
- ArXiv
- 2015

The cross gramian matrix is a tool for model reduction and system identification, but it is only computable for square control systems. For symmetric control systems the cross gramian possesses a useful relation to the associated system’s Hankel singular values. Yet, many real-life models are neither square nor symmetric. In this work, concepts from… (More)

- Christian Himpe, Mario Ohlberger
- Adv. Comput. Math.
- 2015

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)

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)

- Christian Himpe, Mario Ohlberger
- ECC
- 2014

We recently introduced the joint gramian for combined state and parameter reduction [C. Himpe and M. Ohlberger. CrossGramian Based Combined State and Parameter Reduction for Large-Scale Control Systems. arXiv:1302.0634, 2013], which is applied in this work to reduce a parametrized linear time-varying control system modeling a hyperbolic network. The… (More)