Publikationen

We use the recently introduced Weyr characteristic of linear relations in Cn and its relation with the Kronecker canonical form of matrix pencils to describe their dimension. Then, this is applied to study one-dimensional perturbations of linear relations.

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of error resulting from a finite dictionary and only finitely-many data points in the generation of the surrogate model have to be taken into account. We generalize the rigorous analysis of the approximation error to the control setting while simultaneously reducing the impact of the curse of dimensionality by using a recently proposed bilinear approach. In particular, we establish uniform bounds on the approximation error of state-dependent quantities like constraints or a performance index enabling data-based optimal and predictive control with guarantees.

We study the geometric structure of the drift dynamics of Irreversible port-Hamiltonian systems. This drift dynamics is defined with respect to a product of Poisson brackets, reflecting the interconnection structure and the constitutive relations of the irreversible phenomena occuring in the system. We characterise this product of Poisson brackets using a covariant 4-tensor and an associated function. We derive various conditions for which this 4-tensor and the associated function may be reduced to a product of almost Poisson brackets.