@article{19864,
author = {{Meyer, Maurice and Frank, Maximilian and Massmann, Melina and Dumitrescu, Roman}},
journal = {{Proceedings of The 11th International Multi-Conference on Complexity, Informatics and Cybernetics (IMCIC 2020)}},
title = {{{Research and Consulting in Data-Driven Strategic Product Planning}}},
year = {{2020}},
}
@article{19866,
author = {{Meyer, Maurice and Frank, Maximilian and Massmann, Melina and Dumitrescu, Roman}},
journal = {{Journal of Systemics, Cybernetics and Informatics}},
number = {{2}},
pages = {{55--61}},
title = {{{Research and Consulting in Data-Driven Strategic Product Planning}}},
volume = {{18}},
year = {{2020}},
}
@article{19895,
author = {{Steiger, Sören and Pelster, Matthias}},
issn = {{0167-2681}},
journal = {{Journal of Economic Behavior & Organization}},
pages = {{503--522}},
title = {{{Social interactions and asset pricing bubbles}}},
doi = {{10.1016/j.jebo.2020.09.020}},
volume = {{179}},
year = {{2020}},
}
@inproceedings{19899,
abstract = {{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.}},
author = {{Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
booktitle = {{Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings}},
editor = {{Devismes , Stéphane and Mittal, Neeraj }},
isbn = {{978-3-030-64347-8}},
pages = {{65--80}},
publisher = {{Springer}},
title = {{{A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up}}},
doi = {{10.1007/978-3-030-64348-5_6}},
volume = {{12514}},
year = {{2020}},
}
@article{19938,
abstract = {{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. }},
author = {{McLachlan, Robert I and Offen, Christian}},
journal = {{Foundations of Computational Mathematics}},
number = {{6}},
pages = {{1363--1400}},
title = {{{Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation}}},
doi = {{10.1007/s10208-020-09454-z}},
volume = {{20}},
year = {{2020}},
}
@article{19939,
author = {{Kreusser, Lisa Maria and McLachlan, Robert I and Offen, Christian}},
issn = {{0951-7715}},
journal = {{Nonlinearity}},
number = {{5}},
pages = {{2335--2363}},
title = {{{Detection of high codimensional bifurcations in variational PDEs}}},
doi = {{10.1088/1361-6544/ab7293}},
volume = {{33}},
year = {{2020}},
}
@phdthesis{19947,
abstract = {{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.}},
author = {{Offen, Christian}},
publisher = {{Massey University}},
title = {{{Analysis of Hamiltonian boundary value problems and symplectic integration}}},
year = {{2020}},
}
@inproceedings{19953,
abstract = {{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.}},
author = {{Damke, Clemens and Melnikov, Vitaly and Hüllermeier, Eyke}},
booktitle = {{Proceedings of the 12th Asian Conference on Machine Learning (ACML 2020)}},
editor = {{Jialin Pan, Sinno and Sugiyama, Masashi}},
keywords = {{graph neural networks, Weisfeiler-Lehman test, cycle detection}},
location = {{Bangkok, Thailand}},
pages = {{49--64}},
publisher = {{PMLR}},
title = {{{A Novel Higher-order Weisfeiler-Lehman Graph Convolution}}},
volume = {{129}},
year = {{2020}},
}
@inproceedings{19965,
author = {{Grabo, Matti and Acar, Emre and Kenig, Eugeny}},
location = {{Cologne}},
title = {{{Modeling of a Latent Heat Storage System Consisting of Encapsulated PCM- Elements}}},
year = {{2020}},
}
@article{19973,
abstract = {{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.}},
author = {{Uhe, Benedikt and Kuball, Clara-Maria and Merklein, Marion and Meschut, Gerson}},
journal = {{Production Engineering}},
keywords = {{Self-piercing riveting, Joining technology, Rivet geometry, Multi-material design, High-strength steel, Aluminium}},
pages = {{417--423}},
title = {{{Improvement of a rivet geometry for the self-piercing riveting of high-strength steel and multi-material joints}}},
doi = {{10.1007/s11740-020-00973-w}},
volume = {{14}},
year = {{2020}},
}