TY - JOUR
AU - Meyer, Maurice
AU - Frank, Maximilian
AU - Massmann, Melina
AU - Dumitrescu, Roman
ID - 19864
JF - Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)
TI - Research and Consulting in Data-Driven Strategic Product Planning
ER -
TY - JOUR
AU - Meyer, Maurice
AU - Frank, Maximilian
AU - Massmann, Melina
AU - Dumitrescu, Roman
ID - 19866
IS - 2
JF - Journal of Systemics, Cybernetics and Informatics
TI - Research and Consulting in Data-Driven Strategic Product Planning
VL - 18
ER -
TY - JOUR
AU - Steiger, Sören
AU - Pelster, Matthias
ID - 19895
JF - Journal of Economic Behavior & Organization
SN - 0167-2681
TI - Social interactions and asset pricing bubbles
VL - 179
ER -
TY - CONF
AB - Most existing robot formation problems seek a target formation of a certain
minimal and, thus, efficient structure. Examples include the Gathering
and the Chain-Formation problem. In this work, we study formation problems that
try to reach a maximal structure, supporting for example an efficient
coverage in exploration scenarios. A recent example is the NASA Shapeshifter
project, which describes how the robots form a relay chain along which gathered
data from extraterrestrial cave explorations may be sent to a home base.
As a first step towards understanding such maximization tasks, we introduce
and study the Max-Chain-Formation problem, where $n$ robots are ordered along a
winding, potentially self-intersecting chain and must form a connected,
straight line of maximal length connecting its two endpoints. We propose and
analyze strategies in a discrete and in a continuous time model. In the
discrete case, we give a complete analysis if all robots are initially
collinear, showing that the worst-case time to reach an
$\varepsilon$-approximation is upper bounded by $\mathcal{O}(n^2 \cdot \log
(n/\varepsilon))$ and lower bounded by $\Omega(n^2 \cdot~\log
(1/\varepsilon))$. If one endpoint of the chain remains stationary, this result
can be extended to the non-collinear case. If both endpoints move, we identify
a family of instances whose runtime is unbounded. For the continuous model, we
give a strategy with an optimal runtime bound of $\Theta(n)$. Avoiding an
unbounded runtime similar to the discrete case relies crucially on a
counter-intuitive aspect of the strategy: slowing down the endpoints while all
other robots move at full speed. Surprisingly, we can show that a similar trick
does not work in the discrete model.
AU - Castenow, Jannik
AU - Kling, Peter
AU - Knollmann, Till
AU - Meyer auf der Heide, Friedhelm
ED - Devismes , Stéphane
ED - Mittal, Neeraj
ID - 19899
SN - 978-3-030-64347-8
T2 - Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings
TI - A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up
VL - 12514
ER -
TY - JOUR
AB - We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of the breaking of umbilic bifurcations by nonysmplectic integrators. We discover extra structure induced from certain types of boundary value problems, including classical Dirichlet problems, that is useful to locate bifurcations. Geodesics connecting two points are an example of a Hamiltonian boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator that easily computes geodesics and their bifurcations. Finally, we study the periodic pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian systems. It is not preserved by either symplectic on nonsymplectic integrators, but in some circumstances symplecticity greatly reduces the error.
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19938
IS - 6
JF - Foundations of Computational Mathematics
TI - Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation
VL - 20
ER -
TY - JOUR
AU - Kreusser, Lisa Maria
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19939
IS - 5
JF - Nonlinearity
SN - 0951-7715
TI - Detection of high codimensional bifurcations in variational PDEs
VL - 33
ER -
TY - THES
AB - Ordinary differential equations (ODEs) and partial differential equations (PDEs) arise
in most scientific disciplines that make use of mathematical techniques. As exact solutions are in general not computable, numerical methods are used to obtain approximate
solutions. In order to draw valid conclusions from numerical computations, it is crucial
to understand which qualitative aspects numerical solutions have in common with the
exact solution. Symplecticity is a subtle notion that is related to a rich family of geometric properties of Hamiltonian systems. While the effects of preserving symplecticity
under discretisation on long-term behaviour of motions is classically well known, in this
thesis
(a) the role of symplecticity for the bifurcation behaviour of solutions to Hamiltonian
boundary value problems is explained. In parameter dependent systems at a bifurcation
point the solution set to a boundary value problem changes qualitatively. Bifurcation
problems are systematically translated into the framework of classical catastrophe theory. It is proved that existing classification results in catastrophe theory apply to
persistent bifurcations of Hamiltonian boundary value problems. Further results for
symmetric settings are derived.
(b) It is proved that to preserve generic bifurcations under discretisation it is necessary and sufficient to preserve the symplectic structure of the problem.
(c) The catastrophe theory framework for Hamiltonian ODEs is extended to PDEs
with variational structure. Recognition equations for A-series singularities for functionals on Banach spaces are derived and used in a numerical example to locate high-codimensional bifurcations.
(d) The potential of symplectic integration for infinite-dimensional Lie-Poisson systems (Burgers’ equation, KdV, fluid equations, . . . ) using Clebsch variables is analysed.
It is shown that the advantages of symplectic integration can outweigh the disadvantages of integrating over a larger phase space introduced by a Clebsch representation.
(e) Finally, the preservation of variational structure of symmetric solutions in multisymplectic PDEs by multisymplectic integrators on the example of (phase-rotating)
travelling waves in the nonlinear wave equation is discussed.
AU - Offen, Christian
ID - 19947
TI - Analysis of Hamiltonian boundary value problems and symplectic integration
ER -
TY - CONF
AB - Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator that is based on the 2-dimensional WL test. We formally show that the resulting 2-WL-GNN architecture is more discriminative than existing GNN approaches. This theoretical result is complemented by experimental studies using synthetic and real data. On multiple common graph classification benchmarks, we demonstrate that the proposed model is competitive with state-of-the-art graph kernels and GNNs.
AU - Damke, Clemens
AU - Melnikov, Vitaly
AU - Hüllermeier, Eyke
ED - Jialin Pan, Sinno
ED - Sugiyama, Masashi
ID - 19953
KW - graph neural networks
KW - Weisfeiler-Lehman test
KW - cycle detection
T2 - Proceedings of the 12th Asian Conference on Machine Learning (ACML 2020)
TI - A Novel Higher-order Weisfeiler-Lehman Graph Convolution
VL - 129
ER -
TY - CONF
AU - Grabo, Matti
AU - Acar, Emre
AU - Kenig, Eugeny
ID - 19965
TI - Modeling of a Latent Heat Storage System Consisting of Encapsulated PCM- Elements
ER -
TY - JOUR
AB - As a result of lightweight design, increased use is being made of high-strength steel and aluminium in car bodies. Self-piercing riveting is an established technique for joining these materials. The dissimilar properties of the two materials have led to a number of different rivet geometries in the past. Each rivet geometry fulfils the requirements of the materials within a limited range. In the present investigation, an improved rivet geometry is developed, which permits the reliable joining of two material combinations that could only be joined by two different rivet geometries up until now. Material combination 1 consists of high-strength steel on both sides, while material combination 2 comprises aluminium on the punch side and high-strength steel on the die side. The material flow and the stress and strain conditions prevailing during the joining process are analysed by means of numerical simulation. The rivet geometry is then improved step-by-step on the basis of this analysis. Finally, the improved rivet geometry is manufactured and the findings of the investigation are verified in experimental joining tests.
AU - Uhe, Benedikt
AU - Kuball, Clara-Maria
AU - Merklein, Marion
AU - Meschut, Gerson
ID - 19973
JF - Production Engineering
KW - Self-piercing riveting
KW - Joining technology
KW - Rivet geometry
KW - Multi-material design
KW - High-strength steel
KW - Aluminium
TI - Improvement of a rivet geometry for the self-piercing riveting of high-strength steel and multi-material joints
VL - 14
ER -