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 - GEN
AB - In backward error analysis, an approximate solution to an equation is
compared to the exact solution to a nearby "modified" equation. In numerical
ordinary differential equations, the two agree up to any power of the step
size. If the differential equation has a geometric property then the modified
equation may share it. In this way, known properties of differential equations
can be applied to the approximation. But for partial differential equations,
the known modified equations are of higher order, limiting applicability of the
theory. Therefore, we study symmetric solutions of discretized partial
differential equations that arise from a discrete variational principle. These
symmetric solutions obey infinite-dimensional functional equations. We show
that these equations admit second-order modified equations which are
Hamiltonian and also possess first-order Lagrangians in modified coordinates.
The modified equation and its associated structures are computed explicitly for
the case of rotating travelling waves in the nonlinear wave equation.
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19941
T2 - arXiv:2006.14172
TI - Backward error analysis for variational discretisations of partial differential equations
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 - 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, Vitalik
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
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 - CONF
AU - Müller, Michelle
AU - Neumann, Jürgen
AU - Gutt, Dominik
AU - Kundisch, Dennis
ID - 19782
T2 - Proceedings of the 41th International Conference on Information Systems (ICIS)
TI - Toss a Coin to your Host - How Guests End up Paying for the Cost of Regulatory Policies
ER -
TY - GEN
AU - Kramer, Paul
ID - 18638
TI - Comparison of Zero-Knowledge Range Proofs
ER -
TY - THES
AU - Heinzel, Joachim
ID - 15824
TI - Essays on the Theory of Industrial Organization: Credence Goods, Vertical Relations and Product Bundling
ER -
TY - THES
AU - Setzer, Alexander
ID - 18520
TI - Local Graph Transformation Primitives For Some Basic Problems In Overlay Networks
ER -
TY - GEN
ED - Troschitz, Juliane
ED - Vorderbrüggen, Julian
ED - Kupfer, Robert
ED - Gude, Maik
ED - Meschut, Gerson
ID - 20119
T2 - Applied Sciences
TI - Joining of Thermoplastic Composites with Metals Using Resistance ElementWelding
ER -