---
_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: '61759'
abstract:
- lang: eng
text: 'Intersection distribution and non-hitting index are concepts introduced recently
by Li and Pott as a new way to view the behaviour of a collection of finite field
polynomials. With both an algebraic interpretation via the intersection of a polynomial
with a set of lines, and a geometric interpretation via a (q+1)-set possessing
an internal nucleus, the concepts have proved their usefulness as a new way to
view various long-standing problems, and have applications in areas such as Kakeya
sets. In this paper, by exploiting connections with diverse areas including the
theory of algebraic curves, cyclotomy and the enumeration of irreducible polynomials,
we establish new results and resolve various Open Problems of Li and Pott. We
prove geometric results which shed new light on the relationship between intersection
distribution and projective equivalence of polynomials, and algebraic results
which describe and characterise the degree of Sf - the index of the largest non-zero
entry in the intersection distribution of f. We provide new insights into the
non-hitting spectrum, and show the limitations of the non-hitting index as a tool
for characterisation. Finally, the benefits provided by the connections to other
areas are evidenced in two short new proofs of the cubic case. '
article_number: '102828'
article_type: original
author:
- first_name: Lukas-André Dominik
full_name: Klawuhn, Lukas-André Dominik
id: '91965'
last_name: Klawuhn
orcid: 0009-0009-7736-4885
- first_name: Sophie
full_name: Huczynska, Sophie
last_name: Huczynska
- first_name: Maura
full_name: Paterson, Maura
last_name: Paterson
citation:
ama: 'Klawuhn L-AD, Huczynska S, Paterson M. The Intersection Distribution: New
Results and Perspectives. Finite Fields and Their Applications. 2026;114.
doi:10.1016/j.ffa.2026.102828'
apa: 'Klawuhn, L.-A. D., Huczynska, S., & Paterson, M. (2026). The Intersection
Distribution: New Results and Perspectives. Finite Fields and Their Applications,
114, Article 102828. https://doi.org/10.1016/j.ffa.2026.102828'
bibtex: '@article{Klawuhn_Huczynska_Paterson_2026, title={The Intersection Distribution:
New Results and Perspectives}, volume={114}, DOI={10.1016/j.ffa.2026.102828},
number={102828}, journal={Finite Fields and Their Applications}, publisher={Elsevier},
author={Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura},
year={2026} }'
chicago: 'Klawuhn, Lukas-André Dominik, Sophie Huczynska, and Maura Paterson. “The
Intersection Distribution: New Results and Perspectives.” Finite Fields and
Their Applications 114 (2026). https://doi.org/10.1016/j.ffa.2026.102828.'
ieee: 'L.-A. D. Klawuhn, S. Huczynska, and M. Paterson, “The Intersection Distribution:
New Results and Perspectives,” Finite Fields and Their Applications, vol.
114, Art. no. 102828, 2026, doi: 10.1016/j.ffa.2026.102828.'
mla: 'Klawuhn, Lukas-André Dominik, et al. “The Intersection Distribution: New Results
and Perspectives.” Finite Fields and Their Applications, vol. 114, 102828,
Elsevier, 2026, doi:10.1016/j.ffa.2026.102828.'
short: L.-A.D. Klawuhn, S. Huczynska, M. Paterson, Finite Fields and Their Applications
114 (2026).
date_created: 2025-10-08T14:52:20Z
date_updated: 2026-05-06T15:08:06Z
department:
- _id: '100'
doi: 10.1016/j.ffa.2026.102828
intvolume: ' 114'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S1071579726000390
oa: '1'
publication: Finite Fields and Their Applications
publisher: Elsevier
status: public
title: 'The Intersection Distribution: New Results and Perspectives'
type: journal_article
user_id: '91965'
volume: 114
year: '2026'
...
---
_id: '66057'
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 $A$-stable backward difference
full discretizations of Willmore flow of closed surfaces. ArXiv. Published
online 2026. doi:10.48550/arXiv.2606.25934
apa: Bullerjahn, N., & Kovács, B. (2026). Error estimates for $A$-stable backward
difference full discretizations of Willmore flow of closed surfaces. ArXiv.
https://doi.org/10.48550/arXiv.2606.25934
bibtex: '@article{Bullerjahn_Kovács_2026, title={Error estimates for $A$-stable
backward difference full discretizations of Willmore flow of closed surfaces},
DOI={10.48550/arXiv.2606.25934},
journal={ArXiv}, author={Bullerjahn, Nils and Kovács, Balázs}, year={2026} }'
chicago: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for $A$-Stable Backward
Difference Full Discretizations of Willmore Flow of Closed Surfaces.” ArXiv,
2026. https://doi.org/10.48550/arXiv.2606.25934.
ieee: 'N. Bullerjahn and B. Kovács, “Error estimates for $A$-stable backward difference
full discretizations of Willmore flow of closed surfaces,” ArXiv, 2026,
doi: 10.48550/arXiv.2606.25934.'
mla: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for $A$-Stable Backward
Difference Full Discretizations of Willmore Flow of Closed Surfaces.” ArXiv,
2026, doi:10.48550/arXiv.2606.25934.
short: N. Bullerjahn, B. Kovács, ArXiv (2026).
date_created: 2026-06-26T06:03:08Z
date_updated: 2026-06-26T06:09:29Z
department:
- _id: '841'
doi: 10.48550/arXiv.2606.25934
language:
- iso: eng
publication: ArXiv
status: public
title: Error estimates for $A$-stable backward difference full discretizations of
Willmore flow of closed surfaces
type: journal_article
user_id: '103797'
year: '2026'
...
---
_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. Algebraic Combinatorics. 2026;9(3):789-809. doi:10.5802/alco.490
apa: Klawuhn, L.-A. D., & Bamberg, J. (2026). On the association scheme of perfect
matchings and their designs. Algebraic Combinatorics, 9(3), 789–809.
https://doi.org/10.5802/alco.490
bibtex: '@article{Klawuhn_Bamberg_2026, title={On the association scheme of perfect
matchings and their designs}, volume={9}, DOI={10.5802/alco.490},
number={3}, journal={Algebraic Combinatorics}, author={Klawuhn, Lukas-André Dominik
and Bamberg, John}, year={2026}, pages={789–809} }'
chicago: 'Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme
of Perfect Matchings and Their Designs.” Algebraic Combinatorics 9, no.
3 (2026): 789–809. https://doi.org/10.5802/alco.490.'
ieee: 'L.-A. D. Klawuhn and J. Bamberg, “On the association scheme of perfect matchings
and their designs,” Algebraic Combinatorics, vol. 9, no. 3, pp. 789–809,
2026, doi: 10.5802/alco.490.'
mla: Klawuhn, Lukas-André Dominik, and John Bamberg. “On the Association Scheme
of Perfect Matchings and Their Designs.” Algebraic Combinatorics, vol.
9, no. 3, 2026, pp. 789–809, doi:10.5802/alco.490.
short: L.-A.D. Klawuhn, J. Bamberg, Algebraic Combinatorics 9 (2026) 789–809.
date_created: 2025-07-02T07:37:23Z
date_updated: 2026-07-10T12:26:11Z
department:
- _id: '100'
doi: 10.5802/alco.490
intvolume: ' 9'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://alco.centre-mersenne.org/articles/10.5802/alco.490/
oa: '1'
page: 789-809
publication: Algebraic Combinatorics
status: public
title: On the association scheme of perfect matchings and their designs
type: journal_article
user_id: '91965'
volume: 9
year: '2026'
...
---
_id: '66731'
abstract:
- lang: eng
text: "We generalize intersection numbers for combinatorial designs to designs in
finite meet-semilattices satisfying suitable regularity conditions. While designs
in regular semilattices go back to Delsarte, our regularity assumptions are weaker
than his and need not give rise to an association scheme. In this framework, we
extend Mendelsohn's equations, prove a generalized Singleton bound with Steiner
systems as equality cases, and determine the block intersection distribution at
any block of a Steiner system. In particular, this distribution is independent
of the chosen block.\r\n Specializing to several classical semilattice families,
our results recover a number of well-known distributions in coding and design
theory. In the Hamming and the $q$-Hamming (or bilinear forms) schemes, they give
the local distance distributions of MDS and MRD codes, respectively. In the Johnson
and $q$-Johnson (or Graßmann) schemes, they reproduce the block intersection distribution
of classical and $q$-analog Steiner systems, equivalently the distance distribution
of diameter-perfect constant-weight codes and diameter-perfect constant-dimension
subspace codes. For the $q$-Johnson schemes, to the best of our knowledge, this
result is new. As a further illustration, we apply our theory to designs of perfect
matchings.\r\n Our approach provides a unified treatment of these cases in the
strongest form known in the literature, determining the distribution relative
to each individual block or codeword, without averaging and without linearity
or additivity assumptions. Moreover, it identifies the natural double-counting
objects underlying these distributions, leading to formulas in the regularity
parameters of the semilattice and avoiding the more cumbersome expressions that
arise in eigenvalue-based approaches via the ambient association scheme."
author:
- first_name: Michael
full_name: Kiermaier, Michael
last_name: Kiermaier
- first_name: Lukas-André Dominik
full_name: Klawuhn, Lukas-André Dominik
id: '91965'
last_name: Klawuhn
orcid: 0009-0009-7736-4885
citation:
ama: Kiermaier M, Klawuhn L-AD. Intersection numbers for designs in regular semilattices.
Published online 2026.
apa: Kiermaier, M., & Klawuhn, L.-A. D. (2026). Intersection numbers for
designs in regular semilattices.
bibtex: '@article{Kiermaier_Klawuhn_2026, title={Intersection numbers for designs
in regular semilattices}, author={Kiermaier, Michael and Klawuhn, Lukas-André
Dominik}, year={2026} }'
chicago: Kiermaier, Michael, and Lukas-André Dominik Klawuhn. “Intersection Numbers
for Designs in Regular Semilattices,” 2026.
ieee: M. Kiermaier and L.-A. D. Klawuhn, “Intersection numbers for designs in regular
semilattices.” 2026.
mla: Kiermaier, Michael, and Lukas-André Dominik Klawuhn. Intersection Numbers
for Designs in Regular Semilattices. 2026.
short: M. Kiermaier, L.-A.D. Klawuhn, (2026).
date_created: 2026-08-17T10:29:36Z
date_updated: 2026-08-17T10:31:03Z
department:
- _id: '100'
external_id:
arxiv:
- '2608.14437'
language:
- iso: eng
status: public
title: Intersection numbers for designs in regular semilattices
type: preprint
user_id: '91965'
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: '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'
...
---
_id: '62750'
abstract:
- lang: eng
text: 'Diese Dissertation enthält Beiträge zum Bereich der Mehrzieloptimierung mit
einem Fokus auf unbeschränkten Problemen, die auf einem allgemeinen Hilbertraum
definiert sind. Für Mehrzieloptimierungsprobleme mit lokal Lipschitz-stetigen
Zielfunktionen definieren wir ein multikriterielles Subdifferential, das wir erstmals
im Kontext allgemeiner Hilberträume analysieren. Aufbauend auf diesen theoretischen
Untersuchungen präsentieren wir ein Abstiegsverfahren, bei welchem in jeder Iteration
eine Abstiegsrichtung mittels einer numerischen Approximation des multikriteriellen
Subdifferentials bestimmt wird. Im Kontext konvexer, stetig differenzierbarer
Zielfunktionen mit Lipschitz-stetigen Gradienten, führen wir eine Familie von
dynamischen Gradientensystemen mit Trägheitsterm ein, die bekannte kontinuierliche
Systeme aus der skalaren Optimierung verallgemeinern. Wir stellen drei neue Systeme
vor: eines mit konstanter Dämpfung, eines mit asymptotisch abnehmender Dämpfung
und eines, das zusätzlich eine zeitabhängige Tikhonov-Regularisierung beinhaltet.
Aufbauend auf den Untersuchungen der neuen dynamischen Gradientensysteme, entwickeln
wir ein beschleunigtes Gradientenverfahren zur Mehrzieloptimierung, das auf einer
Diskretisierung des multikriteriellen Gradientensystems mit asymptotisch abnehmender
Dämpfung beruht. Das hergeleitete Verfahren bewahrt die günstigen Konvergenzeigenschaften
des kontinuierlichen Systems und erreicht eine schnellere Konvergenz als klassische
Verfahren.'
- lang: eng
text: 'This dissertation contributes to the field of multiobjective optimization,
with a focus on unconstrained problems formulated in a general Hilbert space.
For multiobjective optimization problems with locally Lipschitz continuous objective
functions, we define a multiobjective subdifferential, which we analyze for the
first time in the context of general Hilbert spaces. Building on these theoretical
investigations, we present a descent method in which, at each iteration, a descent
direction is determined via a numerical approximation of the multiobjective subdifferential.
In the setting of convex, continuously differentiable objective functions with
Lipschitz continuous gradients, we introduce a family of inertial gradient dynamical
systems that generalize well-known continuous-time systems from scalar optimization.
We present three novel systems: one with constant damping, one with asymptotic
vanishing damping, and one combining vanishing damping with time-dependent Tikhonov
regularization. Building on the investigation of the novel gradient dynamical
systems, we develop an accelerated gradient method for multiobjective optimization
via discretization of the multiobjective gradient system with asymptotic vanishing
damping. The proposed method retains the favorable convergence properties of the
continuous system while achieving faster convergence than standard approaches,
such as classical methods.'
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
citation:
ama: Sonntag K. First-Order Methods and Gradient Dynamical Systems for Multiobjective
Optimization. Paderborn University; 2025. doi:10.17619/UNIPB/1-2457
apa: Sonntag, K. (2025). First-order methods and gradient dynamical systems for
multiobjective optimization. Paderborn University. https://doi.org/10.17619/UNIPB/1-2457
bibtex: '@book{Sonntag_2025, title={First-order methods and gradient dynamical systems
for multiobjective optimization}, DOI={10.17619/UNIPB/1-2457},
publisher={Paderborn University}, author={Sonntag, Konstantin}, year={2025} }'
chicago: Sonntag, Konstantin. First-Order Methods and Gradient Dynamical Systems
for Multiobjective Optimization. Paderborn University, 2025. https://doi.org/10.17619/UNIPB/1-2457.
ieee: K. Sonntag, First-order methods and gradient dynamical systems for multiobjective
optimization. Paderborn University, 2025.
mla: Sonntag, Konstantin. First-Order Methods and Gradient Dynamical Systems
for Multiobjective Optimization. Paderborn University, 2025, doi:10.17619/UNIPB/1-2457.
short: K. Sonntag, First-Order Methods and Gradient Dynamical Systems for Multiobjective
Optimization, Paderborn University, 2025.
date_created: 2025-12-03T06:55:01Z
date_updated: 2025-12-03T07:04:36Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
doi: 10.17619/UNIPB/1-2457
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/download/pdf/8141881
oa: '1'
publisher: Paderborn University
status: public
supervisor:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
title: First-order methods and gradient dynamical systems for multiobjective optimization
type: dissertation
user_id: '56399'
year: '2025'
...
---
_id: '62980'
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 is 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.
article_number: '033062'
author:
- first_name: Denis A.
full_name: Kopylov, Denis A.
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 R.
full_name: Sharapova, Polina R.
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 DA, Offen C, Ares L, et al. Multiphoton, multimode state classification
for nonlinear optical circuits. Physical Review Research. 2025;7(3). doi:10.1103/sv6z-v1gk
apa: Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S.,
Meier, T., Sharapova, P. R., & Sperling, J. (2025). Multiphoton, multimode
state classification for nonlinear optical circuits. Physical Review Research,
7(3), Article 033062. https://doi.org/10.1103/sv6z-v1gk
bibtex: '@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025,
title={Multiphoton, multimode state classification for nonlinear optical circuits},
volume={7}, DOI={10.1103/sv6z-v1gk},
number={3033062}, journal={Physical Review Research}, publisher={American Physical
Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura
and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova,
Polina R. and Sperling, Jan}, year={2025} }'
chicago: Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo,
Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton,
Multimode State Classification for Nonlinear Optical Circuits.” Physical Review
Research 7, no. 3 (2025). https://doi.org/10.1103/sv6z-v1gk.
ieee: 'D. A. Kopylov et al., “Multiphoton, multimode state classification
for nonlinear optical circuits,” Physical Review Research, vol. 7, no.
3, Art. no. 033062, 2025, doi: 10.1103/sv6z-v1gk.'
mla: Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for
Nonlinear Optical Circuits.” Physical Review Research, vol. 7, no. 3, 033062,
American Physical Society (APS), 2025, doi:10.1103/sv6z-v1gk.
short: D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier,
P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025).
date_created: 2025-12-09T09:08:39Z
date_updated: 2025-12-09T09:10:01Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '623'
doi: 10.1103/sv6z-v1gk
intvolume: ' 7'
issue: '3'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: Physical Review Research
publication_identifier:
issn:
- 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: journal_article
user_id: '16199'
volume: 7
year: '2025'
...
---
_id: '63187'
author:
- first_name: Arnott Jeffery Joel
full_name: Kidner, Arnott Jeffery Joel
id: '111755'
last_name: Kidner
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Weiqiang
full_name: Yu, Weiqiang
id: '117508'
last_name: Yu
citation:
ama: Kidner AJJ, Steffen E, Yu W. Edge-coloring 4- and 5-regular projective planar
graphs with no Petersen-minor. arXiv:251214285. Published online 2025.
apa: Kidner, A. J. J., Steffen, E., & Yu, W. (2025). Edge-coloring 4- and 5-regular
projective planar graphs with no Petersen-minor. In arXiv:2512.14285.
bibtex: '@article{Kidner_Steffen_Yu_2025, title={Edge-coloring 4- and 5-regular
projective planar graphs with no Petersen-minor}, journal={arXiv:2512.14285},
author={Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}, year={2025}
}'
chicago: Kidner, Arnott Jeffery Joel, Eckhard Steffen, and Weiqiang Yu. “Edge-Coloring
4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” ArXiv:2512.14285,
2025.
ieee: A. J. J. Kidner, E. Steffen, and W. Yu, “Edge-coloring 4- and 5-regular projective
planar graphs with no Petersen-minor,” arXiv:2512.14285. 2025.
mla: Kidner, Arnott Jeffery Joel, et al. “Edge-Coloring 4- and 5-Regular Projective
Planar Graphs with No Petersen-Minor.” ArXiv:2512.14285, 2025.
short: A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).
date_created: 2025-12-17T14:40:23Z
date_updated: 2025-12-18T13:17:18Z
department:
- _id: '542'
external_id:
arxiv:
- '2512.14285'
language:
- iso: eng
publication: arXiv:2512.14285
status: public
title: Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor
type: preprint
user_id: '15540'
year: '2025'
...
---
_id: '63384'
abstract:
- lang: eng
text: "Two fundamental ways to represent a group are as permutations and as matrices.
In this paper, we study linear representations of groups that intertwine with
a permutation representation. Recently, D'Alconzo and Di Scala investigated how
small the matrices in such a linear representation can be. The minimal dimension
of such a representation is the \\emph{linear dimension of the group action} and
this has applications in cryptography and cryptosystems.\r\n\r\nWe develop the
idea of linear dimension from an algebraic point of view by using the theory of
permutation modules. We give structural results about representations of minimal
dimension and investigate the implications of faithfulness, transitivity and primitivity
on the linear dimension. Furthermore, we compute the linear dimension of several
classes of finite primitive permutation groups. We also study wreath products,
allowing us to determine the linear dimension of imprimitive group actions. Finally,
we give the linear dimension of almost simple finite $2$-transitive groups, some
of which may be used for further applications in cryptography. Our results also
open up many new questions about linear representations of group actions."
author:
- first_name: Alice
full_name: Devillers, Alice
last_name: Devillers
- first_name: Michael
full_name: Giudici, Michael
last_name: Giudici
- first_name: Daniel R.
full_name: Hawtin, Daniel R.
last_name: Hawtin
- first_name: Lukas-André Dominik
full_name: Klawuhn, Lukas-André Dominik
id: '91965'
last_name: Klawuhn
orcid: 0009-0009-7736-4885
- first_name: Luke
full_name: Morgan, Luke
last_name: Morgan
citation:
ama: Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension
of group actions. Published online 2025.
apa: Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., & Morgan,
L. (2025). Linear dimension of group actions.
bibtex: '@article{Devillers_Giudici_Hawtin_Klawuhn_Morgan_2025, title={Linear dimension
of group actions}, author={Devillers, Alice and Giudici, Michael and Hawtin, Daniel
R. and Klawuhn, Lukas-André Dominik and Morgan, Luke}, year={2025} }'
chicago: Devillers, Alice, Michael Giudici, Daniel R. Hawtin, Lukas-André Dominik
Klawuhn, and Luke Morgan. “Linear Dimension of Group Actions,” 2025.
ieee: A. Devillers, M. Giudici, D. R. Hawtin, L.-A. D. Klawuhn, and L. Morgan, “Linear
dimension of group actions.” 2025.
mla: Devillers, Alice, et al. Linear Dimension of Group Actions. 2025.
short: A. Devillers, M. Giudici, D.R. Hawtin, L.-A.D. Klawuhn, L. Morgan, (2025).
date_created: 2025-12-19T11:20:46Z
date_updated: 2025-12-19T11:23:41Z
department:
- _id: '100'
external_id:
arxiv:
- '2512.16079'
language:
- iso: eng
status: public
title: Linear dimension of group actions
type: preprint
user_id: '91965'
year: '2025'
...