---
_id: '63510'
abstract:
- lang: eng
text: It has been shown recently that optimal control problems with the dynamical
constraint given by a second order system admit a regular Lagrangian formulation.
This implies that the optimality conditions can be obtained in a new form based
on the variational approach. In this paper we extend the first order necessary
optimality conditions obtained previously to second order optimality conditions.
This results in a complete characterization of the optimality conditions in a
new Lagrangian form.
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
last_name: Maslovskaya
- first_name: Sina Ober-Blöbaum
full_name: Sina Ober-Blöbaum, Sina Ober-Blöbaum
last_name: Sina Ober-Blöbaum
- first_name: Rodrigo T. Sato Martín de
full_name: Almagro, Rodrigo T. Sato Martín de
last_name: Almagro
citation:
ama: Konopik M, Leyendecker S, Maslovskaya S, Sina Ober-Blöbaum SO-B, Almagro RTSM
de. Second order optimality conditions in a new Lagrangian formulation for optimal
control problems. arXiv:250706024. Published online 2025.
apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Sina Ober-Blöbaum, S. O.-B.,
& Almagro, R. T. S. M. de. (2025). Second order optimality conditions in a
new Lagrangian formulation for optimal control problems. In arXiv:2507.06024.
bibtex: '@article{Konopik_Leyendecker_Maslovskaya_Sina Ober-Blöbaum_Almagro_2025,
title={Second order optimality conditions in a new Lagrangian formulation for
optimal control problems}, journal={arXiv:2507.06024}, author={Konopik, Michael
and Leyendecker, Sigrid and Maslovskaya, Sofya and Sina Ober-Blöbaum, Sina Ober-Blöbaum
and Almagro, Rodrigo T. Sato Martín de}, year={2025} }'
chicago: Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum
Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “Second Order Optimality
Conditions in a New Lagrangian Formulation for Optimal Control Problems.” ArXiv:2507.06024,
2025.
ieee: M. Konopik, S. Leyendecker, S. Maslovskaya, S. O.-B. Sina Ober-Blöbaum, and
R. T. S. M. de Almagro, “Second order optimality conditions in a new Lagrangian
formulation for optimal control problems,” arXiv:2507.06024. 2025.
mla: Konopik, Michael, et al. “Second Order Optimality Conditions in a New Lagrangian
Formulation for Optimal Control Problems.” ArXiv:2507.06024, 2025.
short: M. Konopik, S. Leyendecker, S. Maslovskaya, S.O.-B. Sina Ober-Blöbaum, R.T.S.M.
de Almagro, ArXiv:2507.06024 (2025).
date_created: 2026-01-06T18:28:18Z
date_updated: 2026-01-06T18:29:15Z
department:
- _id: '636'
external_id:
arxiv:
- '2507.06024'
language:
- iso: eng
publication: arXiv:2507.06024
status: public
title: Second order optimality conditions in a new Lagrangian formulation for optimal
control problems
type: preprint
user_id: '87909'
year: '2025'
...
---
_id: '59797'
author:
- first_name: Michael
full_name: Konopik, Michael
last_name: Konopik
- first_name: Rodrigo
full_name: T. Sato Martín de Almagro, Rodrigo
last_name: T. Sato Martín de Almagro
- 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: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
citation:
ama: Konopik M, T. Sato Martín de Almagro R, Maslovskaya S, Ober-Blöbaum S, Leyendecker
S. Variational integrators for a new Lagrangian approach to control affine systems
with a quadratic Lagrange term. Journal of Nonlinear Science. 2025;36(11).
doi:10.1007/s00332-025-10229-5
apa: Konopik, M., T. Sato Martín de Almagro, R., Maslovskaya, S., Ober-Blöbaum,
S., & Leyendecker, S. (2025). Variational integrators for a new Lagrangian
approach to control affine systems with a quadratic Lagrange term. Journal
of Nonlinear Science, 36(11). https://doi.org/10.1007/s00332-025-10229-5
bibtex: '@article{Konopik_T. Sato Martín de Almagro_Maslovskaya_Ober-Blöbaum_Leyendecker_2025,
title={Variational integrators for a new Lagrangian approach to control affine
systems with a quadratic Lagrange term}, volume={36}, DOI={10.1007/s00332-025-10229-5},
number={11}, journal={Journal of Nonlinear Science}, author={Konopik, Michael
and T. Sato Martín de Almagro, Rodrigo and Maslovskaya, Sofya and Ober-Blöbaum,
Sina and Leyendecker, Sigrid}, year={2025} }'
chicago: Konopik, Michael, Rodrigo T. Sato Martín de Almagro, Sofya Maslovskaya,
Sina Ober-Blöbaum, and Sigrid Leyendecker. “Variational Integrators for a New
Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.”
Journal of Nonlinear Science 36, no. 11 (2025). https://doi.org/10.1007/s00332-025-10229-5.
ieee: 'M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum,
and S. Leyendecker, “Variational integrators for a new Lagrangian approach to
control affine systems with a quadratic Lagrange term,” Journal of Nonlinear
Science, vol. 36, no. 11, 2025, doi: 10.1007/s00332-025-10229-5.'
mla: Konopik, Michael, et al. “Variational Integrators for a New Lagrangian Approach
to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Nonlinear
Science, vol. 36, no. 11, 2025, doi:10.1007/s00332-025-10229-5.
short: M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum,
S. Leyendecker, Journal of Nonlinear Science 36 (2025).
date_created: 2025-05-05T09:35:31Z
date_updated: 2026-01-06T18:26:57Z
department:
- _id: '636'
doi: 10.1007/s00332-025-10229-5
intvolume: ' 36'
issue: '11'
language:
- iso: eng
publication: Journal of Nonlinear Science
status: public
title: Variational integrators for a new Lagrangian approach to control affine systems
with a quadratic Lagrange term
type: journal_article
user_id: '87909'
volume: 36
year: '2025'
...
---
_id: '59799'
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
full_name: T. Sato Martín de Almagro, Rodrigo
last_name: T. Sato Martín de Almagro
citation:
ama: Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, T. Sato Martín de
Almagro R. A new Lagrangian approach to optimal control of second-order systems.
Nonlinearity. 2025;38(11). doi:10.1088/1361-6544/ae1d08
apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., & T. Sato
Martín de Almagro, R. (2025). A new Lagrangian approach to optimal control of
second-order systems. Nonlinearity, 38(11). https://doi.org/10.1088/1361-6544/ae1d08
bibtex: '@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_T. Sato Martín de
Almagro_2025, title={A new Lagrangian approach to optimal control of second-order
systems}, volume={38}, DOI={10.1088/1361-6544/ae1d08},
number={11}, journal={Nonlinearity}, author={Konopik, Michael and Leyendecker,
Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and T. Sato Martín de Almagro,
Rodrigo}, year={2025} }'
chicago: Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum,
and Rodrigo T. Sato Martín de Almagro. “A New Lagrangian Approach to Optimal Control
of Second-Order Systems.” Nonlinearity 38, no. 11 (2025). https://doi.org/10.1088/1361-6544/ae1d08.
ieee: 'M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato
Martín de Almagro, “A new Lagrangian approach to optimal control of second-order
systems,” Nonlinearity, vol. 38, no. 11, 2025, doi: 10.1088/1361-6544/ae1d08.'
mla: Konopik, Michael, et al. “A New Lagrangian Approach to Optimal Control of Second-Order
Systems.” Nonlinearity, vol. 38, no. 11, 2025, doi:10.1088/1361-6544/ae1d08.
short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. Sato Martín
de Almagro, Nonlinearity 38 (2025).
date_created: 2025-05-05T09:37:50Z
date_updated: 2026-01-06T18:24:40Z
department:
- _id: '636'
doi: 10.1088/1361-6544/ae1d08
intvolume: ' 38'
issue: '11'
language:
- iso: eng
publication: Nonlinearity
status: public
title: A new Lagrangian approach to optimal control of second-order systems
type: journal_article
user_id: '87909'
volume: 38
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: '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: '51208'
abstract:
- lang: eng
text: AbstractApproximation of subdifferentials
is one of the main tasks when computing descent directions for nonsmooth optimization
problems. In this article, we propose a bisection method for weakly lower semismooth
functions which is able to compute new subgradients that improve a given approximation
in case a direction with insufficient descent was computed. Combined with a recently
proposed deterministic gradient sampling approach, this yields a deterministic
and provably convergent way to approximate subdifferentials for computing descent
directions.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
optimization. Computational Optimization and Applications. Published online
2024. doi:10.1007/s10589-024-00552-0
apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
in nonsmooth optimization. Computational Optimization and Applications.
https://doi.org/10.1007/s10589-024-00552-0
bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0},
journal={Computational Optimization and Applications}, publisher={Springer Science
and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
2024. https://doi.org/10.1007/s10589-024-00552-0.
ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
in nonsmooth optimization,” Computational Optimization and Applications,
2024, doi: 10.1007/s10589-024-00552-0.'
mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.
short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
issn:
- 0926-6003
- 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...
---
_id: '46019'
abstract:
- lang: eng
text: We derive efficient algorithms to compute weakly Pareto optimal solutions
for smooth, convex and unconstrained multiobjective optimization problems in general
Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
system in the multiobjective setting, which trajectories converge weakly to Pareto
optimal solutions. Discretization of this system yields an inertial multiobjective
algorithm which generates sequences that converge weakly to Pareto optimal solutions.
We employ Nesterov acceleration to define an algorithm with an improved convergence
rate compared to the plain multiobjective steepest descent method (Algorithm 1).
A further improvement in terms of efficiency is achieved by avoiding the solution
of a quadratic subproblem to compute a common step direction for all objective
functions, which is usually required in first-order methods. Using a different
discretization of our inertial gradient-like dynamical system, we obtain an accelerated
multiobjective gradient method that does not require the solution of a subproblem
in each step (Algorithm 2). While this algorithm does not converge in general,
it yields good results on test problems while being faster than standard steepest
descent.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration
via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications.
Published online 2024. doi:10.1007/s10957-024-02389-3
apa: Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with
Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization
Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3},
journal={Journal of Optimization Theory and Applications}, publisher={Springer},
author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }'
chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient
Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal
of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3.
ieee: 'K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov
Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory
and Applications, 2024, doi: 10.1007/s10957-024-02389-3.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of
Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3.
short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).
date_created: 2023-07-12T06:35:58Z
date_updated: 2024-02-21T10:13:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10957-024-02389-3
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf
oa: '1'
publication: Journal of Optimization Theory and Applications
publication_status: published
publisher: Springer
status: public
title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
Gradient-Like Systems
type: journal_article
user_id: '56399'
year: '2024'
...
---
_id: '51334'
abstract:
- lang: eng
text: The efficient optimization method for locally Lipschitz continuous multiobjective
optimization problems from [1] is extended from finite-dimensional problems to
general Hilbert spaces. The method iteratively computes Pareto critical points,
where in each iteration, an approximation of the subdifferential is computed in
an efficient manner and then used to compute a common descent direction for all
objective functions. To prove convergence, we present some new optimality results
for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these,
we can show that every accumulation point of the sequence generated by our algorithm
is Pareto critical under common assumptions. Computational efficiency for finding
Pareto critical points is numerically demonstrated for multiobjective optimal
control of an obstacle problem.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Georg
full_name: Müller, Georg
last_name: Müller
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth
Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published
online 2024.
apa: Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024).
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.
In arXiv:2402.06376.
bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376},
author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian
and Volkwein, Stefan}, year={2024} }'
chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and
Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in
Hilbert Spaces.” ArXiv:2402.06376, 2024.
ieee: K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376.
2024.
mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective
Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.
short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376
(2024).
date_created: 2024-02-13T09:35:26Z
date_updated: 2024-02-21T10:21:03Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- "\t2402.06376"
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2402.06376
oa: '1'
publication: arXiv:2402.06376
status: public
title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
type: preprint
user_id: '56399'
year: '2024'
...
---
_id: '52726'
abstract:
- lang: eng
text: Heteroclinic structures organize global features of dynamical systems. We
analyse whether heteroclinic structures can arise in network dynamics with higher-order
interactions which describe the nonlinear interactions between three or more units.
We find that while commonly analysed model equations such as network dynamics
on undirected hypergraphs may be useful to describe local dynamics such as cluster
synchronization, they give rise to obstructions that allow to design of heteroclinic
structures in phase space. By contrast, directed hypergraphs break the homogeneity
and lead to vector fields that support heteroclinic structures.
article_type: original
author:
- first_name: Christian
full_name: Bick, Christian
last_name: Bick
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
citation:
ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems
with higher-order interactions. Journal of Complex Networks. 2024;12(2).
doi:10.1093/comnet/cnae009
apa: Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network
dynamical systems with higher-order interactions. Journal of Complex Networks,
12(2). https://doi.org/10.1093/comnet/cnae009
bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009},
number={2}, journal={Journal of Complex Networks}, publisher={Oxford University
Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024}
}'
chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks
12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.
ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
systems with higher-order interactions,” Journal of Complex Networks, vol.
12, no. 2, 2024, doi: 10.1093/comnet/cnae009.'
mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks,
vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.
short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
arxiv:
- '2309.02006'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2024-03-22T09:06:07Z
date_updated: 2024-03-22T09:06:07Z
file_id: '52728'
file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
file_size: 649155
relation: main_file
success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: ' 12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
issn:
- 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...
---
_id: '49905'
abstract:
- lang: eng
text: "For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected
r-graph has s pairwise disjoint perfect matchings. There are only a few values
of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for
all t \x03 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤
3l − 6 for every l ≥ 3 and r ≥ 2l."
author:
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
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 Hieronymus
full_name: Wolf, Isaak Hieronymus
id: '88145'
last_name: Wolf
citation:
ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint
Perfect Matchings in Regular Graphs. Combinatorica. 2024;44:429-440. doi:10.1007/s00493-023-00078-9
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2024). Edge-Connectivity
and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica,
44, 429–440. https://doi.org/10.1007/s00493-023-00078-9
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise
Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={10.1007/s00493-023-00078-9},
journal={Combinatorica}, publisher={Springer Science and Business Media LLC},
author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus},
year={2024}, pages={429–440} }'
chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
“Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.”
Combinatorica 44 (2024): 429–40. https://doi.org/10.1007/s00493-023-00078-9.'
ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise
Disjoint Perfect Matchings in Regular Graphs,” Combinatorica, vol. 44,
pp. 429–440, 2024, doi: 10.1007/s00493-023-00078-9.'
mla: Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings
in Regular Graphs.” Combinatorica, vol. 44, Springer Science and Business
Media LLC, 2024, pp. 429–40, doi:10.1007/s00493-023-00078-9.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.
date_created: 2023-12-20T10:31:27Z
date_updated: 2024-03-22T12:11:35Z
department:
- _id: '542'
doi: 10.1007/s00493-023-00078-9
intvolume: ' 44'
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 429-440
publication: Combinatorica
publication_identifier:
issn:
- 0209-9683
- 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
type: journal_article
user_id: '15540'
volume: 44
year: '2024'
...
---
_id: '53101'
abstract:
- lang: eng
text: In this work, we consider optimal control problems for mechanical systems
with fixed initial and free final state and a quadratic Lagrange term. Specifically,
the dynamics is described by a second order ODE containing an affine control term.
Classically, Pontryagin's maximum principle gives necessary optimality conditions
for the optimal control problem. For smooth problems, alternatively, a variational
approach based on an augmented objective can be followed. Here, we propose a new
Lagrangian approach leading to equivalent necessary optimality conditions in the
form of Euler-Lagrange equations. Thus, the differential geometric structure (similar
to classical Lagrangian dynamics) can be exploited in the framework of optimal
control problems. In particular, the formulation enables the symplectic discretisation
of the optimal control problem via variational integrators in a straightforward
way.
article_type: original
author:
- 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. Sato Martín de
full_name: Almagro, Rodrigo T. Sato Martín de
last_name: Almagro
- first_name: Flóra Orsolya
full_name: Szemenyei, Flóra Orsolya
last_name: Szemenyei
citation:
ama: Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO.
A new Lagrangian approach to control affine systems with a quadratic Lagrange
term. Journal of Computational Dynamics. 2024;0(0):0-0. doi:10.3934/jcd.2024017
apa: Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de,
& Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems
with a quadratic Lagrange term. Journal of Computational Dynamics, 0(0),
0–0. https://doi.org/10.3934/jcd.2024017
bibtex: '@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A
new Lagrangian approach to control affine systems with a quadratic Lagrange term},
volume={0}, DOI={10.3934/jcd.2024017},
number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute
of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya,
Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei,
Flóra Orsolya}, year={2024}, pages={0–0} }'
chicago: 'Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T.
Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach
to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational
Dynamics 0, no. 0 (2024): 0–0. https://doi.org/10.3934/jcd.2024017.'
ieee: 'S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro,
and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with
a quadratic Lagrange term,” Journal of Computational Dynamics, vol. 0,
no. 0, pp. 0–0, 2024, doi: 10.3934/jcd.2024017.'
mla: Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems
with a Quadratic Lagrange Term.” Journal of Computational Dynamics, vol.
0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:10.3934/jcd.2024017.
short: S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O.
Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0.
date_created: 2024-03-28T15:58:02Z
date_updated: 2024-03-28T16:07:34Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jcd.2024017
has_accepted_license: '1'
issue: '0'
keyword:
- Optimal control problem
- Lagrangian system
- Hamiltonian system
- Variations
- Pontryagin's maximum principle.
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.aimsciences.org/article/doi/10.3934/jcd.2024017
oa: '1'
page: 0-0
publication: Journal of Computational Dynamics
publication_identifier:
issn:
- 2158-2491
- 2158-2505
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: A new Lagrangian approach to control affine systems with a quadratic Lagrange
term
type: journal_article
user_id: '87909'
volume: '0'
year: '2024'
...
---
_id: '53534'
abstract:
- lang: eng
text: "It is known that the notion of a transitive subgroup of a permutation group\r\n$G$
extends naturally to subsets of $G$. We consider subsets of the general\r\nlinear
group $\\operatorname{GL}(n,q)$ acting transitively on flag-like\r\nstructures,
which are common generalisations of $t$-dimensional subspaces of\r\n$\\mathbb{F}_q^n$
and bases of $t$-dimensional subspaces of $\\mathbb{F}_q^n$. We\r\ngive structural
characterisations of transitive subsets of\r\n$\\operatorname{GL}(n,q)$ using
the character theory of $\\operatorname{GL}(n,q)$\r\nand interpret such subsets
as designs in the conjugacy class association\r\nscheme of $\\operatorname{GL}(n,q)$.
In particular we generalise a theorem of\r\nPerin on subgroups of $\\operatorname{GL}(n,q)$
acting transitively on\r\n$t$-dimensional subspaces. We survey transitive subgroups
of\r\n$\\operatorname{GL}(n,q)$, showing that there is no subgroup of\r\n$\\operatorname{GL}(n,q)$
with $1Mathematische
Zeitschrift. 2024;307(45). doi:10.1007/s00209-024-03511-x
apa: Ernst, A., & Schmidt, K.-U. (2024). Transitivity in finite general linear
groups. Mathematische Zeitschrift, 307(45). https://doi.org/10.1007/s00209-024-03511-x
bibtex: '@article{Ernst_Schmidt_2024, title={Transitivity in finite general linear
groups}, volume={307}, DOI={10.1007/s00209-024-03511-x},
number={45}, journal={Mathematische Zeitschrift}, author={Ernst, Alena and Schmidt,
Kai-Uwe}, year={2024} }'
chicago: Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear
Groups.” Mathematische Zeitschrift 307, no. 45 (2024). https://doi.org/10.1007/s00209-024-03511-x.
ieee: 'A. Ernst and K.-U. Schmidt, “Transitivity in finite general linear groups,”
Mathematische Zeitschrift, vol. 307, no. 45, 2024, doi: 10.1007/s00209-024-03511-x.'
mla: Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear Groups.”
Mathematische Zeitschrift, vol. 307, no. 45, 2024, doi:10.1007/s00209-024-03511-x.
short: A. Ernst, K.-U. Schmidt, Mathematische Zeitschrift 307 (2024).
date_created: 2024-04-17T12:26:51Z
date_updated: 2024-06-17T10:04:29Z
department:
- _id: '100'
doi: 10.1007/s00209-024-03511-x
intvolume: ' 307'
issue: '45'
language:
- iso: eng
publication: Mathematische Zeitschrift
status: public
title: Transitivity in finite general linear groups
type: journal_article
user_id: '46953'
volume: 307
year: '2024'
...
---
_id: '32447'
abstract:
- lang: eng
text: 'We present a new gradient-like dynamical system related to unconstrained
convex smooth multiobjective optimization which involves inertial effects and
asymptotic vanishing damping. To the best of our knowledge, this system is the
first inertial gradient-like system for multiobjective optimization problems including
asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch
and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to
Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions
to this system in finite dimensions and further prove that its bounded solutions
converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence
rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a
merit function. This approach presents a good basis for the development of fast
gradient methods for multiobjective optimization.'
article_type: original
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-Like
Systems with Asymptotic Vanishing Damping. SIAM Journal on Optimization.
2024;34(3):2259-2286. doi:10.1137/23M1588512
apa: Sonntag, K., & Peitz, S. (2024). Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping. SIAM Journal on Optimization,
34(3), 2259–2286. https://doi.org/10.1137/23M1588512
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping}, volume={34}, DOI={10.1137/23M1588512}, number={3},
journal={SIAM Journal on Optimization}, publisher={Society for Industrial and
Applied Mathematics}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024},
pages={2259–2286} }'
chicago: 'Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial
Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping.” SIAM
Journal on Optimization 34, no. 3 (2024): 2259–86. https://doi.org/10.1137/23M1588512.'
ieee: 'K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-Like
Systems with Asymptotic Vanishing Damping,” SIAM Journal on Optimization,
vol. 34, no. 3, pp. 2259–2286, 2024, doi: 10.1137/23M1588512.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping.” SIAM Journal on Optimization,
vol. 34, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 2259–86,
doi:10.1137/23M1588512.
short: K. Sonntag, S. Peitz, SIAM Journal on Optimization 34 (2024) 2259–2286.
date_created: 2022-07-28T11:53:02Z
date_updated: 2024-07-02T09:27:39Z
department:
- _id: '101'
- _id: '655'
doi: 10.1137/23M1588512
intvolume: ' 34'
issue: '3'
keyword:
- multiobjective optimization
- Pareto optimization
- Lyapunov analysis
- gradient-likedynamical systems
- inertial dynamics
- asymptotic vanishing damping
- fast convergence
language:
- iso: eng
page: 2259 - 2286
publication: SIAM Journal on Optimization
publication_identifier:
issn:
- 1095-7189
publication_status: published
publisher: Society for Industrial and Applied Mathematics
status: public
title: Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic
Vanishing Damping
type: journal_article
user_id: '56399'
volume: 34
year: '2024'
...
---
_id: '55276'
author:
- first_name: P.
full_name: Minelli, P.
last_name: Minelli
- first_name: A.
full_name: Sourmelidis, A.
last_name: Sourmelidis
- first_name: Marc
full_name: Technau, Marc
id: '106108'
last_name: Technau
orcid: 0000-0001-9650-2459
citation:
ama: Minelli P, Sourmelidis A, Technau M. On restricted averages of Dedekind sums.
Int Math Res Not IMRN. 2024;2024(10):8485–8502. doi:10.1093/imrn/rnad283
apa: Minelli, P., Sourmelidis, A., & Technau, M. (2024). On restricted averages
of Dedekind sums. Int. Math. Res. Not. IMRN, 2024(10), 8485–8502.
https://doi.org/10.1093/imrn/rnad283
bibtex: '@article{Minelli_Sourmelidis_Technau_2024, title={On restricted averages
of Dedekind sums}, volume={2024}, DOI={10.1093/imrn/rnad283},
number={10}, journal={Int. Math. Res. Not. IMRN}, author={Minelli, P. and Sourmelidis,
A. and Technau, Marc}, year={2024}, pages={8485–8502} }'
chicago: 'Minelli, P., A. Sourmelidis, and Marc Technau. “On Restricted Averages
of Dedekind Sums.” Int. Math. Res. Not. IMRN 2024, no. 10 (2024): 8485–8502.
https://doi.org/10.1093/imrn/rnad283.'
ieee: 'P. Minelli, A. Sourmelidis, and M. Technau, “On restricted averages of Dedekind
sums,” Int. Math. Res. Not. IMRN, vol. 2024, no. 10, pp. 8485–8502, 2024,
doi: 10.1093/imrn/rnad283.'
mla: Minelli, P., et al. “On Restricted Averages of Dedekind Sums.” Int. Math.
Res. Not. IMRN, vol. 2024, no. 10, 2024, pp. 8485–8502, doi:10.1093/imrn/rnad283.
short: P. Minelli, A. Sourmelidis, M. Technau, Int. Math. Res. Not. IMRN 2024 (2024)
8485–8502.
date_created: 2024-07-16T11:09:00Z
date_updated: 2024-07-24T07:23:20Z
department:
- _id: '102'
doi: 10.1093/imrn/rnad283
intvolume: ' 2024'
issue: '10'
language:
- iso: eng
page: 8485–8502
publication: Int. Math. Res. Not. IMRN
status: public
title: On restricted averages of Dedekind sums
type: journal_article
user_id: '106108'
volume: 2024
year: '2024'
...
---
_id: '55278'
author:
- first_name: Marc
full_name: Technau, Marc
id: '106108'
last_name: Technau
orcid: 0000-0001-9650-2459
citation:
ama: Technau M. Remark on the Farey fraction spin chain. Proc Amer Math Soc.
2024;152(1):63–69. doi:10.1090/proc/16520
apa: Technau, M. (2024). Remark on the Farey fraction spin chain. Proc. Amer.
Math. Soc., 152(1), 63–69. https://doi.org/10.1090/proc/16520
bibtex: '@article{Technau_2024, title={Remark on the Farey fraction spin chain},
volume={152}, DOI={10.1090/proc/16520},
number={1}, journal={Proc. Amer. Math. Soc.}, author={Technau, Marc}, year={2024},
pages={63–69} }'
chicago: 'Technau, Marc. “Remark on the Farey Fraction Spin Chain.” Proc. Amer.
Math. Soc. 152, no. 1 (2024): 63–69. https://doi.org/10.1090/proc/16520.'
ieee: 'M. Technau, “Remark on the Farey fraction spin chain,” Proc. Amer. Math.
Soc., vol. 152, no. 1, pp. 63–69, 2024, doi: 10.1090/proc/16520.'
mla: Technau, Marc. “Remark on the Farey Fraction Spin Chain.” Proc. Amer. Math.
Soc., vol. 152, no. 1, 2024, pp. 63–69, doi:10.1090/proc/16520.
short: M. Technau, Proc. Amer. Math. Soc. 152 (2024) 63–69.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:26:12Z
department:
- _id: '102'
doi: 10.1090/proc/16520
extern: '1'
intvolume: ' 152'
issue: '1'
language:
- iso: eng
page: 63–69
publication: Proc. Amer. Math. Soc.
status: public
title: Remark on the Farey fraction spin chain
type: journal_article
user_id: '106108'
volume: 152
year: '2024'
...