Inhalt des Dokuments
AbsolventenSeminar • Numerische Mathematik
Dieses Semester wird das Seminar online auf Zoom stattfinden.
Verantwortliche Dozenten: 
Prof. Dr. Tobias Breiten [1],  Prof. Dr. Christian Mehl
[2], Prof. Dr. Volker Mehrmann
[3]

Koordination:  Ines Ahrens
[4] 
Termine:  Do
10:0012:00 
Inhalt:  Vorträge von
Bachelor und Masterstudenten, Doktoranden, Postdocs und manchmal auch
Gästen zu aktuellen
Forschungsthemen 
Datum  Zeit  Vortragende(r)  Titel 

Do 05.11.  10:15 Uhr  Vorbesprechung  
Tim Moser  A Riemannian Framework
for Ecient H2Optimal Model Reduction of PortHamiltonian Systems  
Do
12.11.  10:15 Uhr  
Do
19.11.  10:15 Uhr  Volker Mehrmann [5]  Structured
backward errors for eigenvalues associated with portHamiltonian
descriptor systems 
Do
26.11.  10:15 Uhr  Martin Isoz  Simulations of
fullyresolved particleladen flows: fundamentals and challenges for
model order reduction 
Do
03.12.  10:15 Uhr  
Do
10.12.  10:15 Uhr  Amon Lahr  Reducedorder design
of suboptimal H∞ controllers using rational Krylov
subspaces 
Daniel Bankmann  Multilevel Optimization Problems with Linear
DifferentialAlgebraic Equations  
Do 17.12.  10:15 Uhr  Florian Stelzer [6]  Deep Learning
with a Single Neuron: Folding a Deep Neural Network in Time using
FeedbackModulated Delay Loops 
Malte
Krümel  IndexAware Model Reduction for
Optimization of Gas Networks  
Do 07.01.  10:15 Uhr  Tobias Breiten [7]  Error bounds
for portHamiltonian model and controllerreduction based on system
balancing 
Felix Black [8]  Model reduction with dynamically transformed modes:
offline stage and path minimization  
Do 14.01.  10:15 Uhr  
Do 21.01.  10:15 Uhr  Ruili Zhang
 Eigenvalues problem of GHamiltonian
matrix 
Do 28.01.  10:15 Uhr  Onkar Jadhav  Hierarchical
modeling to establish a model order reduction framework for financial
risk analysis 
Miriam
Goldack  A simple shifted Proper Orthogonal
Decomposition suitable for large scale problems  
Do 04.02.  10:15 Uhr  Simon
Bäse  Timelimited balanced truncation model
order reduction for descriptor systems 
Do 11.02.  10:15 Uhr  
Do
18.02.  10:15 Uhr  Philipp Schulze [9]  Application
of the Variable Projection Method in Nonlinear Model Reduction

Riccardo Morandin [10]  PortHamiltonian modeling and discretization of isothermal
gas networks  
Do
25.02.  10:15 Uhr  Ines Ahrens [11]  A simple success
check for delay differentialalgebraic equations 
Fabian Common  Optimal Control for
linear portHamiltonian descriptor systems  
Di
09.03.  16:15
Uhr  Marine Froidevaux  PDE eigenvalue iterations with applications in dissipative
twodimensional photonic crystals 
Christoph
Zimmer  Temporal Discretization of Constrained
Partial Differential
Equations 
Marine Froidevaux (TU Berlin)
Dienstag, 09. März 2021
PDE eigenvalue iterations with
applications in dissipative twodimensional photonic
crystals
We consider PDE eigenvalue problems as
they occur in the modeling of twodimensional photonic crystals. In
particular we discuss the modelling of the electric permittivity in
the case of dissipative materials and discuss how to deal with the
occurring nonlinearities in the eigenvalue. Further, we extend the
inverse power method to the case of infinitedimensional and
nonselfadjoint operators.
This is joint work with Robert
Altmann (U Augsburg).
Christoph Zimmer (TU Berlin)
Dienstag, 09. März 2021
Temporal Discretization of Constrained
Partial Differential Equations
I am going to
practice my defense talk for my dissertation. Feedback is very
welcome.
Examples of constrained partial differential
equations (PDEs) appear in all kinds of physical fields such as fluid
dynamics, thermodynamics, electrodynamics, mechanics, chemical
kinetics, as well as in multiphysical applications where different
physical domains are coupled. In this talk, we analyze the application
of time integration schemes to constrained PDEs. Among other things,
time integration schemes can be used to prove the existence of
solutions or to derive temporal error bounds which are independent of
the mesh width of spatial discretization. These bounds are vital for
spatially discretized systems, since the temporal convergence order of
finite systems is maybe higher as of infinitedimensional ones but
fades into these, if the spatial mesh gets finer. In this talk, we
derive spatial meshindependent convergence orders for RungeKutta
methods applied to constrained PDEs with timeindependent constants.
The results are supported by numerical examples. In the other half of
this talk, we use the implicit Euler method to prove the existence of
solutions of constrained PDEs with constraints with timedependent
coefficients.
Ines Ahrens (TU Berlin)
Donnerstag, 25. Februar 2021
A simple success check for delay differentialalgebraic equations
Solutions of differentialalgebraic equations (DAEs) may depend on
derivatives of some of its equations. Structural analysis, like the
Sigma Method, can determine how often each equation needs to be
differentiated. Unfortunately, this number is not always correct, such
that a postprocessing step is required to validate the result. Such a
postprocessing step, the socalled success check, is provided in the
Sigma Method.
In this talk, I will show a
generalization of this success check which can validate any given
number of differentiations. This result leads to a first success check
for delay differentialalgebraic equations (DDAE), where solutions may
depend on derivatives and future evaluations of some
equations.
Fabian Common (TU Berlin)
Donnerstag, 25. Februar 2021
Optimal Control for linear portHamiltonian descriptor systems
In control theory we are interested in properties of control
systems. These include regularity and consistency, which state, if a
system has a solution and if this solution is unique. Other properties
are stability, stabilizability, controllability, observability,
reconstructability and passivity.
In this thesis we have a closer
look on control systems with a special structure, called linear
portHamiltonian descriptor systems. We will see how we can use the
portHamiltonian structure to our advantage to gain some of these
properties.
After we obtain a system with the required properties
by feedback, we are interested in finding a costoptimal control. Here
we will see, that we can apply the same theory for output feedback as
we use for state feedback. We will also have a look, if the
pHstructure gives us advantages regarding KarushKuhnTucker systems
and the associated Riccatiequations.
Philipp Schulze (TU Berlin)
Donnerstag, 18. Februar 2021
Application of the Variable Projection Method in Nonlinear Model Reduction
Classical model reduction methods are usually based on identifying
suitable lowdimensional linear subspaces and subsequent
(Petrov)Galerkin projection of the fullorder model (FOM). However,
for systems whose dynamics feature the transport of sharp fronts, such
as shocks, the FOM solution can usually not be wellapproximated by a
lowdimensional linear subspace. In such cases, the solution may still
approximately evolve on a lowdimensional nonlinear manifold which
motivates the usage of nonlinear model reduction methods. A special
class of nonlinear model reduction methods is based on approximating
the solution by a linear combination of transformed basis functions
where the coordinate transformation aims to mimic the behavior of the
transport within the system.
In this talk we consider the
following problem: Given snapshot data of the FOM solution we seek for
an optimal lowdimensional approximation based on a linear combination
of transformed basis functions. The corresponding minimization problem
is a socalled separable nonlinear leastsquares problem, since a
subset of the optimization parameters occurs linearly. Exploiting this
special structure, we show how the variable projection may be used to
replace the original optimization problem by another one with a
reduced number of parameters. By means of numerical examples, we
illustrate that this application of the variable projection method may
lead to a significant speedup when computing an optimal approximation
of the snapshot data.
Riccardo Morandin (TU Berlin)
Donnerstag, 18. Februar 2021
PortHamiltonian modeling and
discretization of isothermal gas networks
In this
talk we introduce a modeling paradigm for gas networks, based on
portHamiltonian descriptor systems (pHDAE). I will present three
different PDE models to represent pipes containing isothermal gas,
with an increasing degree of accuracy. These models are then replaced
with finitedimensional pHDAEs, through spacediscretization, or
manipulation of the explicit solution. Simplified pHDAE models for
valves and compressors are also introduced.
It is then
shown how to interconnect the network while preserving mass, energy,
and the portHamiltonian structure, introducing pipe junctions,
sources and sinks. The three gas pipe models are allowed to appear at
the same time as different edges of the network. The resulting system
is a semiexplicit nonlinear differentialalgebraic equation of index
2.
I shortly present an algorithm that extracts necessary
and sufficient conditions for the nonsingularity of the DAE from the
structure of the graph associated to the gas network. As a byproduct
of this algorithm, one can achieve index reduction, while at the same
time preserving the pHDAE structure of the system. One can then apply
structurepreserving timediscretization methods, for example the
implicit midpoint rule, or an associated partitioned RungeKutta
scheme.
A partial numerical implementation of these results
is shown.
If time allows for it, some details missing because of
time constraints can be discussed at the end of the talk.
Simon Michael Bäse (TU Berlin)
Donnerstag, 04. Februar 2021
Timelimited balanced
truncation model order reduction for descriptor systems
Balanced truncation is a wellknown model order reduction
technique for largescale systems. In recent years, timelimited
balanced truncation, which restricts the system Gramians to finite
time intervals, has been investigated for different system types. We
extend the ideas to linear timeinvariant continuoustime descriptor
systems using the framework of projected generalized Lyapunov
equations. The formulation of the resulting Lyapunov equations is
challenging since the righthand sides are unknown a priori. We
propose Krylov subspace methods for the efficient computation of the
righthand sides for different system structures. Since the righthand
sides may become indefinite, we use an LDLT factorization based ADI
iteration to solve the Lyapunov equations and obtain the system
balancing transformation. Comparing the timelimited to the classical
approach in numerical experiments, we observe a steeper decay of the
Hankel singular values. This behavior renders useful, especially when
employing lowrank approximation techniques. Further, we show that
timelimited balanced truncation can deliver reducedorder models that
are more accurate in the prescribed time
domain.
Onkar Jadhav (TU Berlin)
Donnerstag, 28. Januar 2021
Hierarchical modeling to establish a model order reduction framework for financial risk analysis
A parametric model order reduction (MOR) approach for simulating
the high dimensional models arising in financial risk analysis is
proposed.
We implement the proper orthogonal decomposition (POD)
approach to generate small model approximations for the high
dimensional parametric convectiondiffusion reaction partial
differential equations (PDE). The proposed technique uses an adaptive
greedy sampling approach based on surrogate modeling to efficiently
locate the most relevant training parameters, thus generating the
optimal reduced basis. The best suitable reduced model is procured
such that the total error is less than the userdefined tolerance. The
three major errors considered are the discretization error associated
with the full model obtained by discretizing the PDE, the model order
reduction error, and the parameter sampling error.
The developed
technique is analyzed, implemented, and tested on industrial data of
different financial instruments under two prominent models (onefactor
and twofactor HullWhite models).
The results illustrate that
the reduced model provides a significant speedup with excellent
accuracy over a full model approach, demonstrating its potential
applications in the historical or Monte Carlo value at risk
calculations.
Miriam Goldack (TU Berlin)
Donnerstag, 28. Januar 2021
A simple shifted Proper Orthogonal Decomposition suitable for large scale problems
In 2018 Reiss et. al introduced the shifted Proper Orthogonal
Decomposition (POD) to speed up the convergence when decomposing
fields of transport dominated systems with the help of the POD. The
method builds on the idea that a single traveling wave or moving
localized structure can be perfectly described by its wave
profile and a timedependent shift. Therefore, the shifted POD
decomposes transport fields by shifting the data field in a so called
comoving frame, in which the wave is stationary and can be
described by a few spatial basis functions determined with the help of
the POD. In the presence of multiple transports, the decomposition
procedure becomes more complex and costly, because high
dimensional nonlinear optimization problems have to be solved.
In this talk, I will present a new shifted POD method, which
is a simplification of the formulation used in [1]. In contrast to the
former formulation, the new method allows to minimize the
singularvaluebased objective function without Newtontype
methods and is therefore well suited for largescale problems. I will
provide results for 1D and 2D datasets. The latter stem from
simulations of incompressible NavierStokes equations, with moving
object boundaries, such as moving wings of an insect or two moving
cylinders at Reynolds number 200.
[1] Reiss, Julius.
"Optimizationbased modal decomposition for systems with multiple
transports." arXiv preprint arXiv:2002.11789
(2020).
Ruili Zhang (Beijing Jiaotong University and TU Berlin)
Donnerstag, 21. Januar 2021
Eigenvalues problem of GHamiltonian
matrix
We find that the linearization of the
DrudeLorentz mode has GHamiltonian structure, and its
eigenvalue problem is actually the eigenvalue problem of GHamiltonian
matrix. The eigenvalues of a GHamiltonian matrix are symmetric with
respect to the imaginary axis. Its eigenvalues move out of the
imaginary only when two different kinds of eigenvalues collide on the
imaginary axis. To give the structurepreserving numerical computation
for the eigenvalues of a GHamiltonian matrix, we view the
GHamiltonian matrix as a generation of a Hamiltonian matrix and
GskewHamiltonian matrix as a generation of a skewHamiltonian matrix
by replacing iJ with a Hermitian matrix G. We generate the idea in the
ref [1] and give some relative lemmas about the GHamiltonian matrix.
[1] P. Benner, R. Byers, V. Mehrmann, and H.
Xu, Numerical computation of deflating subspaces of
skewHamiltonian/Hamiltonian pencils. SIAM Journal on Matrix Analysis
and Applications, 24(1), (2002)
Tobias Breiten (TU Berlin)
Donnerstag, 07. Januar 2021
Error bounds for
portHamiltonian model and controllerreduction based on system
balancing
Linear quadratic Gaussian (LQG) control
design for portHamiltonian systems is studied. A recently proposed
method from the literature is reviewed and modified such that the
resulting controllers have a portHamiltonian (pH) realization. Based
on this new modification, a reducedorder controller is obtained by
truncation of a balanced system. The approach is shown to be closely
related to classical LQG balanced truncation and shares a similar a
priori error bound with respect to the gap metric. With regard to this
error bound, a theoretically optimal pHrepresentation is derived.
Consequences for pHpreserving balanced truncation model reduction are
discussed and shown to yield two different classical
$mathcal{H}_infty$error bounds.
Felix Black (TU Berlin)
Donnerstag, 07. Januar 2021
Model reduction with dynamically transformed modes: offline stage and path minimization
The key goal of model order reduction is to determine high fidelity
approximations of solutions of largescale dynamical systems to reduce
computational effort. Many classical model order reduction methods are
formulated in a projection framework; the solution to the original
system is approximated within a suitable lowdimensional subspace. The
particular way how the subspace is determined is one of the distinct
features of the different model reduction methods. Commonly, the
subspace is determined by solving a minimization problem for the basis
vectors that form the subspace, and the full order solution is
approximated via a linear combination of the fixed basis vectors with
timedependent coefficients. If the dynamical system exhibits
advective transport, however, classical methods often fail to produce
lowdimensional models that result in a high fidelity approximation.
One strategy to remedy this problem is the shifted proper orthogonal
decomposition (shifted POD, see [1]), or, more generally, a
projectionbased ansatz with dynamically transformed modes (see [2]),
which extends the classical approximation ansatz by introducing
transformation operators associated with the basis vectors. Those
transformation operators are parametrized by paths in suitable vector
spaces, allowing the (now nonstationary) subspace to cope with the
advection. However, while in the classical approach, it is sufficient
to solve a minimization problem that depends only on the basis
vectors, the approach with dynamically transformed modes requires to
solve a minimization problem that depends on the basis vectors, as
well as the timedependent coefficients and also the path variables
that parametrize the transformations. In this talk, we discuss the
resulting minimization problem for the determination of suitable basis
vectors, coefficients, and paths, and aim to prove that, under certain
assumptions, there exist solutions.
References:
[1] J.
Reiss, P. Schulze, J. Sesterhenn, V. Mehrmann, The Shifted Proper
Orthogonal Decomposition: A Mode Decomposition for Multiple Transport
Phenomena, SIAM J. Sci. Comput. 40 (2018), no. 3, A1322  A1344.
[2] F. Black, P. Schulze, B. Unger, Projectionbased model
reduction with dynamically transformed modes, ESAIM: Math. Model.
Numer. Anal. 54 (2020), no. 6, 2011  2043.
Florian Stelzer (TU Berlin)
Donnerstag, 17. Dezember 2020
Deep Learning with a Single Neuron:
Folding a Deep Neural Network in Time using FeedbackModulated Delay
Loops
Deep neural networks are among the most
widely applied machine learning tools showing outstanding performance
in a broad range of tasks. We present a method for folding a deep
neural network of arbitrary size into a single neuron with multiple
timedelayed feedback loops. This singleneuron deep neural network
comprises only a single nonlinearity and appropriately adjusted
modulations of the feedback signals. The network states emerge in time
as a temporal unfolding of the neuron's dynamics. By adjusting the
feedbackmodulation within the loops, we adapt the network's
connection weights. These connection weights are determined via a
modified backpropagation algorithm that we designed for such types of
networks. Our approach fully recovers standard Deep Neural Networks
(DNN), encompasses sparse DNNs, and extends the DNN concept toward
dynamical systems implementations. The new method, which we call
Foldedintime DNN (FitDNN), exhibits promising performance in a set
of benchmark tasks.
F. Stelzer, A. Röhm, R. Vicente, I.
Fischer and S. Yanchuk, Deep Learning with a Single Neuron: Folding a
Deep Neural Network in Time using FeedbackModulated Delay Loops. See
arxiv.org/abs/2011.10115 [12].
Malte Krümel (TU Berlin)
Donnerstag, 17. Dezember 2020
IndexAware Model Reduction for
Optimization of Gas Networks
Optimization
problems of gas networks became increasingly important in the age of
energy transition. Solving them numerically poses many challenges and
requires model order reduction (MOR) of nonlinear
differentialalgebraicequations (DAE). The underlying model consists
of 1D Euler equations for flow modelling, Kirchhoff’s law and
further boundary conditions that describe the dynamics and relations
between elemtents of a directed graph. Applying reasonable
simplifications and spatial discretization leads to a DAE system. The
system is reformulated to obtain an InputOutput system that has
traceability index2.
We will first look at an often used
approach of reducing the index to an ODE system. For such systems
common largescale MOR can be applied. Because of computational issues
this approach has some disadvantages. Thus, we will explore the
approach of IndexAware MOR. Here, the system is decoupled into
differential, index1 and index2 equations via projections. The
decoupled system can now be reduced by making use of the properties of
each type of equations. The talk will conclude with the outlook to
incorporating the nonlinear part of the model into the model
reduction process and testing the reduced model in optimal control.
Amon Lahr (TU Berlin)
Donnerstag, 10. Dezember 2020
Reducedorder design of suboptimal H∞ controllers using rational Krylov subspaces
In the field of robust control, H∞ control provides an
established framework to design control laws guaranteeing stability
and performance over a range of perturbations of the nominal system
model. The underlying mathematical problem is usually separated into
finding the (sub)optimal attenuation (γiteration), and designing a
stabilizing controller for which the H∞ norm of the closedloop
transfer function is not greater than γ. For largescale systems,
especially the γgammaiteration proves to be computationally
demanding as it requires the exact solution of two algebraic Riccati
equations (ARE) in every step of the bisection method. Furthermore,
the dimension of the obtained control law needs to be reduced for most
practical applications.
In this talk, we introduce some of
the challenges related to reducedorder design of H∞
controllers. Furthermore, an accelerated implementation of the
γiteration is presented, which is based on lowrank approximations
of the ARE solutions using rational Krylov subspaces. Therein, a
reducedorder controller is constructed and verified at each bisection
step using a largescale H∞ norm computation method and the
calculation of a few eigenvalues of the closedloop matrix. The
results are discussed by means of numerical examples arising from
control of partial differential equations.
Daniel Bankmann (TU Berlin)
Donnerstag, 10. Dezember 2020
Multilevel Optimization Problems with Linear DifferentialAlgebraic Equations
I'm going to practice my defense talk for my dissertation. The talk
is supposed to last no more than 30 minutes. Feedback is very
welcome.
We discuss different multilevel optimization
problems in the context of linear differentialalgebraic equations. On
the one hand, we address multilevel optimal control problems, where
sensitivity information of the necessary conditions of the optimal
control problem can be used to compute solutions of the upper level
problem. When the upper level is given by a nonlinear leastsquares
problem, we present a step size estimator. On the other hand, we show
how the analytic center of the passivity LMI can be used as a good
starting point in the computation of the passivity
radius.
Martin Isoz (UCT Praque)
Donnerstag, 26. November 2020
Simulations of fullyresolved particleladen flows: fundamentals and challenges for model order reduction
Particleladen flows are present in numerous aspects of daytoday life ranging from technical applications such as fluidisation or filtration to medicinal problems, e.g. behavior of clots in blood vessels. Nevertheless, computational fluid dynamics (CFD) simulations containing freely moving and irreguralry shaped bodies are still a challenging topic. More so, if the bodies are large enough to affect the fluid flow and distributed densely enough to come in contact both with each other and with the computational domain boundaries. In this talk, we present a finite volumebased CFD solver for modeling flowinduced movement of interacting irregular bodies. The modeling approach uses a hybrid fictitious domainimmersed boundary method (HFDIB) for inclusion of the solids into the computational domain. The bodies movement and contacts are solved via the discrete element method (DEM). Unfortunately, the coupled HFDIBDEM model structure causes significant limitations with respect to applications of standard projectionbased methods of model order reduction (MOR). While we focus mostly on the HFDIBDEM solver development, the talk is concluded by the challenges the HFDIBDEM approach poses for MOR.
Volker Mehrmann (TU Berlin)
Donnerstag, 19. November 2020
Structured backward errors
for eigenvalues associated with portHamiltonian descriptor systems
When computing the eigenstructure of matrix
pencils associated with the passivity analysis of perturbed
portHamiltonian descriptor systems using a structured generalized
eigenvalue method, one should make sure that the computed spectrum
satises the symmetries that corresponds to this structure and the
underlying physical system. We perform a backward error analysis and
show that for matrix pencils associated with portHamiltonian
descriptor systems and a given computed eigenstructure with the
correct symmetry structure, there always exists a nearby
portHamiltonian descriptor system with exactly that eigenstructure.
We also derive bounds for how near this system is and show that the
stability radius of the system plays a role in that bound.
V. Mehrmann and P. Van Dooren, Structured backward errors for
eigenvalues of linear portHamiltonian descriptor systems, To appear
in SIAM Journal Matrix Analysis and Applications, 2020. See
arxiv.org/abs/2005.04744 [13].
Tim Moser (TU München)
Donnerstag, 05. November 2020
A Riemannian Framework for Ecient H2Optimal Model Reduction of PortHamiltonian Systems
The portHamiltonian systems paradigm provides a powerful framework
for the network modeling of multiphysics systems. By exploiting
inherent system characteristics such as passivity, the modeling in
portHamiltonian form also facilitates the subsequent controller
design. Therefore it is advantageous to preserve the portHamiltonian
structure in the model reduction process for which different
approaches have been proposed (see e.g. [1], [2]).
In [1],
a modified version of the iterative rational Krylov algorithm
(IRKAPH) was proposed for the H2optimal model reduction of
portHamilonian systems. Since IRKAPH is based on PetrovGalerkin
projections, certain degrees of freedom must be given up in order to
preserve the portHamiltonian structure. This inevitably leads to the
fact that it is generally not possible to satisfy all necessary H2
optimality conditions in this projective framework.
We
address this issue and propose a novel Riemannian framework for the
H2optimal reduction of portHamiltonian systems. We incorporate
geometric constraints using the Riemannian problem formulation of [3]
and exploit the computationally efficient poleresidue formulation of
the H2error proposed in [4]. By this means, preservation of the
portHamiltonian structure and H2optimality upon convergence are
guaranteed and the framework is also accessible for the reduction of
largescale systems.
References
[1] S. Gugercin, R.
V. Polyuga, C. Beattie, and A. van der Schaft,
"Structurepreserving tangential interpolation for model
reduction of portHamiltonian systems," Automatica, vol. 48, no.
9, pp. 19631974, 2012.
[2] R. V. Polyuga and A. J. van der
Schaft, "Effort and flowconstraint reduction methods for
structure preserving model reduction of portHamiltonian
systems," Systems & Control Letters, vol. 61, no. 3, pp.
412421, 2012.
[3] K. Sato, "Riemannian optimal model
reduction of linear portHamiltonian systems," Automatica, vol.
93, pp. 428434, 2018.
[4] L. Meier and D. Luenberger,
"Approximation of linear constant systems," IEEE
Transactions on Automatic Control, vol. 12, no. 5, pp. 585588,
1967.
Rückblick
 Absolventen Seminar SS 20 [14]
 Absolventen Seminar WS 19/20 [15]
 Absolventen Seminar SS 19 [16]
 Absolventen Seminar WS 18/19 [17]
 Absolventen Seminar SS 18 [18]
 Absolventen Seminar WS 17/18 [19]
 Absolventen Seminar SS 17 [20]
 Absolventen Seminar WS 16/17 [21]
 Absolventen Seminar SS 16 [22]
 Absolventen Seminar WS 15/16 [23]
 Absolventen Seminar SS 15 [24]
 Absolventen Seminar WS 14/15 [25]
 Absolventen Seminar SS 14 [26]
 Absolventen Seminar WS 13/14 [27]
 Absolventen Seminar SS 13 [28]
 Absolventen Seminar WS 12/13 [29]
 Absolventen Seminar SS 12 [30]
 Absolventen Seminar WS 11/12 [31]
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