---
_id: '44857'
abstract:
- lang: eng
text: Ancestral reconstruction is a classic task in comparative genomics. Here,
we study the genome median problem, a related computational problem which, given
a set of three or more genomes, asks to find a new genome that minimizes the sum
of pairwise distances between it and the given genomes. The distance stands for
the amount of evolution observed at the genome level, for which we determine the
minimum number of rearrangement operations necessary to transform one genome into
the other. For almost all rearrangement operations the median problem is NP-hard,
with the exception of the breakpoint median that can be constructed efficiently
for multichromosomal circular and mixed genomes. In this work, we study the median
problem under a restricted rearrangement measure called c4-distance, which is
closely related to the breakpoint and the DCJ distance. We identify tight bounds
and decomposers of the c4-median and develop algorithms for its construction,
one exact ILP-based and three combinatorial heuristics. Subsequently, we perform
experiments on simulated data sets. Our results suggest that the c4-distance is
useful for the study the genome median problem, from theoretical and practical
perspectives.
author:
- first_name: Helmuth O.M.
full_name: Silva, Helmuth O.M.
last_name: Silva
- first_name: Diego P.
full_name: Rubert, Diego P.
last_name: Rubert
- first_name: Eloi
full_name: Araujo, Eloi
last_name: Araujo
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Daniel
full_name: Doerr, Daniel
last_name: Doerr
- first_name: Fábio V.
full_name: Martinez, Fábio V.
last_name: Martinez
citation:
ama: Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms
for the genome median under a restricted measure of rearrangement. RAIRO -
Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052
apa: Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez,
F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement.
RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052
bibtex: '@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms
for the genome median under a restricted measure of rearrangement}, volume={57},
DOI={10.1051/ro/2023052}, number={3},
journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva,
Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr,
Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }'
chicago: 'Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel
Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted
Measure of Rearrangement.” RAIRO - Operations Research 57, no. 3 (2023):
1045–58. https://doi.org/10.1051/ro/2023052.'
ieee: 'H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V.
Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,”
RAIRO - Operations Research, vol. 57, no. 3, pp. 1045–1058, 2023, doi:
10.1051/ro/2023052.'
mla: Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted
Measure of Rearrangement.” RAIRO - Operations Research, vol. 57, no. 3,
EDP Sciences, 2023, pp. 1045–58, doi:10.1051/ro/2023052.
short: H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez,
RAIRO - Operations Research 57 (2023) 1045–1058.
date_created: 2023-05-16T08:48:22Z
date_updated: 2023-05-16T08:49:30Z
department:
- _id: '542'
doi: 10.1051/ro/2023052
intvolume: ' 57'
issue: '3'
keyword:
- Management Science and Operations Research
- Computer Science Applications
- Theoretical Computer Science
language:
- iso: eng
page: 1045-1058
publication: RAIRO - Operations Research
publication_identifier:
issn:
- 0399-0559
- 2804-7303
publication_status: published
publisher: EDP Sciences
status: public
title: Algorithms for the genome median under a restricted measure of rearrangement
type: journal_article
user_id: '15540'
volume: 57
year: '2023'
...
---
_id: '44859'
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. Sets of r-graphs that color all r-graphs.
arXiv:230508619. Published online 2023.
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Sets of r-graphs
that color all r-graphs. In arXiv:2305.08619.
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color
all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide
and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }'
chicago: Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
“Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023.
ieee: Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color
all r-graphs,” arXiv:2305.08619. 2023.
mla: Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619,
2023.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).
date_created: 2023-05-16T10:07:47Z
date_updated: 2023-05-16T11:17:26Z
department:
- _id: '542'
external_id:
arxiv:
- '2305.08619'
language:
- iso: eng
publication: arXiv:2305.08619
status: public
title: Sets of r-graphs that color all r-graphs
type: preprint
user_id: '15540'
year: '2023'
...
---
_id: '34833'
author:
- first_name: Maximilian
full_name: Hanusch, Maximilian
id: '30905'
last_name: Hanusch
citation:
ama: Hanusch M. Decompositions of Analytic 1-Manifolds. Indagationes Mathematicae.
2023;34(4):752-811. doi:10.1016/j.indag.2023.02.003
apa: Hanusch, M. (2023). Decompositions of Analytic 1-Manifolds. Indagationes
Mathematicae., 34(4), 752–811. https://doi.org/10.1016/j.indag.2023.02.003
bibtex: '@article{Hanusch_2023, title={Decompositions of Analytic 1-Manifolds},
volume={34}, DOI={10.1016/j.indag.2023.02.003},
number={4}, journal={Indagationes Mathematicae.}, author={Hanusch, Maximilian},
year={2023}, pages={752–811} }'
chicago: 'Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” Indagationes
Mathematicae. 34, no. 4 (2023): 752–811. https://doi.org/10.1016/j.indag.2023.02.003.'
ieee: 'M. Hanusch, “Decompositions of Analytic 1-Manifolds,” Indagationes Mathematicae.,
vol. 34, no. 4, pp. 752–811, 2023, doi: 10.1016/j.indag.2023.02.003.'
mla: Hanusch, Maximilian. “Decompositions of Analytic 1-Manifolds.” Indagationes
Mathematicae., vol. 34, no. 4, 2023, pp. 752–811, doi:10.1016/j.indag.2023.02.003.
short: M. Hanusch, Indagationes Mathematicae. 34 (2023) 752–811.
date_created: 2022-12-22T09:46:36Z
date_updated: 2023-05-25T07:32:38Z
department:
- _id: '93'
doi: 10.1016/j.indag.2023.02.003
intvolume: ' 34'
issue: '4'
keyword:
- Lie group actions and analytic 1-submanifolds
language:
- iso: eng
page: 752-811
publication: Indagationes Mathematicae.
publication_status: published
status: public
title: Decompositions of Analytic 1-Manifolds
type: journal_article
user_id: '30905'
volume: 34
year: '2023'
...
---
_id: '45498'
abstract:
- lang: eng
text: "We present a novel method for high-order phase reduction in networks of\r\nweakly
coupled oscillators and, more generally, perturbations of reducible\r\nnormally
hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic
expansion for an embedding of the perturbed invariant torus, as well\r\nas for
the reduced phase dynamics in local coordinates. Both can be determined\r\nto
arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly
be obtained in normal form. We apply the method to predict remote\r\nsynchronisation
in a chain of coupled Stuart-Landau oscillators."
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. A parametrisation method for high-order
phase reduction in coupled oscillator networks. arXiv:230603320.
apa: von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method
for high-order phase reduction in coupled oscillator networks. In arXiv:2306.03320.
bibtex: '@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for
high-order phase reduction in coupled oscillator networks}, journal={arXiv:2306.03320},
author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation
Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320,
n.d.
ieee: S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for
high-order phase reduction in coupled oscillator networks,” arXiv:2306.03320.
.
mla: von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase
Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.
short: S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).
date_created: 2023-06-07T07:57:28Z
date_updated: 2023-06-07T07:59:06Z
department:
- _id: '101'
external_id:
arxiv:
- '2306.03320'
language:
- iso: eng
main_file_link:
- url: https://arxiv.org/pdf/2306.03320
page: '29'
publication: arXiv:2306.03320
publication_status: submitted
status: public
title: A parametrisation method for high-order phase reduction in coupled oscillator
networks
type: preprint
user_id: '97359'
year: '2023'
...
---
_id: '45712'
author:
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: Häsel-Weide U. Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt
von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift.
2023;(339):6-11.
apa: Häsel-Weide, U. (2023). Inklusiver Mathematikunterricht. Mathematiklernen
in Vielfalt von Kompetenzen, Wegen und Lernsituationen. Die Grundschulzeitschrift,
339, 6–11.
bibtex: '@article{Häsel-Weide_2023, title={ Inklusiver Mathematikunterricht. Mathematiklernen
in Vielfalt von Kompetenzen, Wegen und Lernsituationen}, number={339}, journal={Die
Grundschulzeitschrift}, publisher={Friedrich Verlag}, author={Häsel-Weide, Uta},
year={2023}, pages={6–11} }'
chicago: 'Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen
in Vielfalt von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift,
no. 339 (2023): 6–11.'
ieee: U. Häsel-Weide, “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt
von Kompetenzen, Wegen und Lernsituationen,” Die Grundschulzeitschrift,
no. 339, pp. 6–11, 2023.
mla: Häsel-Weide, Uta. “ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt
von Kompetenzen, Wegen und Lernsituationen.” Die Grundschulzeitschrift,
no. 339, Friedrich Verlag, 2023, pp. 6–11.
short: U. Häsel-Weide, Die Grundschulzeitschrift (2023) 6–11.
date_created: 2023-06-22T09:28:22Z
date_updated: 2023-06-22T09:34:13Z
department:
- _id: '543'
issue: '339'
language:
- iso: ger
page: 6-11
publication: Die Grundschulzeitschrift
publisher: Friedrich Verlag
related_material:
link:
- relation: other
url: https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991
status: public
title: ' Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen,
Wegen und Lernsituationen'
type: journal_article
user_id: '44184'
year: '2023'
...
---
_id: '45713'
author:
- first_name: Lara Marie
full_name: Graf, Lara Marie
id: '89837'
last_name: Graf
- first_name: Inga
full_name: Wienhues, Inga
id: '61635'
last_name: Wienhues
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: Graf LM, Wienhues I, Häsel-Weide U. Addition und Subtraktion verstehen. Die
Grundschulzeitschrift. 2023;(339):20-23.
apa: Graf, L. M., Wienhues, I., & Häsel-Weide, U. (2023). Addition und Subtraktion
verstehen. Die Grundschulzeitschrift, 339, 20–23.
bibtex: '@article{Graf_Wienhues_Häsel-Weide_2023, title={Addition und Subtraktion
verstehen}, number={339}, journal={Die Grundschulzeitschrift}, publisher={Friedrich
Verlag}, author={Graf, Lara Marie and Wienhues, Inga and Häsel-Weide, Uta}, year={2023},
pages={20–23} }'
chicago: 'Graf, Lara Marie, Inga Wienhues, and Uta Häsel-Weide. “Addition und Subtraktion
verstehen.” Die Grundschulzeitschrift, no. 339 (2023): 20–23.'
ieee: L. M. Graf, I. Wienhues, and U. Häsel-Weide, “Addition und Subtraktion verstehen,”
Die Grundschulzeitschrift, no. 339, pp. 20–23, 2023.
mla: Graf, Lara Marie, et al. “Addition und Subtraktion verstehen.” Die Grundschulzeitschrift,
no. 339, Friedrich Verlag, 2023, pp. 20–23.
short: L.M. Graf, I. Wienhues, U. Häsel-Weide, Die Grundschulzeitschrift (2023)
20–23.
date_created: 2023-06-22T09:33:59Z
date_updated: 2023-06-22T09:34:18Z
department:
- _id: '543'
issue: '339'
language:
- iso: ger
page: 20-23
publication: Die Grundschulzeitschrift
publisher: Friedrich Verlag
related_material:
link:
- relation: other
url: https://www.friedrich-verlag.de/grundschule/die-grundschulzeitschrift/mathematikunterricht-inklusiv-5991
status: public
title: Addition und Subtraktion verstehen
type: journal_article
user_id: '44184'
year: '2023'
...
---
_id: '46117'
abstract:
- lang: eng
text: "Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact
type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We
show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic
growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain
that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."
author:
- first_name: Tobias
full_name: Weich, Tobias
last_name: Weich
- first_name: Lasse L.
full_name: Wolf, Lasse L.
last_name: Wolf
citation:
ama: 'Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case.
arXiv:230409573. Published online 2023.'
apa: 'Weich, T., & Wolf, L. L. (2023). Temperedness of locally symmetric spaces:
The product case. In arXiv:2304.09573.'
bibtex: '@article{Weich_Wolf_2023, title={Temperedness of locally symmetric spaces:
The product case}, journal={arXiv:2304.09573}, author={Weich, Tobias and Wolf,
Lasse L.}, year={2023} }'
chicago: 'Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces:
The Product Case.” ArXiv:2304.09573, 2023.'
ieee: 'T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product
case,” arXiv:2304.09573. 2023.'
mla: 'Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces:
The Product Case.” ArXiv:2304.09573, 2023.'
short: T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023).
date_created: 2023-07-24T07:52:23Z
date_updated: 2023-07-24T07:53:29Z
department:
- _id: '10'
external_id:
arxiv:
- '2304.09573'
language:
- iso: eng
publication: arXiv:2304.09573
status: public
title: 'Temperedness of locally symmetric spaces: The product case'
type: preprint
user_id: '45027'
year: '2023'
...
---
_id: '46256'
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. Pairwise Disjoint Perfect Matchings in
r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics.
2023;37(3):1548-1565. doi:10.1137/22m1500654
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint
Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete
Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect
Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654},
number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society
for Industrial & Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo,
Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565}
}'
chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
“Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM
Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.'
ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect
Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics,
vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654.'
mla: Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected
r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3,
Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics
37 (2023) 1548–1565.
date_created: 2023-08-01T10:08:32Z
date_updated: 2023-08-01T10:09:35Z
department:
- _id: '542'
doi: 10.1137/22m1500654
intvolume: ' 37'
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
page: 1548-1565
publication: SIAM Journal on Discrete Mathematics
publication_identifier:
issn:
- 0895-4801
- 1095-7146
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs
type: journal_article
user_id: '15540'
volume: 37
year: '2023'
...
---
_id: '29240'
abstract:
- lang: eng
text: "The principle of least action is one of the most fundamental physical principle.
It says that among all possible motions connecting two points in a phase space,
the system will exhibit those motions which extremise an action functional. Many
qualitative features of dynamical systems, such as the presence of conservation
laws and energy balance equations, are related to the existence of an action functional.
Incorporating variational structure into learning algorithms for dynamical systems
is, therefore, crucial in order to make sure that the learned model shares important
features with the exact physical system. In this paper we show how to incorporate
variational principles into trajectory predictions of learned dynamical systems.
The novelty of this work is that (1) our technique relies only on discrete position
data of observed trajectories. Velocities or conjugate momenta do not need to
be observed or approximated and no prior knowledge about the form of the variational
principle is assumed. Instead, they are recovered using backward error analysis.
(2) Moreover, our technique compensates discretisation errors when trajectories
are computed from the learned system. This is important when moderate to large
step-sizes are used and high accuracy is required. For this,\r\nwe introduce and
rigorously analyse the concept of inverse modified Lagrangians by developing an
inverse version of variational backward error analysis. (3) Finally, we introduce
a method to perform system identification from position observations only, based
on variational backward error analysis."
article_type: original
author:
- 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
citation:
ama: Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from
Data. Journal of Computational and Applied Mathematics. 2023;421:114780.
doi:10.1016/j.cam.2022.114780
apa: Ober-Blöbaum, S., & Offen, C. (2023). Variational Learning of Euler–Lagrange
Dynamics from Data. Journal of Computational and Applied Mathematics, 421,
114780. https://doi.org/10.1016/j.cam.2022.114780
bibtex: '@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange
Dynamics from Data}, volume={421}, DOI={10.1016/j.cam.2022.114780},
journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier},
author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780}
}'
chicago: 'Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange
Dynamics from Data.” Journal of Computational and Applied Mathematics 421
(2023): 114780. https://doi.org/10.1016/j.cam.2022.114780.'
ieee: 'S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics
from Data,” Journal of Computational and Applied Mathematics, vol. 421,
p. 114780, 2023, doi: 10.1016/j.cam.2022.114780.'
mla: Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange
Dynamics from Data.” Journal of Computational and Applied Mathematics,
vol. 421, Elsevier, 2023, p. 114780, doi:10.1016/j.cam.2022.114780.
short: S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics
421 (2023) 114780.
date_created: 2022-01-11T13:24:00Z
date_updated: 2023-08-10T08:42:39Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1016/j.cam.2022.114780
external_id:
arxiv:
- '2112.12619'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-06-28T15:25:50Z
date_updated: 2022-06-28T15:25:50Z
description: |-
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions
connecting two points in a phase space, the system will exhibit those motions which extremise an action functional.
Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-
tions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms
for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features
with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-
tions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position
data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no
prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward
error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the
learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,
we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of
variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position
observations only, based on variational backward error analysis.
file_id: '32274'
file_name: ShadowLagrangian_revision1_journal_style_arxiv.pdf
file_size: 3640770
relation: main_file
title: Variational Learning of Euler–Lagrange Dynamics from Data
file_date_updated: 2022-06-28T15:25:50Z
has_accepted_license: '1'
intvolume: ' 421'
keyword:
- Lagrangian learning
- variational backward error analysis
- modified Lagrangian
- variational integrators
- physics informed learning
language:
- iso: eng
oa: '1'
page: '114780'
publication: Journal of Computational and Applied Mathematics
publication_identifier:
issn:
- 0377-0427
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/LagrangianShadowIntegration
status: public
title: Variational Learning of Euler–Lagrange Dynamics from Data
type: journal_article
user_id: '85279'
volume: 421
year: '2023'
...
---
_id: '29236'
abstract:
- lang: eng
text: The numerical solution of an ordinary differential equation can be interpreted
as the exact solution of a nearby modified equation. Investigating the behaviour
of numerical solutions by analysing the modified equation is known as backward
error analysis. If the original and modified equation share structural properties,
then the exact and approximate solution share geometric features such as the existence
of conserved quantities. Conjugate symplectic methods preserve a modified symplectic
form and a modified Hamiltonian when applied to a Hamiltonian system. We show
how a blended version of variational and symplectic techniques can be used to
compute modified symplectic and Hamiltonian structures. In contrast to other approaches,
our backward error analysis method does not rely on an ansatz but computes the
structures systematically, provided that a variational formulation of the method
is known. The technique is illustrated on the example of symmetric linear multistep
methods with matrix coefficients.
article_type: original
author:
- first_name: Robert
full_name: McLachlan, Robert
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods.
Journal of Geometric Mechanics. 2023;15(1):98-115. doi:10.3934/jgm.2023005
apa: McLachlan, R., & Offen, C. (2023). Backward error analysis for conjugate
symplectic methods. Journal of Geometric Mechanics, 15(1), 98–115.
https://doi.org/10.3934/jgm.2023005
bibtex: '@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate
symplectic methods}, volume={15}, DOI={10.3934/jgm.2023005},
number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press},
author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }'
chicago: 'McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate
Symplectic Methods.” Journal of Geometric Mechanics 15, no. 1 (2023): 98–115.
https://doi.org/10.3934/jgm.2023005.'
ieee: 'R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic
methods,” Journal of Geometric Mechanics, vol. 15, no. 1, pp. 98–115, 2023,
doi: 10.3934/jgm.2023005.'
mla: McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate
Symplectic Methods.” Journal of Geometric Mechanics, vol. 15, no. 1, AIMS
Press, 2023, pp. 98–115, doi:10.3934/jgm.2023005.
short: R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.
date_created: 2022-01-11T12:48:39Z
date_updated: 2023-08-10T08:40:30Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jgm.2023005
external_id:
arxiv:
- '2201.03911'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-08-12T16:48:59Z
date_updated: 2022-08-12T16:48:59Z
description: The numerical solution of an ordinary differential equation can be
interpreted as the exact solution of a nearby modified equation. Investigating
the behaviour of numerical solutions by analysing the modified equation is known
as backward error analysis. If the original and modified equation share structural
properties, then the exact and approximate solution share geometric features such
as the existence of conserved quantities. Conjugate symplectic methods preserve
a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian
system. We show how a blended version of variational and symplectic techniques
can be used to compute modified symplectic and Hamiltonian structures. In contrast
to other approaches, our backward error analysis method does not rely on an ansatz
but computes the structures systematically, provided that a variational formulation
of the method is known. The technique is illustrated on the example of symmetric
linear multistep methods with matrix coefficients.
file_id: '32801'
file_name: BEA_MultiStep_Matrix.pdf
file_size: 827030
relation: main_file
title: Backward error analysis for conjugate symplectic methods
file_date_updated: 2022-08-12T16:48:59Z
has_accepted_license: '1'
intvolume: ' 15'
issue: '1'
keyword:
- variational integrators
- backward error analysis
- Euler--Lagrange equations
- multistep methods
- conjugate symplectic methods
language:
- iso: eng
oa: '1'
page: 98-115
publication: Journal of Geometric Mechanics
publication_status: published
publisher: AIMS Press
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/BEAConjugateSymplectic
status: public
title: Backward error analysis for conjugate symplectic methods
type: journal_article
user_id: '85279'
volume: 15
year: '2023'
...
---
_id: '37654'
abstract:
- lang: eng
text: "Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate
prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian
systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven
modeling approach. However, preserving symmetries requires additional attention.
In this research, we\r\nenhance the HNN with a Lie algebra framework to detect
and embed symmetries in the neural network. This approach\r\nallows to simultaneously
learn the symmetry group action and the total energy of the system. As illustrating
examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are
considered."
article_number: '063115'
article_type: original
author:
- first_name: Eva
full_name: Dierkes, Eva
last_name: Dierkes
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
citation:
ama: Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks
with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969
apa: Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian
Neural Networks with Automatic Symmetry Detection. Chaos, 33(6),
Article 063115. https://doi.org/10.1063/5.0142969
bibtex: '@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural
Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969},
number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes,
Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023}
}'
chicago: Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp.
“Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos
33, no. 6 (2023). https://doi.org/10.1063/5.0142969.
ieee: 'E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural
Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art.
no. 063115, 2023, doi: 10.1063/5.0142969.'
mla: Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.”
Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.
short: E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).
date_created: 2023-01-20T09:10:06Z
date_updated: 2023-08-10T08:37:01Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0142969
external_id:
arxiv:
- '2301.07928'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-04-26T16:20:56Z
date_updated: 2023-04-26T16:20:56Z
description: |-
Incorporating physical system knowledge into data-driven
system identification has been shown to be beneficial. The
approach presented in this article combines learning of an
energy-conserving model from data with detecting a Lie
group representation of the unknown system symmetry.
The proposed approach can improve the learned model
and reveal underlying symmetry simultaneously.
file_id: '44205'
file_name: JournalPaper_main.pdf
file_size: 5200111
relation: main_file
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
file_date_updated: 2023-04-26T16:20:56Z
has_accepted_license: '1'
intvolume: ' 33'
issue: '6'
language:
- iso: eng
oa: '1'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/eva-dierkes/HNN_withSymmetries
status: public
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
type: journal_article
user_id: '85279'
volume: 33
year: '2023'
...
---
_id: '23428'
abstract:
- lang: eng
text: "The Koopman operator has become an essential tool for data-driven approximation
of dynamical (control) systems in recent years, e.g., via extended dynamic mode
decomposition. Despite its popularity, convergence results and, in particular,
error bounds are still quite scarce. In this paper, we derive probabilistic bounds
for the approximation error and the prediction error depending on the number of
training data points; for both ordinary and stochastic differential equations.
Moreover, we extend our analysis to nonlinear control-affine systems using either
ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the
Koopman generator to obtain a bilinear system and, thus, circumvent the curse
of dimensionality since we do not autonomize the system by augmenting the state
by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data
error analysis in the stochastic and/or control setting. Finally, we demonstrate
the effectiveness of the proposed approach by comparing it with state-of-the-art
techniques showing its superiority whenever state and control are coupled."
article_number: '14'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Friedrich
full_name: Philipp, Friedrich
last_name: Philipp
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds
for Koopman-based prediction and control. Journal of Nonlinear Science.
2023;33. doi:10.1007/s00332-022-09862-1
apa: Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023).
Finite-data error bounds for Koopman-based prediction and control. Journal
of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1
bibtex: '@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data
error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1},
number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and
Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl},
year={2023} }'
chicago: Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and
Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.”
Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.
ieee: 'F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data
error bounds for Koopman-based prediction and control,” Journal of Nonlinear
Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.'
mla: Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction
and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.
short: F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear
Science 33 (2023).
date_created: 2021-08-17T12:25:09Z
date_updated: 2023-08-24T07:50:12Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s00332-022-09862-1
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf
oa: '1'
publication: Journal of Nonlinear Science
publication_status: published
status: public
title: Finite-data error bounds for Koopman-based prediction and control
type: journal_article
user_id: '47427'
volume: 33
year: '2023'
...
---
_id: '21600'
abstract:
- lang: eng
text: Many problems in science and engineering require an efficient numerical approximation
of integrals or solutions to differential equations. For systems with rapidly
changing dynamics, an equidistant discretization is often inadvisable as it results
in prohibitively large errors or computational effort. To this end, adaptive schemes,
such as solvers based on Runge–Kutta pairs, have been developed which adapt the
step size based on local error estimations at each step. While the classical schemes
apply very generally and are highly efficient on regular systems, they can behave
suboptimally when an inefficient step rejection mechanism is triggered by structurally
complex systems such as chaotic systems. To overcome these issues, we propose
a method to tailor numerical schemes to the problem class at hand. This is achieved
by combining simple, classical quadrature rules or ODE solvers with data-driven
time-stepping controllers. Compared with learning solution operators to ODEs directly,
it generalizes better to unseen initial data as our approach employs classical
numerical schemes as base methods. At the same time it can make use of identified
structures of a problem class and, therefore, outperforms state-of-the-art adaptive
schemes. Several examples demonstrate superior efficiency. Source code is available
at https://github.com/lueckem/quadrature-ML.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Eyke
full_name: Hüllermeier, Eyke
id: '48129'
last_name: Hüllermeier
- first_name: Marvin
full_name: Lücke, Marvin
last_name: Lücke
- 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: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Karlson
full_name: Pfannschmidt, Karlson
id: '13472'
last_name: Pfannschmidt
orcid: 0000-0001-9407-7903
citation:
ama: Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical
integration using reinforcement learning. SIAM Journal on Scientific Computing.
2023;45(2):A579-A595. doi:10.1137/21M1412682
apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz,
S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration
using reinforcement learning. SIAM Journal on Scientific Computing, 45(2),
A579–A595. https://doi.org/10.1137/21M1412682
bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023,
title={Efficient time stepping for numerical integration using reinforcement
learning}, volume={45}, DOI={10.1137/21M1412682},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz,
Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen,
Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595}
}'
chicago: 'Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum,
Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping
for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific
Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.'
ieee: 'M. Dellnitz et al., “Efficient time stepping for numerical integration
using reinforcement learning,” SIAM Journal on Scientific Computing, vol.
45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.'
mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration
Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol.
45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.
short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz,
K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.
date_created: 2021-04-09T07:59:19Z
date_updated: 2023-08-25T09:24:50Z
ddc:
- '510'
department:
- _id: '101'
- _id: '636'
- _id: '355'
- _id: '655'
doi: 10.1137/21M1412682
external_id:
arxiv:
- arXiv:2104.03562
has_accepted_license: '1'
intvolume: ' 45'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/reader/10.1137/21M1412682
page: A579-A595
publication: SIAM Journal on Scientific Computing
publication_status: published
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/lueckem/quadrature-ML
status: public
title: Efficient time stepping for numerical integration using reinforcement learning
type: journal_article
user_id: '47427'
volume: 45
year: '2023'
...
---
_id: '46757'
author:
- first_name: Imke
full_name: Schwerin, Imke
id: '48912'
last_name: Schwerin
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: 'Schwerin I, Häsel-Weide U. Second grader´s understanding of doubling and halfing
in various representations. In: Novotna J, Moraova H, eds. International Symposium
in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education. Charles University; 2023:297-305.'
apa: 'Schwerin, I., & Häsel-Weide, U. (2023). Second grader´s understanding
of doubling and halfing in various representations. In J. Novotna & H. Moraova
(Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings:
New Directions in Elementary Mathematics Education (pp. 297–305). Charles
University.'
bibtex: '@inproceedings{Schwerin_Häsel-Weide_2023, title={Second grader´s understanding
of doubling and halfing in various representations}, booktitle={International
Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education}, publisher={Charles University}, author={Schwerin, Imke
and Häsel-Weide, Uta}, editor={Novotna, J. and Moraova, H.}, year={2023}, pages={297–305}
}'
chicago: 'Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of
Doubling and Halfing in Various Representations.” In International Symposium
in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education, edited by J. Novotna and H. Moraova, 297–305. Charles
University, 2023.'
ieee: 'I. Schwerin and U. Häsel-Weide, “Second grader´s understanding of doubling
and halfing in various representations,” in International Symposium in Elementary
Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education,
Prag, 2023, pp. 297–305.'
mla: 'Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of Doubling
and Halfing in Various Representations.” International Symposium in Elementary
Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education,
edited by J. Novotna and H. Moraova, Charles University, 2023, pp. 297–305.'
short: 'I. Schwerin, U. Häsel-Weide, in: J. Novotna, H. Moraova (Eds.), International
Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education, Charles University, 2023, pp. 297–305.'
conference:
location: Prag
name: International Symposium in Elementary Mathematics Teaching
date_created: 2023-08-30T09:40:23Z
date_updated: 2023-08-30T09:55:41Z
department:
- _id: '543'
editor:
- first_name: J.
full_name: Novotna, J.
last_name: Novotna
- first_name: H.
full_name: Moraova, H.
last_name: Moraova
language:
- iso: eng
page: 297-305
publication: 'International Symposium in Elementary Mathematics Teaching. Proceedings:
New Directions in Elementary Mathematics Education'
publisher: Charles University
status: public
title: Second grader´s understanding of doubling and halfing in various representations
type: conference
user_id: '44184'
year: '2023'
...
---
_id: '46758'
author:
- first_name: Rebekka
full_name: Schmidt, Rebekka
id: '58565'
last_name: Schmidt
- first_name: Claudia
full_name: Tenberge, Claudia
id: '67302'
last_name: Tenberge
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: 'Schmidt R, Tenberge C, Häsel-Weide U. Lehre in Zeiten von Digitalisierung
und Inklusion - Beispiele aus drei Fächern. In: Vöing N, Schmidt R, Neiske I,
eds. Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre.
Visual Ink Publishing; 2023:297-318.'
apa: Schmidt, R., Tenberge, C., & Häsel-Weide, U. (2023). Lehre in Zeiten von
Digitalisierung und Inklusion - Beispiele aus drei Fächern. In N. Vöing, R. Schmidt,
& I. Neiske (Eds.), Aktive Teilhabe fördern – ICM und Student Engagement
in der Hochschullehre (pp. 297–318). Visual Ink Publishing.
bibtex: '@inbook{Schmidt_Tenberge_Häsel-Weide_2023, title={Lehre in Zeiten von Digitalisierung
und Inklusion - Beispiele aus drei Fächern}, booktitle={Aktive Teilhabe fördern
– ICM und Student Engagement in der Hochschullehre}, publisher={Visual Ink Publishing},
author={Schmidt, Rebekka and Tenberge, Claudia and Häsel-Weide, Uta}, editor={Vöing,
N. and Schmidt, R. and Neiske, I.}, year={2023}, pages={297–318} }'
chicago: Schmidt, Rebekka, Claudia Tenberge, and Uta Häsel-Weide. “Lehre in Zeiten
von Digitalisierung und Inklusion - Beispiele aus drei Fächern.” In Aktive
Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, edited
by N. Vöing, R. Schmidt, and I. Neiske, 297–318. Visual Ink Publishing, 2023.
ieee: R. Schmidt, C. Tenberge, and U. Häsel-Weide, “Lehre in Zeiten von Digitalisierung
und Inklusion - Beispiele aus drei Fächern,” in Aktive Teilhabe fördern – ICM
und Student Engagement in der Hochschullehre, N. Vöing, R. Schmidt, and I.
Neiske, Eds. Visual Ink Publishing, 2023, pp. 297–318.
mla: Schmidt, Rebekka, et al. “Lehre in Zeiten von Digitalisierung und Inklusion
- Beispiele aus drei Fächern.” Aktive Teilhabe fördern – ICM und Student Engagement
in der Hochschullehre, edited by N. Vöing et al., Visual Ink Publishing, 2023,
pp. 297–318.
short: 'R. Schmidt, C. Tenberge, U. Häsel-Weide, in: N. Vöing, R. Schmidt, I. Neiske
(Eds.), Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre,
Visual Ink Publishing, 2023, pp. 297–318.'
date_created: 2023-08-30T09:54:47Z
date_updated: 2023-08-30T09:55:46Z
department:
- _id: '543'
editor:
- first_name: N.
full_name: Vöing, N.
last_name: Vöing
- first_name: R.
full_name: Schmidt, R.
last_name: Schmidt
- first_name: I.
full_name: Neiske, I.
last_name: Neiske
language:
- iso: ger
page: 297-318
publication: Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre
publisher: Visual Ink Publishing
status: public
title: Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern
type: book_chapter
user_id: '44184'
year: '2023'
...
---
_id: '56200'
abstract:
- lang: eng
text: AbstractIntending to counteract Klein’s second
discontinuity in teacher education, we explored and applied the innovation of
“interface ePortfolio” in the context of a geometry
course for preservice teachers (PSTs). The tool offers the possibility of implementing
the design principle of profession orientation. In
the article, we theoretically clarify what we understand by this principle and
locate our innovative concept against this theoretical background. We empirically
investigate the extent to which counteraction against the second discontinuity
is successful by analyzing reflection texts created in the interface ePortfolio,
focusing on PSTs’ perspectives. Our qualitative content analysis shows that most
of them perceive the innovation as helpful in the intended sense and indicates
that the course concept, in general, and the interface ePortfolio, in particular,
have helped establish relevant links between the course content and their later
work as teachers.
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: Hoffmann M, Biehler R. Implementing profession orientation as a design principle
for overcoming Klein’s second discontinuity – preservice teacher’s perspectives
on interface activities in the context of a geometry course. ZDM – Mathematics
Education. 2023;55(4):737-751. doi:10.1007/s11858-023-01505-3
apa: Hoffmann, M., & Biehler, R. (2023). Implementing profession orientation
as a design principle for overcoming Klein’s second discontinuity – preservice
teacher’s perspectives on interface activities in the context of a geometry course.
ZDM – Mathematics Education, 55(4), 737–751. https://doi.org/10.1007/s11858-023-01505-3
bibtex: '@article{Hoffmann_Biehler_2023, title={Implementing profession orientation
as a design principle for overcoming Klein’s second discontinuity – preservice
teacher’s perspectives on interface activities in the context of a geometry course},
volume={55}, DOI={10.1007/s11858-023-01505-3},
number={4}, journal={ZDM – Mathematics Education}, publisher={Springer Science
and Business Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2023},
pages={737–751} }'
chicago: 'Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation
as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice
Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.”
ZDM – Mathematics Education 55, no. 4 (2023): 737–51. https://doi.org/10.1007/s11858-023-01505-3.'
ieee: 'M. Hoffmann and R. Biehler, “Implementing profession orientation as a design
principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives
on interface activities in the context of a geometry course,” ZDM – Mathematics
Education, vol. 55, no. 4, pp. 737–751, 2023, doi: 10.1007/s11858-023-01505-3.'
mla: Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a
Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s
Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM
– Mathematics Education, vol. 55, no. 4, Springer Science and Business Media
LLC, 2023, pp. 737–51, doi:10.1007/s11858-023-01505-3.
short: M. Hoffmann, R. Biehler, ZDM – Mathematics Education 55 (2023) 737–751.
date_created: 2024-09-23T07:51:34Z
date_updated: 2024-09-25T08:26:34Z
department:
- _id: '363'
doi: 10.1007/s11858-023-01505-3
intvolume: ' 55'
issue: '4'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/s11858-023-01505-3
page: 737-751
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Implementing profession orientation as a design principle for overcoming Klein’s
second discontinuity – preservice teacher’s perspectives on interface activities
in the context of a geometry course
type: journal_article
user_id: '37888'
volume: 55
year: '2023'
...
---
_id: '40607'
abstract:
- lang: eng
text: AbstractTeachers’ in-depth diagnostic thinking
has been shown to be crucial for student-centered teaching as they need to perceive
and interpret students’ understanding for well-informed decision-making on adaptive
teaching practices. The paper presents a content-related approach to analyzing
diagnostic thinking processes with respect to the mathematical knowledge elements
that prospective teachers identify as students’ resources and obstacles. Prospective
teachers’ challenge is that some relevant knowledge elements first have to be
unpacked, because compact concepts (such as the place value concept) or procedures
(such as for multi-digit multiplication) comprise several smaller knowledge elements
(such as the positional property) that have to be made explicit for students to
foster their learning processes adequately. Our study examines what knowledge
elements prospective teachers perceive and interpret in a transcript vignettes
on multi-digit multiplication (of decimal and natural numbers) and its underlying
basic arithmetic concepts (place value understanding and meaning of multiplication)
in written diagnostic judgments on students’ resources and obstacles (N = 196).
A comparative design within the vignette is used to investigate how far the process
of perceiving can be supported by thematic cues. The analysis reveals that those
knowledge elements cued in the vignette by being already unpacked and explicitly
addressed are perceived and interpreted more often (but with lower correctness)
than those that are uncued and therefore have to be unpacked by the prospective
teachers themselves. This confirms the need to prepare prospective teachers for
unpacking mathematical concepts themselves.
author:
- first_name: Jennifer
full_name: Dröse, Jennifer
last_name: Dröse
- first_name: Susanne
full_name: Prediger, Susanne
last_name: Prediger
citation:
ama: 'Dröse J, Prediger S. Prospective Teachers’ Diagnostic Thinking on Students’
Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking
of Knowledge Elements. Journal für Mathematik-Didaktik. Published online
2023. doi:10.1007/s13138-022-00214-w'
apa: 'Dröse, J., & Prediger, S. (2023). Prospective Teachers’ Diagnostic Thinking
on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis
on Unpacking of Knowledge Elements. Journal Für Mathematik-Didaktik. https://doi.org/10.1007/s13138-022-00214-w'
bibtex: '@article{Dröse_Prediger_2023, title={Prospective Teachers’ Diagnostic Thinking
on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis
on Unpacking of Knowledge Elements}, DOI={10.1007/s13138-022-00214-w},
journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business
Media LLC}, author={Dröse, Jennifer and Prediger, Susanne}, year={2023} }'
chicago: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic
Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related
Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik,
2023. https://doi.org/10.1007/s13138-022-00214-w.'
ieee: 'J. Dröse and S. Prediger, “Prospective Teachers’ Diagnostic Thinking on Students’
Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking
of Knowledge Elements,” Journal für Mathematik-Didaktik, 2023, doi: 10.1007/s13138-022-00214-w.'
mla: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking
on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis
on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, Springer
Science and Business Media LLC, 2023, doi:10.1007/s13138-022-00214-w.'
short: J. Dröse, S. Prediger, Journal Für Mathematik-Didaktik (2023).
date_created: 2023-01-27T18:47:24Z
date_updated: 2025-01-15T08:36:09Z
department:
- _id: '98'
doi: 10.1007/s13138-022-00214-w
keyword:
- Education
- General Mathematics
language:
- iso: eng
publication: Journal für Mathematik-Didaktik
publication_identifier:
issn:
- 0173-5322
- 1869-2699
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: 'Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit
Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements'
type: journal_article
user_id: '85820'
year: '2023'
...
---
_id: '45374'
author:
- first_name: S.
full_name: Prediger, S.
last_name: Prediger
- first_name: Jennifer
full_name: Dröse, Jennifer
id: '85820'
last_name: Dröse
- first_name: R.
full_name: Stahnke, R.
last_name: Stahnke
- first_name: C.
full_name: Ademmer, C.
last_name: Ademmer
citation:
ama: 'Prediger S, Dröse J, Stahnke R, Ademmer C. Teacher expertise for fostering
at-risk students’ understanding of basic concepts: conceptual model and evidence
for growth. Journal of Mathematics Teacher Education. Published online
2023. doi:https://doi.org/10.1007/s10857-022-09538-3'
apa: 'Prediger, S., Dröse, J., Stahnke, R., & Ademmer, C. (2023). Teacher expertise
for fostering at-risk students’ understanding of basic concepts: conceptual model
and evidence for growth. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-022-09538-3'
bibtex: '@article{Prediger_Dröse_Stahnke_Ademmer_2023, title={Teacher expertise
for fostering at-risk students’ understanding of basic concepts: conceptual model
and evidence for growth}, DOI={https://doi.org/10.1007/s10857-022-09538-3},
journal={Journal of Mathematics Teacher Education}, author={Prediger, S. and Dröse,
Jennifer and Stahnke, R. and Ademmer, C.}, year={2023} }'
chicago: 'Prediger, S., Jennifer Dröse, R. Stahnke, and C. Ademmer. “Teacher Expertise
for Fostering At-Risk Students’ Understanding of Basic Concepts: Conceptual Model
and Evidence for Growth.” Journal of Mathematics Teacher Education, 2023.
https://doi.org/10.1007/s10857-022-09538-3.'
ieee: 'S. Prediger, J. Dröse, R. Stahnke, and C. Ademmer, “Teacher expertise for
fostering at-risk students’ understanding of basic concepts: conceptual model
and evidence for growth,” Journal of Mathematics Teacher Education, 2023,
doi: https://doi.org/10.1007/s10857-022-09538-3.'
mla: 'Prediger, S., et al. “Teacher Expertise for Fostering At-Risk Students’ Understanding
of Basic Concepts: Conceptual Model and Evidence for Growth.” Journal of Mathematics
Teacher Education, 2023, doi:https://doi.org/10.1007/s10857-022-09538-3.'
short: S. Prediger, J. Dröse, R. Stahnke, C. Ademmer, Journal of Mathematics Teacher
Education (2023).
date_created: 2023-05-31T06:27:51Z
date_updated: 2025-01-15T08:34:36Z
department:
- _id: '98'
doi: https://doi.org/10.1007/s10857-022-09538-3
language:
- iso: eng
publication: Journal of Mathematics Teacher Education
quality_controlled: '1'
status: public
title: 'Teacher expertise for fostering at-risk students’ understanding of basic concepts:
conceptual model and evidence for growth'
type: journal_article
user_id: '85820'
year: '2023'
...
---
_id: '46155'
article_number: '104270'
author:
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: Maike
full_name: Hagena, Maike
last_name: Hagena
- first_name: Hedwig
full_name: Gasteiger, Hedwig
last_name: Gasteiger
citation:
ama: 'Bruns J, Hagena M, Gasteiger H. Professional Development Enacted by Facilitators
in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?
Teaching and Teacher Education. 2023;132. doi:10.1016/j.tate.2023.104270'
apa: 'Bruns, J., Hagena, M., & Gasteiger, H. (2023). Professional Development
Enacted by Facilitators in the Context of Early Mathematics Education: Scaling
up or Dilution of Effects? Teaching and Teacher Education, 132,
Article 104270. https://doi.org/10.1016/j.tate.2023.104270'
bibtex: '@article{Bruns_Hagena_Gasteiger_2023, title={Professional Development Enacted
by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution
of Effects?}, volume={132}, DOI={10.1016/j.tate.2023.104270},
number={104270}, journal={Teaching and Teacher Education}, publisher={Elsevier
BV}, author={Bruns, Julia and Hagena, Maike and Gasteiger, Hedwig}, year={2023}
}'
chicago: 'Bruns, Julia, Maike Hagena, and Hedwig Gasteiger. “Professional Development
Enacted by Facilitators in the Context of Early Mathematics Education: Scaling
up or Dilution of Effects?” Teaching and Teacher Education 132 (2023).
https://doi.org/10.1016/j.tate.2023.104270.'
ieee: 'J. Bruns, M. Hagena, and H. Gasteiger, “Professional Development Enacted
by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution
of Effects?,” Teaching and Teacher Education, vol. 132, Art. no. 104270,
2023, doi: 10.1016/j.tate.2023.104270.'
mla: 'Bruns, Julia, et al. “Professional Development Enacted by Facilitators in
the Context of Early Mathematics Education: Scaling up or Dilution of Effects?”
Teaching and Teacher Education, vol. 132, 104270, Elsevier BV, 2023, doi:10.1016/j.tate.2023.104270.'
short: J. Bruns, M. Hagena, H. Gasteiger, Teaching and Teacher Education 132 (2023).
date_created: 2023-07-26T08:55:26Z
date_updated: 2025-06-02T12:59:11Z
department:
- _id: '611'
doi: 10.1016/j.tate.2023.104270
intvolume: ' 132'
keyword:
- Education
language:
- iso: eng
publication: Teaching and Teacher Education
publication_identifier:
issn:
- 0742-051X
publication_status: published
publisher: Elsevier BV
status: public
title: 'Professional Development Enacted by Facilitators in the Context of Early Mathematics
Education: Scaling up or Dilution of Effects?'
type: journal_article
user_id: '72183'
volume: 132
year: '2023'
...
---
_id: '59984'
author:
- first_name: Irene
full_name: Garnelo Abellanas, Irene
id: '93843'
last_name: Garnelo Abellanas
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
citation:
ama: 'Garnelo Abellanas I, Liebendörfer M. Introducing mathematics undergraduate
students to the theorem prover lean. In: Thirteenth Congress of the European
Society for Research in Mathematics (CERME13). ; 2023.'
apa: Garnelo Abellanas, I., & Liebendörfer, M. (2023). Introducing mathematics
undergraduate students to the theorem prover lean. Thirteenth Congress of the
European Society for Research in Mathematics (CERME13). Thirteenth Congress
of the European Society for Research in Mathematics Education (CERME13), Budapest.
bibtex: '@inproceedings{Garnelo Abellanas_Liebendörfer_2023, title={Introducing
mathematics undergraduate students to the theorem prover lean}, booktitle={Thirteenth
Congress of the European Society for Research in Mathematics (CERME13)}, author={Garnelo
Abellanas, Irene and Liebendörfer, Michael}, year={2023} }'
chicago: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Introducing Mathematics
Undergraduate Students to the Theorem Prover Lean.” In Thirteenth Congress
of the European Society for Research in Mathematics (CERME13), 2023.
ieee: I. Garnelo Abellanas and M. Liebendörfer, “Introducing mathematics undergraduate
students to the theorem prover lean,” presented at the Thirteenth Congress of
the European Society for Research in Mathematics Education (CERME13), Budapest,
2023.
mla: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Introducing Mathematics
Undergraduate Students to the Theorem Prover Lean.” Thirteenth Congress of
the European Society for Research in Mathematics (CERME13), 2023.
short: 'I. Garnelo Abellanas, M. Liebendörfer, in: Thirteenth Congress of the European
Society for Research in Mathematics (CERME13), 2023.'
conference:
location: Budapest
name: Thirteenth Congress of the European Society for Research in Mathematics Education
(CERME13)
date_created: 2025-05-19T07:19:01Z
date_updated: 2026-01-15T10:36:11Z
department:
- _id: '983'
language:
- iso: eng
publication: Thirteenth Congress of the European Society for Research in Mathematics
(CERME13)
related_material:
link:
- relation: confirmation
url: https://hal.science/hal-04406679v1/file/TWG_14-Garnelo-218.pdf
status: public
title: Introducing mathematics undergraduate students to the theorem prover lean
type: conference
user_id: '93843'
year: '2023'
...