---
_id: '64865'
abstract:
- lang: eng
text: We provide a method to systematically construct vector fields for which the
dynamics display transitions corresponding to a desired hierarchical connection
structure. This structure is given as a finite set of directed graphs $\mathbf{G}_1,\dotsc,\mathbf{G}_N$
(the lower level), together with another digraph $\mathbfΓ$ on $N$ vertices (the
top level). The dynamic realizations of $\mathbf{G}_1,\dotsc,\mathbf{G}_N$ are
heteroclinic networks and they can be thought of as individual connection patterns
on a given set of states. Edges in $\mathbfΓ$ correspond to transitions between
these different patterns. In our construction, the connections given through $\mathbfΓ$
are not heteroclinic, but excitable with zero threshold. This describes a dynamical
transition between two invariant sets where every $δ$-neighborhood of the first
set contains an initial condition with $ω$-limit in the second set. Thus, we prove
a theorem that allows the systematic creation of hierarchical networks that are
excitable on the top level, and heteroclinic on the lower level. Our results modify
and extend the simplex realization method by Ashwin & Postlethwaite.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Alexander
full_name: Lohse, Alexander
last_name: Lohse
citation:
ama: von der Gracht S, Lohse A. Design of Hierarchical Excitable Networks. arXiv:260306157.
Published online 2026.
apa: von der Gracht, S., & Lohse, A. (2026). Design of Hierarchical Excitable
Networks. In arXiv:2603.06157.
bibtex: '@article{von der Gracht_Lohse_2026, title={Design of Hierarchical Excitable
Networks}, journal={arXiv:2603.06157}, author={von der Gracht, Sören and Lohse,
Alexander}, year={2026} }'
chicago: Gracht, Sören von der, and Alexander Lohse. “Design of Hierarchical Excitable
Networks.” ArXiv:2603.06157, 2026.
ieee: S. von der Gracht and A. Lohse, “Design of Hierarchical Excitable Networks,”
arXiv:2603.06157. 2026.
mla: von der Gracht, Sören, and Alexander Lohse. “Design of Hierarchical Excitable
Networks.” ArXiv:2603.06157, 2026.
short: S. von der Gracht, A. Lohse, ArXiv:2603.06157 (2026).
date_created: 2026-03-09T08:22:58Z
date_updated: 2026-03-09T08:26:49Z
ddc:
- '510'
department:
- _id: '101'
- _id: '841'
external_id:
arxiv:
- '2603.06157'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2026-03-09T08:26:04Z
date_updated: 2026-03-09T08:26:04Z
file_id: '64866'
file_name: design-of-hierarchical-excitable-networks.pdf
file_size: 5179491
relation: main_file
success: 1
file_date_updated: 2026-03-09T08:26:04Z
has_accepted_license: '1'
language:
- iso: eng
publication: arXiv:2603.06157
related_material:
link:
- relation: research_paper
url: https://s-vdg.github.io/publication/design-of-hierarchical-excitable-networks/design-of-hierarchical-excitable-networks.pdf
status: public
title: Design of Hierarchical Excitable Networks
type: preprint
user_id: '97359'
year: '2026'
...
---
_id: '63557'
abstract:
- lang: eng
text: We discretise a recently proposed new Lagrangian approach to optimal control
problems with dynamics described by force-controlled Euler-Lagrange equations
(Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are
in the form of discrete Lagrangians. We show that the discrete necessary conditions
for optimality obtained provide variational integrators for the continuous problem,
akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This
approach paves the way for the use of variational error analysis to derive the
order of convergence of the resulting numerical schemes for both state and costate
variables and to apply discrete Noether’s theorem to compute conserved quantities,
distinguishing itself from existing geometric approaches. We show for a family
of low-order discretisations that the resulting numerical schemes are ‘doubly-symplectic’,
meaning they yield forced symplectic integrators for the underlying controlled
mechanical system and overall symplectic integrators in the state-adjoint space.
Multi-body dynamics examples are solved numerically using the new approach. In
addition, the new approach is compared to standard direct approaches in terms
of computational performance and error convergence. The results highlight the
advantages of the new approach, namely, better performance and convergence behaviour
of state and costate variables consistent with variational error analysis and
automatic preservation of certain first integrals.
author:
- first_name: Michael
full_name: Konopik, Michael
last_name: Konopik
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Rodrigo T.
full_name: Sato Martín de Almagro, Rodrigo T.
last_name: Sato Martín de Almagro
citation:
ama: Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martín de Almagro
RT. On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics. Multibody System Dynamics. Published online 2026.
doi:10.1007/s11044-025-10138-1
apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., & Sato Martín de Almagro,
R. T. (2026). On the variational discretisation of optimal control problems for
unconstrained Lagrangian dynamics. Multibody System Dynamics. https://doi.org/10.1007/s11044-025-10138-1
bibtex: '@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_Sato Martín de Almagro_2026,
title={On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics}, DOI={10.1007/s11044-025-10138-1},
journal={Multibody System Dynamics}, publisher={Springer Science and Business
Media LLC}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya,
Sofya and Ober-Blöbaum, Sina and Sato Martín de Almagro, Rodrigo T.}, year={2026}
}'
chicago: Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum,
and Rodrigo T. Sato Martín de Almagro. “On the Variational Discretisation of Optimal
Control Problems for Unconstrained Lagrangian Dynamics.” Multibody System Dynamics,
2026. https://doi.org/10.1007/s11044-025-10138-1.
ieee: 'M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro,
“On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics,” Multibody System Dynamics, 2026, doi: 10.1007/s11044-025-10138-1.'
mla: Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control
Problems for Unconstrained Lagrangian Dynamics.” Multibody System Dynamics,
Springer Science and Business Media LLC, 2026, doi:10.1007/s11044-025-10138-1.
short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro,
Multibody System Dynamics (2026).
date_created: 2026-01-12T11:33:54Z
date_updated: 2026-01-12T11:35:27Z
department:
- _id: '636'
doi: 10.1007/s11044-025-10138-1
language:
- iso: eng
publication: Multibody System Dynamics
publication_identifier:
issn:
- 1384-5640
- 1573-272X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics
type: journal_article
user_id: '87909'
year: '2026'
...
---
_id: '64979'
abstract:
- lang: eng
text: We investigate homogeneous coupled cell systems with high-dimensional internal
dynamics. In many studies on network dynamics, the analysis is restricted to networks
with one-dimensional internal dynamics. Here, we show how symmetry explains the
relation between dynamical behavior of systems with one-dimensional internal dynamics
and with higher dimensional internal dynamics, when the underlying network topology
is the same. Fundamental networks of homogeneous coupled cell systems (B. Rink,
J. Sanders. Coupled Cell Networks and Their Hidden Symmetries. SIAM J. Math. Anal.
46.2 (2014)) can be expressed in terms of monoid representations, which uniquely
decompose into indecomposable subrepresentations. In the high-dimensional internal
dynamics case, these subrepresentations are isomorphic to multiple copies of those
one computes in the one-dimensional internal dynamics case. This has interesting
implications for possible center subspaces in bifurcation analysis. We describe
the effect on steady state and Hopf bifurcations in l-parameter families of network
vector fields. The main results in that regard are that (1) generic one-parameter
steady state bifurcations are qualitatively independent of the dimension of the
internal dynamics and that, (2) in order to observe all generic l-parameter bifurcations
that may occur for internal dynamics of any dimension, the internal dynamics has
to be at least l-dimensional for steady state bifurcations and 2l-dimensional
for Hopf bifurcations. Furthermore, we illustrate how additional structure in
the network can be exploited to obtain even greater understanding of bifurcation
scenarios in the high-dimensional case beyond qualitative statements about the
collective dynamics. One-parameter steady state bifurcations in feedforward networks
exhibit an unusual amplification in the asymptotic growth rates of individual
cells, when these are one-dimensional (S. von der Gracht, E. Nijholt, B. Rink.
Amplified steady state bifurcations in feedforward networks. Nonlinearity 35.4
(2022)). As another main result, we prove that (3) the same cells exhibit this
amplifying effect with the same growth rates when the internal dynamics is high-dimensional.
article_number: '118196'
article_type: original
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: von der Gracht S, Nijholt E, Rink B. Homogeneous coupled cell systems with
high-dimensional internal dynamics. Chaos, Solitons & Fractals. 2026;208.
doi:10.1016/j.chaos.2026.118196
apa: von der Gracht, S., Nijholt, E., & Rink, B. (2026). Homogeneous coupled
cell systems with high-dimensional internal dynamics. Chaos, Solitons &
Fractals, 208, Article 118196. https://doi.org/10.1016/j.chaos.2026.118196
bibtex: '@article{von der Gracht_Nijholt_Rink_2026, title={Homogeneous coupled cell
systems with high-dimensional internal dynamics}, volume={208}, DOI={10.1016/j.chaos.2026.118196},
number={118196}, journal={Chaos, Solitons & Fractals}, publisher={Elsevier
BV}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2026}
}'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Homogeneous Coupled
Cell Systems with High-Dimensional Internal Dynamics.” Chaos, Solitons &
Fractals 208 (2026). https://doi.org/10.1016/j.chaos.2026.118196.
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Homogeneous coupled cell systems
with high-dimensional internal dynamics,” Chaos, Solitons & Fractals,
vol. 208, Art. no. 118196, 2026, doi: 10.1016/j.chaos.2026.118196.'
mla: von der Gracht, Sören, et al. “Homogeneous Coupled Cell Systems with High-Dimensional
Internal Dynamics.” Chaos, Solitons & Fractals, vol. 208, 118196, Elsevier
BV, 2026, doi:10.1016/j.chaos.2026.118196.
short: S. von der Gracht, E. Nijholt, B. Rink, Chaos, Solitons & Fractals 208
(2026).
date_created: 2026-03-16T08:39:07Z
date_updated: 2026-03-16T08:42:56Z
ddc:
- '510'
department:
- _id: '101'
- _id: '841'
doi: 10.1016/j.chaos.2026.118196
external_id:
arxiv:
- '2510.06740'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2026-03-16T08:40:04Z
date_updated: 2026-03-16T08:40:04Z
file_id: '64980'
file_name: homogeneous-coupled-cell-systems-with-high-dimensional-internal-dynamics.pdf
file_size: 1951746
relation: main_file
success: 1
file_date_updated: 2026-03-16T08:40:04Z
has_accepted_license: '1'
intvolume: ' 208'
keyword:
- Coupled cell systems
- Network dynamics
- Dimension reduction
- Bifurcation theory
- Symmetry
- Monoid representation theory
language:
- iso: eng
publication: Chaos, Solitons & Fractals
publication_identifier:
issn:
- 0960-0779
publication_status: published
publisher: Elsevier BV
status: public
title: Homogeneous coupled cell systems with high-dimensional internal dynamics
type: journal_article
user_id: '97359'
volume: 208
year: '2026'
...
---
_id: '59792'
abstract:
- lang: eng
text: "Abstract\r\n Motivated by mechanical
systems with symmetries, we focus on optimal control problems possessing certain
symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788
2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized
the classical concept of static turnpike to manifold turnpike
we extend the exponential turnpike property to the
exponential trim turnpike for control systems with
symmetries induced by abelian or non-abelian groups. Our analysis is mainly based
on the geometric reduction of control systems with symmetries. More concretely,
we first reduce the control system on the quotient space and state the turnpike
theorem for the reduced problem. Then we use the group properties to obtain the
trim turnpike theorem for the full problem. Finally,
we illustrate our results on the Kepler problem and the rigid body problem.\r\n"
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for
optimal control problems with symmetries. Mathematics of Control, Signals,
and Systems. Published online 2025. doi:10.1007/s00498-025-00408-w
apa: Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., & Wembe Moafo, B. E. (2025).
Trim turnpikes for optimal control problems with symmetries. Mathematics of
Control, Signals, and Systems. https://doi.org/10.1007/s00498-025-00408-w
bibtex: '@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim
turnpikes for optimal control problems with symmetries}, DOI={10.1007/s00498-025-00408-w},
journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science
and Business Media LLC}, author={Flaßkamp, Kathrin and Maslovskaya, Sofya and
Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}, year={2025} }'
chicago: Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar
Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” Mathematics
of Control, Signals, and Systems, 2025. https://doi.org/10.1007/s00498-025-00408-w.
ieee: 'K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim
turnpikes for optimal control problems with symmetries,” Mathematics of Control,
Signals, and Systems, 2025, doi: 10.1007/s00498-025-00408-w.'
mla: Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with
Symmetries.” Mathematics of Control, Signals, and Systems, Springer Science
and Business Media LLC, 2025, doi:10.1007/s00498-025-00408-w.
short: K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics
of Control, Signals, and Systems (2025).
date_created: 2025-05-05T09:23:38Z
date_updated: 2025-05-05T09:24:09Z
department:
- _id: '636'
doi: 10.1007/s00498-025-00408-w
language:
- iso: eng
publication: Mathematics of Control, Signals, and Systems
publication_identifier:
issn:
- 0932-4194
- 1435-568X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Trim turnpikes for optimal control problems with symmetries
type: journal_article
user_id: '87909'
year: '2025'
...
---
_id: '59806'
abstract:
- lang: eng
text: We introduce a model of information dissemination in signed networks. It is
a discrete-time process in which uninformed actors incrementally receive information
from their informed neighbors or from the outside. Our goal is to minimize the
number of confused actors — that is, the number of actors who receive contradictory
information. We prove upper bounds for the number of confused actors in signed
networks and in equivalence classes of signed networks. In particular, we show
that there are signed networks where, for any information placement strategy,
almost 60% of the actors are confused. Furthermore, this is also the case when
considering the minimum number of confused actors within an equivalence class
of signed graphs.
author:
- first_name: Ligang
full_name: Jin, Ligang
last_name: Jin
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: Jin L, Steffen E. Information dissemination and confusion in signed networks.
Discrete Applied Mathematics. 2025;373:99-106. doi:10.1016/j.dam.2025.04.049
apa: Jin, L., & Steffen, E. (2025). Information dissemination and confusion
in signed networks. Discrete Applied Mathematics, 373, 99–106. https://doi.org/10.1016/j.dam.2025.04.049
bibtex: '@article{Jin_Steffen_2025, title={Information dissemination and confusion
in signed networks}, volume={373}, DOI={10.1016/j.dam.2025.04.049},
journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Jin,
Ligang and Steffen, Eckhard}, year={2025}, pages={99–106} }'
chicago: 'Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion
in Signed Networks.” Discrete Applied Mathematics 373 (2025): 99–106. https://doi.org/10.1016/j.dam.2025.04.049.'
ieee: 'L. Jin and E. Steffen, “Information dissemination and confusion in signed
networks,” Discrete Applied Mathematics, vol. 373, pp. 99–106, 2025, doi:
10.1016/j.dam.2025.04.049.'
mla: Jin, Ligang, and Eckhard Steffen. “Information Dissemination and Confusion
in Signed Networks.” Discrete Applied Mathematics, vol. 373, Elsevier BV,
2025, pp. 99–106, doi:10.1016/j.dam.2025.04.049.
short: L. Jin, E. Steffen, Discrete Applied Mathematics 373 (2025) 99–106.
date_created: 2025-05-06T07:38:49Z
date_updated: 2025-05-06T07:39:58Z
department:
- _id: '542'
doi: 10.1016/j.dam.2025.04.049
intvolume: ' 373'
language:
- iso: eng
page: 99-106
publication: Discrete Applied Mathematics
publication_identifier:
issn:
- 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Information dissemination and confusion in signed networks
type: journal_article
user_id: '15540'
volume: 373
year: '2025'
...
---
_id: '60048'
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
orcid: 0009-0002-4750-2051
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Gerlach R, von der Gracht S, Dellnitz M. On the Dynamical Hierarchy in Gathering
Protocols with Circulant Topologies. In: Lecture Notes in Computer Science.
Springer Nature Switzerland; 2025. doi:10.1007/978-3-031-91736-3_19'
apa: Gerlach, R., von der Gracht, S., & Dellnitz, M. (2025). On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies. In Lecture Notes
in Computer Science. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-91736-3_19
bibtex: '@inbook{Gerlach_von der Gracht_Dellnitz_2025, place={Cham}, title={On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies}, DOI={10.1007/978-3-031-91736-3_19},
booktitle={Lecture Notes in Computer Science}, publisher={Springer Nature Switzerland},
author={Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael}, year={2025}
}'
chicago: 'Gerlach, Raphael, Sören von der Gracht, and Michael Dellnitz. “On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies.” In Lecture Notes
in Computer Science. Cham: Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-91736-3_19.'
ieee: 'R. Gerlach, S. von der Gracht, and M. Dellnitz, “On the Dynamical Hierarchy
in Gathering Protocols with Circulant Topologies,” in Lecture Notes in Computer
Science, Cham: Springer Nature Switzerland, 2025.'
mla: Gerlach, Raphael, et al. “On the Dynamical Hierarchy in Gathering Protocols
with Circulant Topologies.” Lecture Notes in Computer Science, Springer
Nature Switzerland, 2025, doi:10.1007/978-3-031-91736-3_19.
short: 'R. Gerlach, S. von der Gracht, M. Dellnitz, in: Lecture Notes in Computer
Science, Springer Nature Switzerland, Cham, 2025.'
date_created: 2025-05-27T08:17:03Z
date_updated: 2025-05-27T08:22:42Z
department:
- _id: '101'
doi: 10.1007/978-3-031-91736-3_19
external_id:
arxiv:
- '2503.07576'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' ArXiv:2503.07576'
oa: '1'
place: Cham
project:
- _id: '106'
grant_number: '453112019'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: Lecture Notes in Computer Science
publication_identifier:
isbn:
- '9783031917356'
- '9783031917363'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature Switzerland
status: public
title: On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies
type: book_chapter
user_id: '32655'
year: '2025'
...
---
_id: '55459'
article_type: original
author:
- first_name: Nils
full_name: Bullerjahn, Nils
id: '103797'
last_name: Bullerjahn
orcid: https://orcid.org/0009-0003-8460-1574
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Bullerjahn N, Kovács B. Error estimates for full discretization of Cahn--Hilliard
equation with dynamic boundary conditions. IMA Journal of Numerical Analysis.
doi:10.1093/imanum/draf009
apa: Bullerjahn, N., & Kovács, B. (n.d.). Error estimates for full discretization
of Cahn--Hilliard equation with dynamic boundary conditions. IMA Journal of
Numerical Analysis. https://doi.org/10.1093/imanum/draf009
bibtex: '@article{Bullerjahn_Kovács, title={Error estimates for full discretization
of Cahn--Hilliard equation with dynamic boundary conditions}, DOI={10.1093/imanum/draf009},
journal={IMA Journal of Numerical Analysis}, author={Bullerjahn, Nils and Kovács,
Balázs} }'
chicago: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization
of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” IMA Journal of
Numerical Analysis, n.d. https://doi.org/10.1093/imanum/draf009.
ieee: 'N. Bullerjahn and B. Kovács, “Error estimates for full discretization of
Cahn--Hilliard equation with dynamic boundary conditions,” IMA Journal of Numerical
Analysis, doi: 10.1093/imanum/draf009.'
mla: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization
of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” IMA Journal of
Numerical Analysis, doi:10.1093/imanum/draf009.
short: N. Bullerjahn, B. Kovács, IMA Journal of Numerical Analysis (n.d.).
date_created: 2024-07-31T09:03:45Z
date_updated: 2026-02-18T14:46:18Z
department:
- _id: '841'
doi: 10.1093/imanum/draf009
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_status: accepted
status: public
title: Error estimates for full discretization of Cahn--Hilliard equation with dynamic
boundary conditions
type: journal_article
user_id: '100441'
year: '2025'
...
---
_id: '53141'
author:
- first_name: Dominik
full_name: Edelmann, Dominik
last_name: Edelmann
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: Edelmann D, Kovács B, Lubich C. Numerical analysis of an evolving bulk--surface
model of tumour growth. IMA Journal of Numerical Analysis. 2025;45(5):2581--2627.
doi:10.1093/imanum/drae077
apa: Edelmann, D., Kovács, B., & Lubich, C. (2025). Numerical analysis of an
evolving bulk--surface model of tumour growth. IMA Journal of Numerical Analysis,
45(5), 2581--2627. https://doi.org/10.1093/imanum/drae077
bibtex: '@article{Edelmann_Kovács_Lubich_2025, title={Numerical analysis of an evolving
bulk--surface model of tumour growth}, volume={45}, DOI={10.1093/imanum/drae077},
number={5}, journal={IMA Journal of Numerical Analysis}, author={Edelmann, Dominik
and Kovács, Balázs and Lubich, Christian}, year={2025}, pages={2581--2627} }'
chicago: 'Edelmann, Dominik, Balázs Kovács, and Christian Lubich. “Numerical Analysis
of an Evolving Bulk--Surface Model of Tumour Growth.” IMA Journal of Numerical
Analysis 45, no. 5 (2025): 2581--2627. https://doi.org/10.1093/imanum/drae077.'
ieee: 'D. Edelmann, B. Kovács, and C. Lubich, “Numerical analysis of an evolving
bulk--surface model of tumour growth,” IMA Journal of Numerical Analysis,
vol. 45, no. 5, pp. 2581--2627, 2025, doi: 10.1093/imanum/drae077.'
mla: Edelmann, Dominik, et al. “Numerical Analysis of an Evolving Bulk--Surface
Model of Tumour Growth.” IMA Journal of Numerical Analysis, vol. 45, no.
5, 2025, pp. 2581--2627, doi:10.1093/imanum/drae077.
short: D. Edelmann, B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 45 (2025)
2581--2627.
date_created: 2024-04-03T09:11:36Z
date_updated: 2026-02-18T14:44:54Z
department:
- _id: '841'
doi: 10.1093/imanum/drae077
intvolume: ' 45'
issue: '5'
language:
- iso: eng
page: 2581--2627
publication: IMA Journal of Numerical Analysis
status: public
title: Numerical analysis of an evolving bulk--surface model of tumour growth
type: journal_article
user_id: '100441'
volume: 45
year: '2025'
...
---
_id: '55781'
abstract:
- lang: eng
text: "In this paper, we prove that spatially semi-discrete evolving finite element\r\nmethod
for parabolic equations on a given evolving hypersurface of arbitrary\r\ndimensions
preserves the maximal $L^p$-regularity at the discrete level. We\r\nfirst establish
the results on a stationary surface and then extend them, via a\r\nperturbation
argument, to the case where the underlying surface is evolving\r\nunder a prescribed
velocity field. The proof combines techniques in evolving\r\nfinite element method,
properties of Green's functions on (discretised) closed\r\nsurfaces, and local
energy estimates for finite element methods"
author:
- first_name: Genming
full_name: Bai, Genming
last_name: Bai
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Buyang
full_name: Li, Buyang
last_name: Li
citation:
ama: Bai G, Kovács B, Li B. Maximal regularity of evolving FEMs for parabolic equations
on an evolving surface. IMA Journal of Numerical Analysis. Published online
2025. doi:10.1093/imanum/draf082.
apa: Bai, G., Kovács, B., & Li, B. (2025). Maximal regularity of evolving FEMs
for parabolic equations on an evolving surface. IMA Journal of Numerical Analysis.
https://doi.org/10.1093/imanum/draf082.
bibtex: '@article{Bai_Kovács_Li_2025, title={Maximal regularity of evolving FEMs
for parabolic equations on an evolving surface}, DOI={10.1093/imanum/draf082.},
journal={IMA Journal of Numerical Analysis}, author={Bai, Genming and Kovács,
Balázs and Li, Buyang}, year={2025} }'
chicago: Bai, Genming, Balázs Kovács, and Buyang Li. “Maximal Regularity of Evolving
FEMs for Parabolic Equations on an Evolving Surface.” IMA Journal of Numerical
Analysis, 2025. https://doi.org/10.1093/imanum/draf082.
ieee: 'G. Bai, B. Kovács, and B. Li, “Maximal regularity of evolving FEMs for parabolic
equations on an evolving surface,” IMA Journal of Numerical Analysis,
2025, doi: 10.1093/imanum/draf082.'
mla: Bai, Genming, et al. “Maximal Regularity of Evolving FEMs for Parabolic Equations
on an Evolving Surface.” IMA Journal of Numerical Analysis, 2025, doi:10.1093/imanum/draf082.
short: G. Bai, B. Kovács, B. Li, IMA Journal of Numerical Analysis (2025).
date_created: 2024-08-27T07:37:39Z
date_updated: 2026-02-18T14:47:34Z
department:
- _id: '841'
doi: 10.1093/imanum/draf082.
external_id:
arxiv:
- '2408.14096'
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
status: public
title: Maximal regularity of evolving FEMs for parabolic equations on an evolving
surface
type: journal_article
user_id: '100441'
year: '2025'
...
---
_id: '50299'
abstract:
- lang: eng
text: "A finite classical polar space of rank $n$ consists of the totally isotropic\r\nsubspaces
of a finite vector space over $\\mathbb{F}_q$ equipped with a\r\nnondegenerate
form such that $n$ is the maximal dimension of such a subspace. A\r\n$t$-$(n,k,\\lambda)$
design in a finite classical polar space of rank $n$ is a\r\ncollection $Y$ of
totally isotropic $k$-spaces such that each totally isotropic\r\n$t$-space is
contained in exactly $\\lambda$ members of $Y$. Nontrivial examples\r\nare currently
only known for $t\\leq 2$. We show that $t$-$(n,k,\\lambda)$\r\ndesigns in polar
spaces exist for all $t$ and $q$ provided that\r\n$k>\\frac{21}{2}t$ and $n$ is
sufficiently large enough. The proof is based on a\r\nprobabilistic method by
Kuperberg, Lovett, and Peled, and it is thus\r\nnonconstructive."
author:
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. Des Codes
Cryptogr. 2025;93:971-981. doi:10.1007/s10623-024-01471-1
apa: Weiß, C. (2025). Nontrivial $t$-designs in polar spaces exist for all $t$.
Des. Codes Cryptogr., 93, 971–981. https://doi.org/10.1007/s10623-024-01471-1
bibtex: '@article{Weiß_2025, title={Nontrivial $t$-designs in polar spaces exist
for all $t$}, volume={93}, DOI={10.1007/s10623-024-01471-1},
journal={Des. Codes Cryptogr.}, author={Weiß, Charlene}, year={2025}, pages={971–981}
}'
chicago: 'Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All
$t$.” Des. Codes Cryptogr. 93 (2025): 971–81. https://doi.org/10.1007/s10623-024-01471-1.'
ieee: 'C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” Des.
Codes Cryptogr., vol. 93, pp. 971–981, 2025, doi: 10.1007/s10623-024-01471-1.'
mla: Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.”
Des. Codes Cryptogr., vol. 93, 2025, pp. 971–81, doi:10.1007/s10623-024-01471-1.
short: C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981.
date_created: 2024-01-08T14:39:54Z
date_updated: 2026-02-25T13:51:50Z
department:
- _id: '100'
doi: 10.1007/s10623-024-01471-1
intvolume: ' 93'
language:
- iso: eng
page: 971 - 981
publication: Des. Codes Cryptogr.
publication_status: published
status: public
title: Nontrivial $t$-designs in polar spaces exist for all $t$
type: journal_article
user_id: '70420'
volume: 93
year: '2025'
...
---
_id: '56298'
abstract:
- lang: eng
text: "In the general pattern formation (GPF) problem, a swarm of simple autonomous,\r\ndisoriented
robots must form a given pattern. The robots' simplicity imply a\r\nstrong limitation:
When the initial configuration is rotationally symmetric,\r\nonly patterns with
a similar symmetry can be formed [Yamashita, Suzyuki; TCS\r\n2010]. The only known
algorithm to form large patterns with limited visibility\r\nand without memory
requires the robots to start in a near-gathering (a swarm of\r\nconstant diameter)
[Hahn et al.; SAND 2024]. However, not only do we not know\r\nany near-gathering
algorithm guaranteed to preserve symmetry but most natural\r\ngathering strategies
trivially increase symmetries [Castenow et al.; OPODIS\r\n2022].\r\n Thus, we
study near-gathering without changing the swarm's rotational\r\nsymmetry for disoriented,
oblivious robots with limited visibility (the\r\nOBLOT-model, see [Flocchini et
al.; 2019]). We introduce a technique based on\r\nthe theory of dynamical systems
to analyze how a given algorithm affects\r\nsymmetry and provide sufficient conditions
for symmetry preservation. Until\r\nnow, it was unknown whether the considered
OBLOT-model allows for any\r\nnon-trivial algorithm that always preserves symmetry.
Our first result shows\r\nthat a variant of Go-to-the-Average always preserves
symmetry but may sometimes\r\nlead to multiple, unconnected near-gathering clusters.
Our second result is a\r\nsymmetry-preserving near-gathering algorithm that works
on swarms with a convex\r\nboundary (the outer boundary of the unit disc graph)
and without holes (circles\r\nof diameter 1 inside the boundary without any robots)."
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
orcid: 0009-0002-4750-2051
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Christopher
full_name: Hahn, Christopher
last_name: Hahn
- first_name: Jonas
full_name: Harbig, Jonas
id: '47213'
last_name: Harbig
- first_name: Peter
full_name: Kling, Peter
last_name: Kling
citation:
ama: 'Gerlach R, von der Gracht S, Hahn C, Harbig J, Kling P. Symmetry Preservation
in Swarms of Oblivious Robots with Limited Visibility. In: Bonomi S, Galletta
L, Rivière Etienne, Schiavoni Valerio, eds. 28th International Conference
on Principles of Distributed Systems (OPODIS 2024). Vol 324. Leibniz International
Proceedings in Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik;
2025. doi:10.4230/LIPIcs.OPODIS.2024.13'
apa: Gerlach, R., von der Gracht, S., Hahn, C., Harbig, J., & Kling, P. (2025).
Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility.
In S. Bonomi, L. Galletta, Etienne Rivière, & Valerio Schiavoni (Eds.),
28th International Conference on Principles of Distributed Systems (OPODIS
2024) (Vol. 324). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.OPODIS.2024.13
bibtex: '@inproceedings{Gerlach_von der Gracht_Hahn_Harbig_Kling_2025, series={Leibniz
International Proceedings in Informatics (LIPIcs)}, title={Symmetry Preservation
in Swarms of Oblivious Robots with Limited Visibility}, volume={324}, DOI={10.4230/LIPIcs.OPODIS.2024.13},
booktitle={28th International Conference on Principles of Distributed Systems
(OPODIS 2024)}, publisher={Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
author={Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig,
Jonas and Kling, Peter}, editor={Bonomi, Silvia and Galletta, Letterio and Rivière, Etienne
and Schiavoni, Valerio}, year={2025}, collection={Leibniz International Proceedings
in Informatics (LIPIcs)} }'
chicago: Gerlach, Raphael, Sören von der Gracht, Christopher Hahn, Jonas Harbig,
and Peter Kling. “Symmetry Preservation in Swarms of Oblivious Robots with Limited
Visibility.” In 28th International Conference on Principles of Distributed
Systems (OPODIS 2024), edited by Silvia Bonomi, Letterio Galletta, Etienne
Rivière, and Valerio Schiavoni, Vol. 324. Leibniz International Proceedings in
Informatics (LIPIcs). Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2025.
https://doi.org/10.4230/LIPIcs.OPODIS.2024.13.
ieee: 'R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, and P. Kling, “Symmetry
Preservation in Swarms of Oblivious Robots with Limited Visibility,” in 28th
International Conference on Principles of Distributed Systems (OPODIS 2024),
Lucca, Italy, 2025, vol. 324, doi: 10.4230/LIPIcs.OPODIS.2024.13.'
mla: Gerlach, Raphael, et al. “Symmetry Preservation in Swarms of Oblivious Robots
with Limited Visibility.” 28th International Conference on Principles of Distributed
Systems (OPODIS 2024), edited by Silvia Bonomi et al., vol. 324, Schloss Dagstuhl
-- Leibniz-Zentrum für Informatik, 2025, doi:10.4230/LIPIcs.OPODIS.2024.13.
short: 'R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, P. Kling, in: S. Bonomi,
L. Galletta, Etienne Rivière, Valerio Schiavoni (Eds.), 28th International Conference
on Principles of Distributed Systems (OPODIS 2024), Schloss Dagstuhl -- Leibniz-Zentrum
für Informatik, 2025.'
conference:
end_date: 2024-12-13
location: Lucca, Italy
name: 28th International Conference on Principles of Distributed Systems (OPODIS
2024)
start_date: 2024-12-11
date_created: 2024-10-01T13:29:43Z
date_updated: 2025-01-09T11:39:19Z
department:
- _id: '101'
doi: 10.4230/LIPIcs.OPODIS.2024.13
editor:
- first_name: Silvia
full_name: Bonomi, Silvia
last_name: Bonomi
- first_name: Letterio
full_name: Galletta, Letterio
last_name: Galletta
- first_name: ' Etienne'
full_name: Rivière, Etienne
last_name: Rivière
- first_name: ' Valerio'
full_name: Schiavoni, Valerio
last_name: Schiavoni
external_id:
arxiv:
- '2409.19277'
intvolume: ' 324'
keyword:
- Swarm Algorithm
- Swarm Robots
- Distributed Algorithm
- Pattern Formation
- Limited Visibility
- Oblivious
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2409.19277
oa: '1'
project:
- _id: '106'
grant_number: '453112019'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: 28th International Conference on Principles of Distributed Systems (OPODIS
2024)
publication_identifier:
isbn:
- 978-3-95977-360-7
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
series_title: Leibniz International Proceedings in Informatics (LIPIcs)
status: public
title: Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility
type: conference
user_id: '97359'
volume: 324
year: '2025'
...
---
_id: '58532'
author:
- first_name: Nils
full_name: Bullerjahn, Nils
id: '103797'
last_name: Bullerjahn
orcid: https://orcid.org/0009-0003-8460-1574
citation:
ama: Bullerjahn N. Error estimates for full discretization by an almost mass conservation
technique for Cahn--Hilliard systems with dynamic boundary conditions. arXiv.
Published online 2025. doi:10.48550/ARXIV.2502.03847
apa: Bullerjahn, N. (2025). Error estimates for full discretization by an almost
mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions.
ArXiv. https://doi.org/10.48550/ARXIV.2502.03847
bibtex: '@article{Bullerjahn_2025, title={Error estimates for full discretization
by an almost mass conservation technique for Cahn--Hilliard systems with dynamic
boundary conditions}, DOI={10.48550/ARXIV.2502.03847},
journal={arXiv}, author={Bullerjahn, Nils}, year={2025} }'
chicago: Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost
Mass Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.”
ArXiv, 2025. https://doi.org/10.48550/ARXIV.2502.03847.
ieee: 'N. Bullerjahn, “Error estimates for full discretization by an almost mass
conservation technique for Cahn--Hilliard systems with dynamic boundary conditions,”
arXiv, 2025, doi: 10.48550/ARXIV.2502.03847.'
mla: Bullerjahn, Nils. “Error Estimates for Full Discretization by an Almost Mass
Conservation Technique for Cahn--Hilliard Systems with Dynamic Boundary Conditions.”
ArXiv, 2025, doi:10.48550/ARXIV.2502.03847.
short: N. Bullerjahn, ArXiv (2025).
date_created: 2025-02-07T08:27:10Z
date_updated: 2025-02-07T08:28:48Z
department:
- _id: '841'
doi: 10.48550/ARXIV.2502.03847
language:
- iso: eng
publication: arXiv
status: public
title: Error estimates for full discretization by an almost mass conservation technique
for Cahn--Hilliard systems with dynamic boundary conditions
type: journal_article
user_id: '103797'
year: '2025'
...
---
_id: '58544'
abstract:
- lang: eng
text: 'We introduce a new classification of multimode states with a fixed number
of photons. This classification is based on the factorizability of homogeneous
multivariate polynomials and is invariant under unitary transformations. The classes
physically correspond to field excitations in terms of single and multiple photons,
each of which being in an arbitrary irreducible superposition of quantized modes.
We further show how the transitions between classes are rendered possible by photon
addition, photon subtraction, and photon-projection nonlinearities. We explicitly
put forward a design for a multilayer interferometer in which the states for different
classes can be generated with state-of-the-art experimental techniques. Limitations
of the proposed designs are analyzed using the introduced classification, providing
a benchmark for the robustness of certain states and classes. '
author:
- first_name: Denis
full_name: Kopylov, Denis
id: '98502'
last_name: Kopylov
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina
full_name: Sharapova, Polina
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification
for nonlinear optical circuits .
apa: Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier,
T., Sharapova, P., & Sperling, J. (n.d.). Multiphoton, multimode state
classification for nonlinear optical circuits .
bibtex: '@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling,
title={Multiphoton, multimode state classification for nonlinear optical circuits
}, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo,
Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and
Sperling, Jan} }'
chicago: Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina
Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton,
Multimode State Classification for Nonlinear Optical Circuits ,” n.d.
ieee: D. Kopylov et al., “Multiphoton, multimode state classification for
nonlinear optical circuits .” .
mla: Kopylov, Denis, et al. Multiphoton, Multimode State Classification for Nonlinear
Optical Circuits .
short: D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier,
P. Sharapova, J. Sperling, (n.d.).
date_created: 2025-02-10T08:26:45Z
date_updated: 2025-02-10T08:36:12Z
department:
- _id: '623'
- _id: '15'
- _id: '636'
external_id:
arxiv:
- '2502.05123'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2502.05123
oa: '1'
publication_status: submitted
status: public
title: 'Multiphoton, multimode state classification for nonlinear optical circuits '
type: preprint
user_id: '85279'
year: '2025'
...
---
_id: '58953'
abstract:
- lang: eng
text: In this article, we investigate symmetry properties of distributed systems
of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze
their collective Fsync dynamics using of equivariant dynamical systems theory.
To this end, we show that the corresponding evolution function commutes with rotational
and reflective transformations of R^2. These form a group that is isomorphic to
O(2) x S_n, the product group of the orthogonal group and the permutation on n
elements. The theory of equivariant dynamical systems is used to deduce a hierarchy
along which symmetries of a robot swarm can potentially increase following an
arbitrary protocol. By decoupling the Look phase from the Compute and Move phases
in the mathematical description of an LCM cycle, this hierarchy can be characterized
in terms of automorphisms of connectivity graphs. In particular, we find all possible
types of symmetry increase, if the decoupled Compute and Move phase is invertible.
Finally, we apply our results to protocols which induce state-dependent linear
dynamics, where the reduced system consisting of only the Compute and Move phase
is linear.
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
orcid: 0009-0002-4750-2051
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
citation:
ama: Gerlach R, von der Gracht S. Analyzing Symmetries of Swarms of Mobile Robots
Using Equivariant Dynamical Systems. arXiv:250307576. Published online
2025.
apa: Gerlach, R., & von der Gracht, S. (2025). Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems. In arXiv:2503.07576.
bibtex: '@article{Gerlach_von der Gracht_2025, title={Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems}, journal={arXiv:2503.07576},
author={Gerlach, Raphael and von der Gracht, Sören}, year={2025} }'
chicago: Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems.” ArXiv:2503.07576,
2025.
ieee: R. Gerlach and S. von der Gracht, “Analyzing Symmetries of Swarms of Mobile
Robots Using Equivariant Dynamical Systems,” arXiv:2503.07576. 2025.
mla: Gerlach, Raphael, and Sören von der Gracht. “Analyzing Symmetries of Swarms
of Mobile Robots Using Equivariant Dynamical Systems.” ArXiv:2503.07576,
2025.
short: R. Gerlach, S. von der Gracht, ArXiv:2503.07576 (2025).
date_created: 2025-03-11T08:21:05Z
date_updated: 2025-03-11T08:53:02Z
ddc:
- '004'
department:
- _id: '101'
external_id:
arxiv:
- '2503.07576'
file:
- access_level: open_access
content_type: application/pdf
creator: svdg
date_created: 2025-03-11T08:27:32Z
date_updated: 2025-03-11T08:27:32Z
file_id: '58954'
file_name: Analyzing_Symmetries_of_Swarms_of_Mobile_Robots_Using_Equivariant_Dynamical_Systems.pdf
file_size: 812198
relation: main_file
file_date_updated: 2025-03-11T08:27:32Z
has_accepted_license: '1'
keyword:
- dynamical systems
- coupled systems
- distributed computing
- robot swarms
- autonomous mobile robots
- symmetry
- equivariant dynamics
language:
- iso: eng
oa: '1'
page: '23'
project:
- _id: '106'
grant_number: '453112019'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: arXiv:2503.07576
status: public
title: Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant Dynamical
Systems
type: preprint
user_id: '97359'
year: '2025'
...
---
_id: '59169'
abstract:
- lang: eng
text: An r-regular graph is an r-graph, if every odd set of vertices is connected
to its complement by at least r edges. Let G and H be r-graphs. An H-coloring
of G is a mapping such that each r adjacent edges of G are mapped to r adjacent
edges of H. For every , let be an inclusion-wise minimal set of connected r-graphs,
such that for every connected r-graph G there is an which colors G. The Petersen
Coloring Conjecture states that consists of the Petersen graph P. We show that
if true, then this is a very exclusive situation. Our main result is that either
or is an infinite set and if , then is an infinite set. In particular, for all
, is unique. We first characterize and then prove that if contains more than one
element, then it is an infinite set. To obtain our main result we show that contains
the smallest r-graphs of class 2 and the smallest poorly matchable r-graphs, and
we determine the smallest r-graphs of class 2.
article_number: '16'
author:
- first_name: Yulai
full_name: Ma, Yulai
last_name: Ma
- first_name: Davide
full_name: Mattiolo, Davide
last_name: Mattiolo
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Isaak H.
full_name: Wolf, Isaak H.
last_name: Wolf
citation:
ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-Graphs that Color All r-Graphs.
Combinatorica. 2025;45(2). doi:10.1007/s00493-025-00144-4
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2025). Sets of r-Graphs
that Color All r-Graphs. Combinatorica, 45(2), Article 16. https://doi.org/10.1007/s00493-025-00144-4
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2025, title={Sets of r-Graphs that Color
All r-Graphs}, volume={45}, DOI={10.1007/s00493-025-00144-4},
number={216}, journal={Combinatorica}, publisher={Springer Science and Business
Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf,
Isaak H.}, year={2025} }'
chicago: Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak H. Wolf. “Sets of
R-Graphs That Color All r-Graphs.” Combinatorica 45, no. 2 (2025). https://doi.org/10.1007/s00493-025-00144-4.
ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-Graphs that Color
All r-Graphs,” Combinatorica, vol. 45, no. 2, Art. no. 16, 2025, doi: 10.1007/s00493-025-00144-4.'
mla: Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” Combinatorica,
vol. 45, no. 2, 16, Springer Science and Business Media LLC, 2025, doi:10.1007/s00493-025-00144-4.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 45 (2025).
date_created: 2025-03-27T09:46:34Z
date_updated: 2025-03-27T09:48:48Z
department:
- _id: '542'
doi: 10.1007/s00493-025-00144-4
intvolume: ' 45'
issue: '2'
language:
- iso: eng
publication: Combinatorica
publication_identifier:
issn:
- 0209-9683
- 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Sets of r-Graphs that Color All r-Graphs
type: journal_article
user_id: '15540'
volume: 45
year: '2025'
...
---
_id: '53805'
abstract:
- lang: eng
text: The article introduces a method to learn dynamical systems that are governed
by Euler–Lagrange equations from data. The method is based on Gaussian process
regression and identifies continuous or discrete Lagrangians and is, therefore,
structure preserving by design. A rigorous proof of convergence as the distance
between observation data points converges to zero and lower bounds for convergence
rates are provided. Next to convergence guarantees, the method allows for quantification
of model uncertainty, which can provide a basis of adaptive sampling techniques.
We provide efficient uncertainty quantification of any observable that is linear
in the Lagrangian, including of Hamiltonian functions (energy) and symplectic
structures, which is of interest in the context of system identification. The
article overcomes major practical and theoretical difficulties related to the
ill-posedness of the identification task of (discrete) Lagrangians through a careful
design of geometric regularisation strategies and through an exploit of a relation
to convex minimisation problems in reproducing kernel Hilbert spaces.
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Offen C. Machine learning of continuous and discrete variational ODEs with
convergence guarantee and uncertainty quantification. Mathematics of Computation.
Published online 2025. doi:10.1090/mcom/4120
apa: Offen, C. (2025). Machine learning of continuous and discrete variational ODEs
with convergence guarantee and uncertainty quantification. Mathematics of Computation.
https://doi.org/10.1090/mcom/4120
bibtex: '@article{Offen_2025, title={Machine learning of continuous and discrete
variational ODEs with convergence guarantee and uncertainty quantification}, DOI={10.1090/mcom/4120}, journal={Mathematics
of Computation}, publisher={American Mathematical Society}, author={Offen, Christian},
year={2025} }'
chicago: Offen, Christian. “Machine Learning of Continuous and Discrete Variational
ODEs with Convergence Guarantee and Uncertainty Quantification.” Mathematics
of Computation, 2025. https://doi.org/10.1090/mcom/4120.
ieee: 'C. Offen, “Machine learning of continuous and discrete variational ODEs with
convergence guarantee and uncertainty quantification,” Mathematics of Computation,
2025, doi: 10.1090/mcom/4120.'
mla: Offen, Christian. “Machine Learning of Continuous and Discrete Variational
ODEs with Convergence Guarantee and Uncertainty Quantification.” Mathematics
of Computation, American Mathematical Society, 2025, doi:10.1090/mcom/4120.
short: C. Offen, Mathematics of Computation (2025).
date_created: 2024-04-30T16:04:40Z
date_updated: 2025-06-29T13:03:55Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1090/mcom/4120
external_id:
arxiv:
- arXiv:2404.19626
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2025-05-02T13:20:31Z
date_updated: 2025-05-02T13:20:31Z
description: |-
The article introduces a method to learn dynamical systems that
are governed by Euler–Lagrange equations from data. The method is based on
Gaussian process regression and identifies continuous or discrete Lagrangians
and is, therefore, structure preserving by design. A rigorous proof of con-
vergence as the distance between observation data points converges to zero
and lower bounds for convergence rates are provided. Next to convergence
guarantees, the method allows for quantification of model uncertainty, which
can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian,
including of Hamiltonian functions (energy) and symplectic structures, which
is of interest in the context of system identification. The article overcomes
major practical and theoretical difficulties related to the ill-posedness of the
identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex
minimisation problems in reproducing kernel Hilbert spaces.
file_id: '59759'
file_name: L_Collocation_ODE_mcom-l-template.pdf
file_size: 1819189
relation: main_file
title: 'Machine learning of continuous and discrete variational ODEs with convergence
guarantee and uncertainty quantification '
file_date_updated: 2025-05-02T13:20:31Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Mathematics of Computation
publication_status: epub_ahead
publisher: American Mathematical Society
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/Lagrangian_GP
status: public
title: Machine learning of continuous and discrete variational ODEs with convergence
guarantee and uncertainty quantification
type: journal_article
user_id: '85279'
year: '2025'
...
---
_id: '60491'
abstract:
- lang: eng
text: We investigate generalisations of 1-factorisations and hyperfactorisations
of the complete graph $K_{2n}$. We show that they are special subsets of the association
scheme obtained from the Gelfand pair $(S_{2n},S_2 \wr S_n)$. This unifies and
extends results by Cameron (1976) and gives rise to new existence and non-existence
results. Our methods involve working in the group algebra $\mathbb{C}[S_{2n}]$
and using the representation theory of $S_{2n}$.
author:
- first_name: Lukas-André Dominik
full_name: Klawuhn, Lukas-André Dominik
id: '91965'
last_name: Klawuhn
orcid: 0009-0009-7736-4885
- first_name: John
full_name: Bamberg, John
last_name: Bamberg
citation:
ama: Klawuhn L-AD, Bamberg J. On the association scheme of perfect matchings and
their designs. Published online 2025.
apa: Klawuhn, L.-A. D., & Bamberg, J. (2025). On the association scheme of
perfect matchings and their designs.
bibtex: '@article{Klawuhn_Bamberg_2025, title={On the association scheme of perfect
matchings and their designs}, author={Klawuhn, Lukas-André Dominik and Bamberg,
John}, year={2025} }'
chicago: Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme
of Perfect Matchings and Their Designs,” 2025.
ieee: L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings
and their designs.” 2025.
mla: Klawuhn, Lukas-André Dominik, and John Bamberg. On the Association Scheme
of Perfect Matchings and Their Designs. 2025.
short: L.-A.D. Klawuhn, J. Bamberg, (2025).
date_created: 2025-07-02T07:37:23Z
date_updated: 2025-07-02T07:47:09Z
department:
- _id: '100'
external_id:
arxiv:
- '2507.00813'
language:
- iso: eng
status: public
title: On the association scheme of perfect matchings and their designs
type: preprint
user_id: '91965'
year: '2025'
...
---
_id: '61042'
abstract:
- lang: eng
text: We introduce the concept of a k-token signed graph and study some of its combinatorial
and algebraic properties. We prove that two switching isomorphic signed graphs
have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum
of a balanced signed graph is contained in the Laplacian spectra of its k-token
signed graph. Besides, we introduce and study the unbalance level of a signed
graph, which is a new parameter that measures how far a signed graph is from being
balanced. Moreover, we study the relation between the frustration index and the
unbalance level of signed graphs and their token signed graphs.
article_number: '7'
author:
- first_name: C.
full_name: Dalfó, C.
last_name: Dalfó
- first_name: M. A.
full_name: Fiol, M. A.
last_name: Fiol
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: Dalfó C, Fiol MA, Steffen E. On token signed graphs. Journal of Algebraic
Combinatorics. 2025;62(1). doi:10.1007/s10801-025-01416-4
apa: Dalfó, C., Fiol, M. A., & Steffen, E. (2025). On token signed graphs. Journal
of Algebraic Combinatorics, 62(1), Article 7. https://doi.org/10.1007/s10801-025-01416-4
bibtex: '@article{Dalfó_Fiol_Steffen_2025, title={On token signed graphs}, volume={62},
DOI={10.1007/s10801-025-01416-4},
number={17}, journal={Journal of Algebraic Combinatorics}, publisher={Springer
Science and Business Media LLC}, author={Dalfó, C. and Fiol, M. A. and Steffen,
Eckhard}, year={2025} }'
chicago: Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” Journal
of Algebraic Combinatorics 62, no. 1 (2025). https://doi.org/10.1007/s10801-025-01416-4.
ieee: 'C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” Journal
of Algebraic Combinatorics, vol. 62, no. 1, Art. no. 7, 2025, doi: 10.1007/s10801-025-01416-4.'
mla: Dalfó, C., et al. “On Token Signed Graphs.” Journal of Algebraic Combinatorics,
vol. 62, no. 1, 7, Springer Science and Business Media LLC, 2025, doi:10.1007/s10801-025-01416-4.
short: C. Dalfó, M.A. Fiol, E. Steffen, Journal of Algebraic Combinatorics 62 (2025).
date_created: 2025-08-28T07:50:03Z
date_updated: 2025-08-28T07:57:27Z
department:
- _id: '542'
doi: 10.1007/s10801-025-01416-4
intvolume: ' 62'
issue: '1'
language:
- iso: eng
publication: Journal of Algebraic Combinatorics
publication_identifier:
issn:
- 0925-9899
- 1572-9192
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On token signed graphs
type: journal_article
user_id: '15540'
volume: 62
year: '2025'
...
---
_id: '59794'
abstract:
- lang: eng
text: The depth of networks plays a crucial role in the effectiveness of deep learning.
However, the memory requirement for backpropagation scales linearly with the number
of layers, which leads to memory bottlenecks during training. Moreover, deep networks
are often unable to handle time-series data appearing at irregular intervals.
These issues can be resolved by considering continuous-depth networks based on
the neural ODE framework in combination with reversible integration methods that
allow for variable time-steps. Reversibility of the method ensures that the memory
requirement for training is independent of network depth, while variable time-steps
are required for assimilating time-series data on irregular intervals. However,
at present, there are no known higher-order reversible methods with this property.
High-order methods are especially important when a high level of accuracy in learning
is required or when small time-steps are necessary due to large errors in time
integration of neural ODEs, for instance in context of complex dynamical systems
such as Kepler systems and molecular dynamics. The requirement of small time-steps
when using a low-order method can significantly increase the computational cost
of training as well as inference. In this work, we present an approach for constructing
high-order reversible methods that allow adaptive time-stepping. Our numerical
tests show the advantages in computational speed when applied to the task of learning
dynamical systems.
author:
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Pranav
full_name: Singh, Pranav
last_name: Singh
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Maslovskaya S, Ober-Blöbaum S, Offen C, Singh P, Wembe Moafo BE. Adaptive higher
order reversible integrators for memory efficient deep learning. Published online
2025.
apa: Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., & Wembe Moafo,
B. E. (2025). Adaptive higher order reversible integrators for memory efficient
deep learning.
bibtex: '@article{Maslovskaya_Ober-Blöbaum_Offen_Singh_Wembe Moafo_2025, title={Adaptive
higher order reversible integrators for memory efficient deep learning}, author={Maslovskaya,
Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe
Moafo, Boris Edgar}, year={2025} }'
chicago: Maslovskaya, Sofya, Sina Ober-Blöbaum, Christian Offen, Pranav Singh, and
Boris Edgar Wembe Moafo. “Adaptive Higher Order Reversible Integrators for Memory
Efficient Deep Learning,” 2025.
ieee: S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, and B. E. Wembe Moafo,
“Adaptive higher order reversible integrators for memory efficient deep learning.”
2025.
mla: Maslovskaya, Sofya, et al. Adaptive Higher Order Reversible Integrators
for Memory Efficient Deep Learning. 2025.
short: S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).
date_created: 2025-05-05T09:25:28Z
date_updated: 2025-09-30T15:16:09Z
ddc:
- '510'
department:
- _id: '636'
external_id:
arxiv:
- '2410.09537'
file:
- access_level: closed
content_type: application/pdf
creator: sofyam
date_created: 2025-05-05T09:28:02Z
date_updated: 2025-05-05T09:28:02Z
file_id: '59795'
file_name: 2410.09537v2.pdf
file_size: 1830758
relation: main_file
success: 1
file_date_updated: 2025-05-05T09:28:02Z
has_accepted_license: '1'
language:
- iso: eng
status: public
title: Adaptive higher order reversible integrators for memory efficient deep learning
type: preprint
user_id: '85279'
year: '2025'
...
---
_id: '57472'
abstract:
- lang: eng
text: In this paper we introduce, in a Hilbert space setting, a second order dynamical
system with asymptotically vanishing damping and vanishing Tikhonov regularization
that approaches a multiobjective optimization problem with convex and differentiable
components of the objective function. Trajectory solutions are shown to exist
in finite dimensions. We prove fast convergence of the function values, quantified
in terms of a merit function. Based on the regime considered, we establish both
weak and, in some cases, strong convergence of trajectory solutions toward a weak
Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually
to each component of the objective function. This work extends results from single
objective convex optimization into the multiobjective setting.
author:
- first_name: Radu Ioan
full_name: Bot, Radu Ioan
last_name: Bot
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
citation:
ama: Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization
for multobjective optimization. Journal of Mathematical Analysis and Applications.
Published online 2025.
apa: Bot, R. I., & Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov
regularization for multobjective optimization. Journal of Mathematical Analysis
and Applications.
bibtex: '@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov
regularization for multobjective optimization}, journal={Journal of Mathematical
Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025}
}'
chicago: Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing
Tikhonov Regularization for Multobjective Optimization.” Journal of Mathematical
Analysis and Applications, 2025.
ieee: R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization
for multobjective optimization,” Journal of Mathematical Analysis and Applications,
2025.
mla: Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov
Regularization for Multobjective Optimization.” Journal of Mathematical Analysis
and Applications, 2025.
short: R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).
date_created: 2024-11-28T08:58:17Z
date_updated: 2025-10-16T11:56:36Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
- _id: '655'
external_id:
arxiv:
- '2411.18422'
file:
- access_level: open_access
content_type: application/pdf
creator: sonntagk
date_created: 2024-11-28T08:58:00Z
date_updated: 2024-11-28T08:58:00Z
file_id: '57473'
file_name: Inertial dynamics with vanishing Tikhonov regularization for multobjective
optimization.pdf
file_size: 4291134
relation: main_file
file_date_updated: 2024-11-28T08:58:00Z
has_accepted_license: '1'
keyword:
- Pareto optimization
- Lyapunov analysis
- gradient-like dynamical systems
- inertial dynamics
- asymptotic vanishing damping
- Tikhonov regularization
- strong convergence
language:
- iso: eng
main_file_link:
- url: https://arxiv.org/pdf/2411.18422
oa: '1'
publication: Journal of Mathematical Analysis and Applications
status: public
title: Inertial dynamics with vanishing Tikhonov regularization for multobjective
optimization
type: journal_article
user_id: '56399'
year: '2025'
...