---
_id: '59171'
abstract:
- lang: eng
text: To model dynamical systems on networks with higher-order (non-pairwise) interactions,
we recently introduced a new class of ordinary differential equations (ODEs) on
hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations
in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if
it is tangent to a synchrony space, but does not lie inside it. We prove that
reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing
a large class of examples that support it. We also give an explicit formula for
the order of tangency to the synchrony space of a reluctant steady-state branch.
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. Higher-order interactions lead to ‘reluctant’
synchrony breaking. Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. 2024;480(2301). doi:10.1098/rspa.2023.0945'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2024). Higher-order interactions
lead to ‘reluctant’ synchrony breaking. Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences, 480(2301). https://doi.org/10.1098/rspa.2023.0945'
bibtex: '@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions
lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={10.1098/rspa.2023.0945},
number={2301}, journal={Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences}, publisher={The Royal Society}, author={von der Gracht,
Sören and Nijholt, Eddie and Rink, Bob}, year={2024} }'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions
Lead to ‘Reluctant’ Synchrony Breaking.” Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences 480, no. 2301 (2024). https://doi.org/10.1098/rspa.2023.0945.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead
to ‘reluctant’ synchrony breaking,” Proceedings of the Royal Society A: Mathematical,
Physical and Engineering Sciences, vol. 480, no. 2301, 2024, doi: 10.1098/rspa.2023.0945.'
mla: 'von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’
Synchrony Breaking.” Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences, vol. 480, no. 2301, The Royal Society, 2024, doi:10.1098/rspa.2023.0945.'
short: 'S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society
A: Mathematical, Physical and Engineering Sciences 480 (2024).'
date_created: 2025-03-27T10:15:06Z
date_updated: 2025-03-27T10:19:56Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1098/rspa.2023.0945
file:
- access_level: open_access
content_type: application/pdf
creator: svdg
date_created: 2025-03-27T10:16:20Z
date_updated: 2025-03-27T10:19:48Z
file_id: '59172'
file_name: higher-order-interactions-lead-to-reluctant-synchrony-breaking.pdf
file_size: 820435
relation: main_file
file_date_updated: 2025-03-27T10:19:48Z
has_accepted_license: '1'
intvolume: ' 480'
issue: '2301'
keyword:
- higher-order interactions
- synchrony breaking
- network dynamics
- coupled cell systems
language:
- iso: eng
oa: '1'
publication: 'Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences'
publication_identifier:
issn:
- 1364-5021
- 1471-2946
publication_status: published
publisher: The Royal Society
status: public
title: Higher-order interactions lead to ‘reluctant’ synchrony breaking
type: journal_article
user_id: '97359'
volume: 480
year: '2024'
...
---
_id: '59581'
author:
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
orcid: 0000-0001-6278-4240
- first_name: M.
full_name: Nührenbörger, M.
last_name: Nührenbörger
citation:
ama: 'Häsel-Weide U, Nührenbörger M. Praktiken der Förderung im inklusiven Mathematikunterricht.
In: Ebers P, Rösken F, Barzel B, Büchter A, Schacht F, Scherer P, eds. Beiträge
zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft für Didaktik der
Mathematik. ; 2024:207-210. doi:https://doi.ohttps://doi.org/10.37626/GA9783959872782.0
rg/10.37626/GA9783959872782.0'
apa: Häsel-Weide, U., & Nührenbörger, M. (2024). Praktiken der Förderung im
inklusiven Mathematikunterricht. In P. Ebers, F. Rösken, B. Barzel, A. Büchter,
F. Schacht, & P. Scherer (Eds.), Beiträge zum Mathematikuntericht 2024.
57. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 207–210).
https://doi.ohttps://doi.org/10.37626/GA9783959872782.0
rg/10.37626/GA9783959872782.0
bibtex: '@inbook{Häsel-Weide_Nührenbörger_2024, title={ Praktiken der Förderung
im inklusiven Mathematikunterricht}, DOI={https://doi.ohttps://doi.org/10.37626/GA9783959872782.0
rg/10.37626/GA9783959872782.0}, booktitle={Beiträge zum Mathematikuntericht
2024. 57. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, author={Häsel-Weide,
Uta and Nührenbörger, M.}, editor={Ebers, P. and Rösken, F. and Barzel, B. and
Büchter, A. and Schacht, F. and Scherer, P.}, year={2024}, pages={207–210} }'
chicago: Häsel-Weide, Uta, and M. Nührenbörger. “ Praktiken der Förderung im inklusiven
Mathematikunterricht.” In Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung
der Gesellschaft für Didaktik der Mathematik, edited by P. Ebers, F. Rösken,
B. Barzel, A. Büchter, F. Schacht, and P. Scherer, 207–10, 2024. https://doi.ohttps://doi.org/10.37626/GA9783959872782.0
rg/10.37626/GA9783959872782.0.
ieee: U. Häsel-Weide and M. Nührenbörger, “ Praktiken der Förderung im inklusiven
Mathematikunterricht,” in Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung
der Gesellschaft für Didaktik der Mathematik, P. Ebers, F. Rösken, B. Barzel,
A. Büchter, F. Schacht, and P. Scherer, Eds. 2024, pp. 207–210.
mla: Häsel-Weide, Uta, and M. Nührenbörger. “ Praktiken der Förderung im inklusiven
Mathematikunterricht.” Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung
der Gesellschaft für Didaktik der Mathematik, edited by P. Ebers et al., 2024,
pp. 207–10, doi:https://doi.ohttps://doi.org/10.37626/GA9783959872782.0
rg/10.37626/GA9783959872782.0.
short: 'U. Häsel-Weide, M. Nührenbörger, in: P. Ebers, F. Rösken, B. Barzel, A.
Büchter, F. Schacht, P. Scherer (Eds.), Beiträge zum Mathematikuntericht 2024.
57. Jahrestagung der Gesellschaft für Didaktik der Mathematik, 2024, pp. 207–210.'
date_created: 2025-04-15T10:06:42Z
date_updated: 2025-09-08T07:32:38Z
department:
- _id: '543'
doi: https://doi.ohttps://doi.org/10.37626/GA9783959872782.0 rg/10.37626/GA9783959872782.0
editor:
- first_name: P.
full_name: Ebers, P.
last_name: Ebers
- first_name: F.
full_name: Rösken, F.
last_name: Rösken
- first_name: B.
full_name: Barzel, B.
last_name: Barzel
- first_name: A.
full_name: Büchter, A.
last_name: Büchter
- first_name: F.
full_name: Schacht, F.
last_name: Schacht
- first_name: P.
full_name: Scherer, P.
last_name: Scherer
language:
- iso: ger
page: 207-210
publication: Beiträge zum Mathematikuntericht 2024. 57. Jahrestagung der Gesellschaft
für Didaktik der Mathematik
status: public
title: ' Praktiken der Förderung im inklusiven Mathematikunterricht'
type: book_chapter
user_id: '44184'
year: '2024'
...
---
_id: '58873'
abstract:
- lang: eng
text: "We prove that the Patterson-Sullivan and Wigner distributions on the unit\r\nsphere
bundle of a convex-cocompact hyperbolic surface are asymptotically\r\nidentical.
This generalizes results in the compact case by\r\nAnantharaman-Zelditch and Hansen-Hilgert-Schr\\\"oder."
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
id: '70575'
last_name: Delarue
- first_name: Guendalina
full_name: Palmirotta, Guendalina
id: '109467'
last_name: Palmirotta
citation:
ama: Delarue B, Palmirotta G. Patterson-Sullivan and Wigner distributions of convex-cocompact
hyperbolic surfaces. arXiv:241119782. Published online 2024.
apa: Delarue, B., & Palmirotta, G. (2024). Patterson-Sullivan and Wigner distributions
of convex-cocompact hyperbolic surfaces. In arXiv:2411.19782.
bibtex: '@article{Delarue_Palmirotta_2024, title={Patterson-Sullivan and Wigner
distributions of convex-cocompact hyperbolic surfaces}, journal={arXiv:2411.19782},
author={Delarue, Benjamin and Palmirotta, Guendalina}, year={2024} }'
chicago: Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner
Distributions of Convex-Cocompact Hyperbolic Surfaces.” ArXiv:2411.19782,
2024.
ieee: B. Delarue and G. Palmirotta, “Patterson-Sullivan and Wigner distributions
of convex-cocompact hyperbolic surfaces,” arXiv:2411.19782. 2024.
mla: Delarue, Benjamin, and Guendalina Palmirotta. “Patterson-Sullivan and Wigner
Distributions of Convex-Cocompact Hyperbolic Surfaces.” ArXiv:2411.19782,
2024.
short: B. Delarue, G. Palmirotta, ArXiv:2411.19782 (2024).
date_created: 2025-02-28T10:32:30Z
date_updated: 2026-03-30T12:01:12Z
department:
- _id: '548'
external_id:
arxiv:
- '2411.19782'
language:
- iso: eng
project:
- _id: '356'
name: 'TRR 358; TP B02: Spektraltheorie in höherem Rang und unendlichem Volumen'
publication: arXiv:2411.19782
status: public
title: Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic
surfaces
type: preprint
user_id: '109467'
year: '2024'
...
---
_id: '53542'
abstract:
- lang: eng
text: "AbstractThis work deals with the extension
problem for the fractional Laplacian on Riemannian symmetric spaces G/K
of noncompact type and of general rank, which gives rise to a family of convolution
operators, including the Poisson operator. More precisely, motivated by Euclidean
results for the Poisson semigroup, we study the long-time asymptotic behavior
of solutions to the extension problem for $$L^1$$\r\n \r\n
\ L\r\n 1\r\n
\ \r\n
initial data. In the case of the Laplace–Beltrami operator, we show that if the
initial data are bi-K-invariant, then the solution
to the extension problem behaves asymptotically as the mass times the fundamental
solution, but this convergence may break down in the non-bi-K-invariant
case. In the second part, we investigate the long-time asymptotic behavior of
the extension problem associated with the so-called distinguished Laplacian on
G/K. In this case, we observe
phenomena which are similar to the Euclidean setting for the Poisson semigroup,
such as $$L^1$$\r\n \r\n
\ L\r\n 1\r\n
\ \r\n
asymptotic convergence without the assumption of bi-K-invariance."
article_number: '34'
author:
- first_name: Efthymia
full_name: Papageorgiou, Efthymia
id: '100325'
last_name: Papageorgiou
citation:
ama: Papageorgiou E. Asymptotic behavior of solutions to the extension problem for
the fractional Laplacian on noncompact symmetric spaces. Journal of Evolution
Equations. 2024;24(2). doi:10.1007/s00028-024-00959-6
apa: Papageorgiou, E. (2024). Asymptotic behavior of solutions to the extension
problem for the fractional Laplacian on noncompact symmetric spaces. Journal
of Evolution Equations, 24(2), Article 34. https://doi.org/10.1007/s00028-024-00959-6
bibtex: '@article{Papageorgiou_2024, title={Asymptotic behavior of solutions to
the extension problem for the fractional Laplacian on noncompact symmetric spaces},
volume={24}, DOI={10.1007/s00028-024-00959-6},
number={234}, journal={Journal of Evolution Equations}, publisher={Springer Science
and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2024} }'
chicago: Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension
Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” Journal
of Evolution Equations 24, no. 2 (2024). https://doi.org/10.1007/s00028-024-00959-6.
ieee: 'E. Papageorgiou, “Asymptotic behavior of solutions to the extension problem
for the fractional Laplacian on noncompact symmetric spaces,” Journal of Evolution
Equations, vol. 24, no. 2, Art. no. 34, 2024, doi: 10.1007/s00028-024-00959-6.'
mla: Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension
Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” Journal
of Evolution Equations, vol. 24, no. 2, 34, Springer Science and Business
Media LLC, 2024, doi:10.1007/s00028-024-00959-6.
short: E. Papageorgiou, Journal of Evolution Equations 24 (2024).
date_created: 2024-04-17T13:18:30Z
date_updated: 2026-07-03T12:35:54Z
department:
- _id: '555'
doi: 10.1007/s00028-024-00959-6
intvolume: ' 24'
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
publication: Journal of Evolution Equations
publication_identifier:
issn:
- 1424-3199
- 1424-3202
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Asymptotic behavior of solutions to the extension problem for the fractional
Laplacian on noncompact symmetric spaces
type: journal_article
user_id: '100325'
volume: 24
year: '2024'
...
---
_id: '21199'
abstract:
- lang: eng
text: "As in almost every other branch of science, the major advances in data\r\nscience
and machine learning have also resulted in significant improvements\r\nregarding
the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays
possible to make accurate medium to long-term predictions of highly\r\ncomplex
systems such as the weather, the dynamics within a nuclear fusion\r\nreactor,
of disease models or the stock market in a very efficient manner. In\r\nmany cases,
predictive methods are advertised to ultimately be useful for\r\ncontrol, as the
control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge
with huge potential in areas such as clean and efficient energy\r\nproduction,
or the development of advanced medical devices. However, the\r\nquestion of how
to use a predictive model for control is often left unanswered\r\ndue to the associated
challenges, namely a significantly higher system\r\ncomplexity, the requirement
of much larger data sets and an increased and often\r\nproblem-specific modeling
effort. To solve these issues, we present a universal\r\nframework (which we call
QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive
models into control systems and use them for feedback control. The\r\nadvantages
of our approach are a linear increase in data requirements with\r\nrespect to
the control dimension, performance guarantees that rely exclusively\r\non the
accuracy of the predictive model, and only little prior knowledge\r\nrequirements
in control theory to solve complex control problems. In particular\r\nthe latter
point is of key importance to enable a large number of researchers\r\nand practitioners
to exploit the ever increasing capabilities of predictive\r\nmodels for control
in a straight-forward and systematic fashion."
article_number: '110840'
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
citation:
ama: Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to
Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840
apa: Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven
Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840
bibtex: '@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven
Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840},
number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian
and Bieker, Katharina}, year={2023} }'
chicago: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation
of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840.
ieee: 'S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models
to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi:
10.1016/j.automatica.2022.110840.'
mla: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of
Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier,
2023, doi:10.1016/j.automatica.2022.110840.
short: S. Peitz, K. Bieker, Automatica 149 (2023).
date_created: 2021-02-10T07:04:15Z
date_updated: 2023-01-07T12:01:58Z
department:
- _id: '101'
- _id: '655'
doi: 10.1016/j.automatica.2022.110840
intvolume: ' 149'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true
oa: '1'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Automatica
publication_status: published
publisher: Elsevier
status: public
title: On the Universal Transformation of Data-Driven Models to Control Systems
type: journal_article
user_id: '47427'
volume: 149
year: '2023'
...
---
_id: '46756'
author:
- first_name: Melina
full_name: Wallner, Melina
id: '45445'
last_name: Wallner
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: 'Wallner M, Häsel-Weide U. Conceptual understanding of third grades for axial
symmetry. In: Novotna J, Moraova H, eds. International Symposium in Elementary
Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education.
Charles University; 2023:346-354.'
apa: 'Wallner, M., & Häsel-Weide, U. (2023). Conceptual understanding of third
grades for axial symmetry. In J. Novotna & H. Moraova (Eds.), International
Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education (pp. 346–354). Charles University.'
bibtex: '@inproceedings{Wallner_Häsel-Weide_2023, title={Conceptual understanding
of third grades for axial symmetry}, booktitle={International Symposium in Elementary
Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education},
publisher={Charles University}, author={Wallner, Melina and Häsel-Weide, Uta},
editor={Novotna, J. and Moraova, H.}, year={2023}, pages={346–354} }'
chicago: 'Wallner, Melina, and Uta Häsel-Weide. “Conceptual Understanding of Third
Grades for Axial Symmetry.” In International Symposium in Elementary Mathematics
Teaching. Proceedings: New Directions in Elementary Mathematics Education,
edited by J. Novotna and H. Moraova, 346–54. Charles University, 2023.'
ieee: 'M. Wallner and U. Häsel-Weide, “Conceptual understanding of third grades
for axial symmetry,” in International Symposium in Elementary Mathematics Teaching.
Proceedings: New Directions in Elementary Mathematics Education, Prag, 2023,
pp. 346–354.'
mla: 'Wallner, Melina, and Uta Häsel-Weide. “Conceptual Understanding of Third Grades
for Axial Symmetry.” International Symposium in Elementary Mathematics Teaching.
Proceedings: New Directions in Elementary Mathematics Education, edited by
J. Novotna and H. Moraova, Charles University, 2023, pp. 346–54.'
short: 'M. Wallner, 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. 346–354.'
conference:
location: Prag
name: International Symposium in Elementary Mathematics Teaching
date_created: 2023-08-30T09:24:29Z
date_updated: 2023-11-24T16:33:37Z
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
main_file_link:
- url: https://semt.cz/proceedings/semt-23.pdf
page: 346-354
publication: 'International Symposium in Elementary Mathematics Teaching. Proceedings:
New Directions in Elementary Mathematics Education'
publisher: Charles University
status: public
title: Conceptual understanding of third grades for axial symmetry
type: conference
user_id: '45445'
year: '2023'
...
---
_id: '49326'
abstract:
- lang: eng
text: Many networked systems are governed by non-pairwise interactions between nodes.
The resulting higher-order interaction structure can then be encoded by means
of a hypernetwork. In this paper we consider dynamical systems on hypernetworks
by defining a class of admissible maps for every such hypernetwork. We explain
how to classify robust cluster synchronization patterns on hypernetworks by finding
balanced partitions, and we generalize the concept of a graph fibration to the
hypernetwork context. We also show that robust synchronization patterns are only
fully determined by polynomial admissible maps of high order. This means that,
unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order,
i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork,
for the degree of the polynomial admissible maps that determine robust synchronization
patterns. We also demonstrate that this degree is optimal by investigating a class
of examples. We conclude by demonstrating how this effect may cause remarkable
synchrony breaking bifurcations that occur at high polynomial degree.
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. Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect. SIAM Journal on Applied Mathematics. 2023;83(6):2329-2353.
doi:10.1137/23m1561075'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2023). Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics,
83(6), 2329–2353. https://doi.org/10.1137/23m1561075'
bibtex: '@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect}, volume={83}, DOI={10.1137/23m1561075},
number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society
for Industrial & Applied Mathematics (SIAM)}, author={von der Gracht, Sören
and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics
83, no. 6 (2023): 2329–53. https://doi.org/10.1137/23m1561075.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect,” SIAM Journal on Applied Mathematics, vol. 83,
no. 6, pp. 2329–2353, 2023, doi: 10.1137/23m1561075.'
mla: 'von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a
Higher-Order Effect.” SIAM Journal on Applied Mathematics, vol. 83, no.
6, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2329–53,
doi:10.1137/23m1561075.'
short: S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics
83 (2023) 2329–2353.
date_created: 2023-11-29T10:50:05Z
date_updated: 2023-11-29T10:52:23Z
department:
- _id: '101'
doi: 10.1137/23m1561075
external_id:
arxiv:
- '2302.08974'
intvolume: ' 83'
issue: '6'
keyword:
- Applied Mathematics
language:
- iso: eng
page: 2329-2353
publication: SIAM Journal on Applied Mathematics
publication_identifier:
issn:
- 0036-1399
- 1095-712X
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: 'Hypernetworks: Cluster Synchronization Is a Higher-Order Effect'
type: journal_article
user_id: '97359'
volume: 83
year: '2023'
...
---
_id: '49372'
author:
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
- first_name: Jiuya
full_name: Wang, Jiuya
last_name: Wang
citation:
ama: Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. La
Matematica. Published online 2023. doi:10.1007/s44007-023-00067-w
apa: Klüners, J., & Wang, J. (2023). Idélic Approach in Enumerating Heisenberg
Extensions. La Matematica. https://doi.org/10.1007/s44007-023-00067-w
bibtex: '@article{Klüners_Wang_2023, title={Idélic Approach in Enumerating Heisenberg
Extensions}, DOI={10.1007/s44007-023-00067-w},
journal={La Matematica}, publisher={Springer Science and Business Media LLC},
author={Klüners, Jürgen and Wang, Jiuya}, year={2023} }'
chicago: Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg
Extensions.” La Matematica, 2023. https://doi.org/10.1007/s44007-023-00067-w.
ieee: 'J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,”
La Matematica, 2023, doi: 10.1007/s44007-023-00067-w.'
mla: Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg
Extensions.” La Matematica, Springer Science and Business Media LLC, 2023,
doi:10.1007/s44007-023-00067-w.
short: J. Klüners, J. Wang, La Matematica (2023).
date_created: 2023-12-01T09:23:59Z
date_updated: 2023-12-06T09:50:43Z
department:
- _id: '102'
doi: 10.1007/s44007-023-00067-w
language:
- iso: eng
publication: La Matematica
publication_identifier:
issn:
- 2730-9657
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Idélic Approach in Enumerating Heisenberg Extensions
type: journal_article
user_id: '21202'
year: '2023'
...
---
_id: '49425'
author:
- first_name: Simone
full_name: Seitz, Simone
last_name: Seitz
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: Yannik
full_name: Wilke, Yannik
last_name: Wilke
- first_name: Melina
full_name: Wallner, Melina
id: '45445'
last_name: Wallner
citation:
ama: 'Seitz S, Häsel-Weide U, Wilke Y, Wallner M. Expertise and professionalism
for inclusive (mathematics) teaching and learning: reflections on findings from
interdisciplinary professionalisation research. Teachers and Teaching.
Published online 2023:1-16. doi:https://doi.org/10.1080/13540602.2023.2284876 '
apa: 'Seitz, S., Häsel-Weide, U., Wilke, Y., & Wallner, M. (2023). Expertise
and professionalism for inclusive (mathematics) teaching and learning: reflections
on findings from interdisciplinary professionalisation research. Teachers and
Teaching, 1–16. https://doi.org/10.1080/13540602.2023.2284876
'
bibtex: '@article{Seitz_Häsel-Weide_Wilke_Wallner_2023, title={Expertise and professionalism
for inclusive (mathematics) teaching and learning: reflections on findings from
interdisciplinary professionalisation research}, DOI={https://doi.org/10.1080/13540602.2023.2284876 }, journal={Teachers and Teaching},
author={Seitz, Simone and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina},
year={2023}, pages={1–16} }'
chicago: 'Seitz, Simone, Uta Häsel-Weide, Yannik Wilke, and Melina Wallner. “Expertise
and Professionalism for Inclusive (Mathematics) Teaching and Learning: Reflections
on Findings from Interdisciplinary Professionalisation Research.” Teachers
and Teaching, 2023, 1–16. https://doi.org/10.1080/13540602.2023.2284876 .'
ieee: 'S. Seitz, U. Häsel-Weide, Y. Wilke, and M. Wallner, “Expertise and professionalism
for inclusive (mathematics) teaching and learning: reflections on findings from
interdisciplinary professionalisation research,” Teachers and Teaching,
pp. 1–16, 2023, doi: https://doi.org/10.1080/13540602.2023.2284876
.'
mla: 'Seitz, Simone, et al. “Expertise and Professionalism for Inclusive (Mathematics)
Teaching and Learning: Reflections on Findings from Interdisciplinary Professionalisation
Research.” Teachers and Teaching, 2023, pp. 1–16, doi:https://doi.org/10.1080/13540602.2023.2284876 .'
short: S. Seitz, U. Häsel-Weide, Y. Wilke, M. Wallner, Teachers and Teaching (2023)
1–16.
date_created: 2023-12-04T09:45:04Z
date_updated: 2023-12-13T12:51:03Z
department:
- _id: '543'
doi: 'https://doi.org/10.1080/13540602.2023.2284876 '
language:
- iso: eng
page: 1-16
publication: Teachers and Teaching
status: public
title: 'Expertise and professionalism for inclusive (mathematics) teaching and learning:
reflections on findings from interdisciplinary professionalisation research'
type: journal_article
user_id: '45445'
year: '2023'
...
---
_id: '34135'
abstract:
- lang: eng
text: By one of the most fundamental principles in physics, a dynamical system will
exhibit those motions which extremise an action functional. This leads to the
formation of the Euler-Lagrange equations, which serve as a model of how the system
will behave in time. If the dynamics exhibit additional symmetries, then the motion
fulfils additional conservation laws, such as conservation of energy (time invariance),
momentum (translation invariance), or angular momentum (rotational invariance).
To learn a system representation, one could learn the discrete Euler-Lagrange
equations, or alternatively, learn the discrete Lagrangian function Ld which defines
them. Based on ideas from Lie group theory, in this work we introduce a framework
to learn a discrete Lagrangian along with its symmetry group from discrete observations
of motions and, therefore, identify conserved quantities. The learning process
does not restrict the form of the Lagrangian, does not require velocity or momentum
observations or predictions and incorporates a cost term which safeguards against
unwanted solutions and against potential numerical issues in forward simulations.
The learnt discrete quantities are related to their continuous analogues using
variational backward error analysis and numerical results demonstrate the improvement
such models can have both qualitatively and quantitatively even in the presence
of noise.
author:
- first_name: Yana
full_name: Lishkova, Yana
last_name: Lishkova
- first_name: Paul
full_name: Scherer, Paul
last_name: Scherer
- first_name: Steffen
full_name: Ridderbusch, Steffen
last_name: Ridderbusch
- first_name: Mateja
full_name: Jamnik, Mateja
last_name: Jamnik
- first_name: Pietro
full_name: Liò, Pietro
last_name: Liò
- 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: 'Lishkova Y, Scherer P, Ridderbusch S, et al. Discrete Lagrangian Neural Networks
with Automatic Symmetry Discovery. In: IFAC-PapersOnLine. Vol 56. Elsevier;
2023:3203-3210. doi:10.1016/j.ifacol.2023.10.1457'
apa: Lishkova, Y., Scherer, P., Ridderbusch, S., Jamnik, M., Liò, P., Ober-Blöbaum,
S., & Offen, C. (2023). Discrete Lagrangian Neural Networks with Automatic
Symmetry Discovery. IFAC-PapersOnLine, 56(2), 3203–3210. https://doi.org/10.1016/j.ifacol.2023.10.1457
bibtex: '@inproceedings{Lishkova_Scherer_Ridderbusch_Jamnik_Liò_Ober-Blöbaum_Offen_2023,
title={Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery},
volume={56}, DOI={10.1016/j.ifacol.2023.10.1457},
number={2}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier}, author={Lishkova,
Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro
and Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={3203–3210} }'
chicago: Lishkova, Yana, Paul Scherer, Steffen Ridderbusch, Mateja Jamnik, Pietro
Liò, Sina Ober-Blöbaum, and Christian Offen. “Discrete Lagrangian Neural Networks
with Automatic Symmetry Discovery.” In IFAC-PapersOnLine, 56:3203–10. Elsevier,
2023. https://doi.org/10.1016/j.ifacol.2023.10.1457.
ieee: 'Y. Lishkova et al., “Discrete Lagrangian Neural Networks with Automatic
Symmetry Discovery,” in IFAC-PapersOnLine, Yokohama, Japan, 2023, vol.
56, no. 2, pp. 3203–3210, doi: 10.1016/j.ifacol.2023.10.1457.'
mla: Lishkova, Yana, et al. “Discrete Lagrangian Neural Networks with Automatic
Symmetry Discovery.” IFAC-PapersOnLine, vol. 56, no. 2, Elsevier, 2023,
pp. 3203–10, doi:10.1016/j.ifacol.2023.10.1457.
short: 'Y. Lishkova, P. Scherer, S. Ridderbusch, M. Jamnik, P. Liò, S. Ober-Blöbaum,
C. Offen, in: IFAC-PapersOnLine, Elsevier, 2023, pp. 3203–3210.'
conference:
end_date: 2023-07-14
location: ' Yokohama, Japan'
name: The 22nd World Congress of the International Federation of Automatic Control
start_date: 2023-07-09
date_created: 2022-11-23T08:17:10Z
date_updated: 2023-12-29T14:26:00Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1016/j.ifacol.2023.10.1457
external_id:
arxiv:
- '2211.10830'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-04-17T08:05:55Z
date_updated: 2023-04-17T08:05:55Z
description: |-
By one of the most fundamental principles in physics, a dynamical system will
exhibit those motions which extremise an action functional. This leads to the formation of
the Euler-Lagrange equations, which serve as a model of how the system will behave in time.
If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation
laws, such as conservation of energy (time invariance), momentum (translation invariance), or
angular momentum (rotational invariance). To learn a system representation, one could learn
the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function
Ld which defines them. Based on ideas from Lie group theory, we introduce a framework to learn
a discrete Lagrangian along with its symmetry group from discrete observations of motions and,
therefore, identify conserved quantities. The learning process does not restrict the form of the
Lagrangian, does not require velocity or momentum observations or predictions and incorporates
a cost term which safeguards against unwanted solutions and against potential numerical issues
in forward simulations. The learnt discrete quantities are related to their continuous analogues
using variational backward error analysis and numerical results demonstrate the improvement
such models can have both qualitatively and quantitatively even in the presence of noise.
file_id: '44037'
file_name: LNN_project.pdf
file_size: 576115
relation: main_file
title: Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery
file_date_updated: 2023-04-17T08:05:55Z
has_accepted_license: '1'
intvolume: ' 56'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://www.sciencedirect.com/science/article/pii/S2405896323018657
oa: '1'
page: 3203-3210
publication: IFAC-PapersOnLine
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/yanalish/SymDLNN
status: public
title: Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery
type: conference
user_id: '85279'
volume: 56
year: '2023'
...
---
_id: '50298'
abstract:
- lang: eng
text: A finite classical polar space of rank $n$ consists of the totally isotropic
subspaces of a finite vector space equipped with a nondegenerate form such that
$n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite
classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces
such that each totally isotropic $t$-space is contained in exactly one member
of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost
complete classification of such $t$-Steiner systems, showing that such objects
can only exist in some corner cases. This classification result arises from a
more general result on packings in polar spaces.
author:
- first_name: Kai-Uwe
full_name: Schmidt, Kai-Uwe
last_name: Schmidt
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Schmidt K-U, Weiß C. Packings and Steiner systems in polar spaces. Combinatorial
Theory. 2023;3(1). doi:10.5070/c63160424
apa: Schmidt, K.-U., & Weiß, C. (2023). Packings and Steiner systems in polar
spaces. Combinatorial Theory, 3(1). https://doi.org/10.5070/c63160424
bibtex: '@article{Schmidt_Weiß_2023, title={Packings and Steiner systems in polar
spaces}, volume={3}, DOI={10.5070/c63160424},
number={1}, journal={Combinatorial Theory}, author={Schmidt, Kai-Uwe and Weiß,
Charlene}, year={2023} }'
chicago: Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar
Spaces.” Combinatorial Theory 3, no. 1 (2023). https://doi.org/10.5070/c63160424.
ieee: 'K.-U. Schmidt and C. Weiß, “Packings and Steiner systems in polar spaces,”
Combinatorial Theory, vol. 3, no. 1, 2023, doi: 10.5070/c63160424.'
mla: Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar
Spaces.” Combinatorial Theory, vol. 3, no. 1, 2023, doi:10.5070/c63160424.
short: K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023).
date_created: 2024-01-08T14:33:54Z
date_updated: 2024-01-08T14:39:20Z
department:
- _id: '100'
doi: 10.5070/c63160424
intvolume: ' 3'
issue: '1'
language:
- iso: eng
publication: Combinatorial Theory
publication_status: published
status: public
title: Packings and Steiner systems in polar spaces
type: journal_article
user_id: '70420'
volume: 3
year: '2023'
...
---
_id: '50297'
abstract:
- lang: eng
text: We show that there exist ordered orthogonal arrays, whose sizes deviate from
the Rao bound by a factor that is polynomial in the parameters of the ordered
orthogonal array. The proof is nonconstructive and based on a probabilistic method
due to Kuperberg, Lovett and Peled.
author:
- first_name: Kai‐Uwe
full_name: Schmidt, Kai‐Uwe
last_name: Schmidt
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Schmidt K, Weiß C. Existence of small ordered orthogonal arrays. Journal
of Combinatorial Designs. 2023;31(9):422-431. doi:10.1002/jcd.21903
apa: Schmidt, K., & Weiß, C. (2023). Existence of small ordered orthogonal arrays.
Journal of Combinatorial Designs, 31(9), 422–431. https://doi.org/10.1002/jcd.21903
bibtex: '@article{Schmidt_Weiß_2023, title={Existence of small ordered orthogonal
arrays}, volume={31}, DOI={10.1002/jcd.21903},
number={9}, journal={Journal of Combinatorial Designs}, publisher={Wiley}, author={Schmidt,
Kai‐Uwe and Weiß, Charlene}, year={2023}, pages={422–431} }'
chicago: 'Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal
Arrays.” Journal of Combinatorial Designs 31, no. 9 (2023): 422–31. https://doi.org/10.1002/jcd.21903.'
ieee: 'K. Schmidt and C. Weiß, “Existence of small ordered orthogonal arrays,” Journal
of Combinatorial Designs, vol. 31, no. 9, pp. 422–431, 2023, doi: 10.1002/jcd.21903.'
mla: Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal
Arrays.” Journal of Combinatorial Designs, vol. 31, no. 9, Wiley, 2023,
pp. 422–31, doi:10.1002/jcd.21903.
short: K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 422–431.
date_created: 2024-01-08T14:25:28Z
date_updated: 2024-01-08T14:38:53Z
department:
- _id: '100'
doi: 10.1002/jcd.21903
intvolume: ' 31'
issue: '9'
language:
- iso: eng
page: 422-431
publication: Journal of Combinatorial Designs
publication_status: published
publisher: Wiley
status: public
title: Existence of small ordered orthogonal arrays
type: journal_article
user_id: '70420'
volume: 31
year: '2023'
...
---
_id: '50300'
abstract:
- lang: eng
text: Digital communications relies heavily on the usage of different types of codes.
Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs
of binary codes and binary codes with constant weight. All these codes can be
viewed as subsets of classical association schemes. A central coding-theoretic
problem is to derive upper bounds for the size of codes. This thesis investigates
Delsartes powerful linear program whose optimum is precisely such a bound for
codes in association schemes. The linear programs for binary codes and binary
constant-weight codes have been extensively studied since the 1970s, but their
optimum is still unknown. We determine in a unified way the optimum of the linear
program in several ordinary q-analogs as well as in their affine counterparts.
In particular, bounds and constructions for codes in polar spaces are established,
where the bounds are sharp up to a constant factor in many cases. Moreover, based
on these results, an almost complete classification of Steiner systems in polar
spaces is provided by showing that they could only exist in some corner cases.
author:
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Weiß C. Linear Programming Bounds in Classical Association Schemes.;
2023. doi:10.17619/UNIPB/1-1672
apa: Weiß, C. (2023). Linear programming bounds in classical association schemes.
https://doi.org/10.17619/UNIPB/1-1672
bibtex: '@book{Weiß_2023, title={Linear programming bounds in classical association
schemes}, DOI={10.17619/UNIPB/1-1672},
author={Weiß, Charlene}, year={2023} }'
chicago: Weiß, Charlene. Linear Programming Bounds in Classical Association Schemes,
2023. https://doi.org/10.17619/UNIPB/1-1672.
ieee: C. Weiß, Linear programming bounds in classical association schemes.
2023.
mla: Weiß, Charlene. Linear Programming Bounds in Classical Association Schemes.
2023, doi:10.17619/UNIPB/1-1672.
short: C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023.
date_created: 2024-01-08T14:42:12Z
date_updated: 2024-01-08T14:46:14Z
department:
- _id: '100'
doi: 10.17619/UNIPB/1-1672
language:
- iso: eng
status: public
title: Linear programming bounds in classical association schemes
type: dissertation
user_id: '70420'
year: '2023'
...
---
_id: '51131'
author:
- first_name: Lara Marie
full_name: Graf, Lara Marie
id: '89837'
last_name: Graf
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: K.
full_name: Höveler, K.
last_name: Höveler
- first_name: M.
full_name: Nührenbörger, M.
last_name: Nührenbörger
citation:
ama: 'Graf LM, Häsel-Weide U, Höveler K, Nührenbörger M. Insights into out-of-field
teachers’ self-reports: Fostering the understanding of addition and subtraction
as a basis for children to overcome difficulties in mathematics. In: Drijvers
P, Csapodi C, Palmér H, Gosztonyi K, Kónya E, Alfréd Rényi Institute of Mathematics
and ERME, eds. Proceedings of the Thirteenth Congress of the European Society
for Research in Mathematics Education (CERME13). ; 2023:3203-3210.'
apa: 'Graf, L. M., Häsel-Weide, U., Höveler, K., & Nührenbörger, M. (2023).
Insights into out-of-field teachers’ self-reports: Fostering the understanding
of addition and subtraction as a basis for children to overcome difficulties in
mathematics. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, &
Alfréd Rényi Institute of Mathematics and ERME (Eds.), Proceedings of the Thirteenth
Congress of the European Society for Research in Mathematics Education (CERME13)
(pp. 3203–3210).'
bibtex: '@inproceedings{Graf_Häsel-Weide_Höveler_Nührenbörger_2023, title={Insights
into out-of-field teachers’ self-reports: Fostering the understanding of addition
and subtraction as a basis for children to overcome difficulties in mathematics},
booktitle={Proceedings of the Thirteenth Congress of the European Society for
Research in Mathematics Education (CERME13)}, author={Graf, Lara Marie and Häsel-Weide,
Uta and Höveler, K. and Nührenbörger, M.}, editor={Drijvers, P. and Csapodi, C.
and Palmér, H. and Gosztonyi, K. and Kónya, E. and Alfréd Rényi Institute of Mathematics
and ERME}, year={2023}, pages={3203–3210} }'
chicago: 'Graf, Lara Marie, Uta Häsel-Weide, K. Höveler, and M. Nührenbörger. “Insights
into Out-of-Field Teachers’ Self-Reports: Fostering the Understanding of Addition
and Subtraction as a Basis for Children to Overcome Difficulties in Mathematics.”
In Proceedings of the Thirteenth Congress of the European Society for Research
in Mathematics Education (CERME13), edited by P. Drijvers, C. Csapodi, H.
Palmér, K. Gosztonyi, E. Kónya, and Alfréd Rényi Institute of Mathematics and
ERME, 3203–10, 2023.'
ieee: 'L. M. Graf, U. Häsel-Weide, K. Höveler, and M. Nührenbörger, “Insights into
out-of-field teachers’ self-reports: Fostering the understanding of addition and
subtraction as a basis for children to overcome difficulties in mathematics,”
in Proceedings of the Thirteenth Congress of the European Society for Research
in Mathematics Education (CERME13), 2023, pp. 3203–3210.'
mla: 'Graf, Lara Marie, et al. “Insights into Out-of-Field Teachers’ Self-Reports:
Fostering the Understanding of Addition and Subtraction as a Basis for Children
to Overcome Difficulties in Mathematics.” Proceedings of the Thirteenth Congress
of the European Society for Research in Mathematics Education (CERME13), edited
by P. Drijvers et al., 2023, pp. 3203–10.'
short: 'L.M. Graf, U. Häsel-Weide, K. Höveler, M. Nührenbörger, in: P. Drijvers,
C. Csapodi, H. Palmér, K. Gosztonyi, E. Kónya, Alfréd Rényi Institute of Mathematics
and ERME (Eds.), Proceedings of the Thirteenth Congress of the European Society
for Research in Mathematics Education (CERME13), 2023, pp. 3203–3210.'
corporate_editor:
- Alfréd Rényi Institute of Mathematics and ERME
date_created: 2024-02-05T08:47:35Z
date_updated: 2024-02-05T08:55:43Z
department:
- _id: '543'
editor:
- first_name: P.
full_name: Drijvers, P.
last_name: Drijvers
- first_name: C.
full_name: Csapodi, C.
last_name: Csapodi
- first_name: H.
full_name: Palmér, H.
last_name: Palmér
- first_name: K.
full_name: Gosztonyi, K.
last_name: Gosztonyi
- first_name: E.
full_name: Kónya, E.
last_name: Kónya
language:
- iso: eng
page: 3203-3210
publication: Proceedings of the Thirteenth Congress of the European Society for Research
in Mathematics Education (CERME13)
status: public
title: 'Insights into out-of-field teachers’ self-reports: Fostering the understanding
of addition and subtraction as a basis for children to overcome difficulties in
mathematics'
type: conference
user_id: '14931'
year: '2023'
...
---
_id: '31189'
abstract:
- lang: eng
text: "Given a geometrically finite hyperbolic surface of infinite volume it is
a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator
has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization
of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential
operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of
higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe
geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding
principal eigenvalues. A large class of examples fulfilling these\r\nassumptions
are the non-compact quotients by Anosov subgroups."
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
citation:
ama: Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally
symmetric spaces. Communications in Mathematical Physics. 2023;403. doi:https://doi.org/10.1007/s00220-023-04819-1
apa: Weich, T., & Wolf, L. L. (2023). Absence of principal eigenvalues for higher
rank locally symmetric spaces. Communications in Mathematical Physics,
403. https://doi.org/10.1007/s00220-023-04819-1
bibtex: '@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher
rank locally symmetric spaces}, volume={403}, DOI={https://doi.org/10.1007/s00220-023-04819-1},
journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf,
Lasse Lennart}, year={2023} }'
chicago: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues
for Higher Rank Locally Symmetric Spaces.” Communications in Mathematical
Physics 403 (2023). https://doi.org/10.1007/s00220-023-04819-1.
ieee: 'T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank
locally symmetric spaces,” Communications in Mathematical Physics, vol.
403, 2023, doi: https://doi.org/10.1007/s00220-023-04819-1.'
mla: Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for
Higher Rank Locally Symmetric Spaces.” Communications in Mathematical Physics,
vol. 403, 2023, doi:https://doi.org/10.1007/s00220-023-04819-1.
short: T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).
date_created: 2022-05-11T10:38:11Z
date_updated: 2024-02-06T20:52:40Z
department:
- _id: '10'
- _id: '548'
- _id: '623'
doi: https://doi.org/10.1007/s00220-023-04819-1
external_id:
arxiv:
- '2205.03167'
intvolume: ' 403'
language:
- iso: eng
publication: Communications in Mathematical Physics
publication_identifier:
unknown:
- 1275-1295
status: public
title: Absence of principal eigenvalues for higher rank locally symmetric spaces
type: journal_article
user_id: '49178'
volume: 403
year: '2023'
...
---
_id: '51206'
abstract:
- lang: eng
text: "We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions
on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the
connection between invariant Ruelle distributions and residues\r\nof meromorphically
continued weighted zeta functions established by the authors\r\ntogether with
Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted
zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm
determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer
operator has to include a contracting direction which\r\nwe account for with techniques
developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed
for our algorithm in the case of surfaces with\r\nadditional symmetries by proving
and applying a symmetry reduction of weighted\r\nzeta functions."
author:
- first_name: Philipp
full_name: Schütte, Philipp
id: '50168'
last_name: Schütte
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic
Surfaces -- A Numerical Algorithm via Weighted Zeta Functions. arXiv:230813463.
Published online 2023.
apa: Schütte, P., & Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions. In
arXiv:2308.13463.
bibtex: '@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463},
author={Schütte, Philipp and Weich, Tobias}, year={2023} }'
chicago: Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on
Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta
Functions.” ArXiv:2308.13463, 2023.
ieee: P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions,” arXiv:2308.13463.
2023.
mla: Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact
Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions.” ArXiv:2308.13463,
2023.
short: P. Schütte, T. Weich, ArXiv:2308.13463 (2023).
date_created: 2024-02-06T20:58:35Z
date_updated: 2024-02-11T19:56:01Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- '2308.13463'
language:
- iso: eng
publication: arXiv:2308.13463
status: public
title: Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces --
A Numerical Algorithm via Weighted Zeta Functions
type: preprint
user_id: '49178'
year: '2023'
...
---
_id: '51351'
author:
- 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: Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. Discrete
Applied Mathematics. 2023;337:185-189. doi:10.1016/j.dam.2023.05.008
apa: Steffen, E., & Wolf, I. H. (2023). Bounds for the chromatic index of signed
multigraphs. Discrete Applied Mathematics, 337, 185–189. https://doi.org/10.1016/j.dam.2023.05.008
bibtex: '@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed
multigraphs}, volume={337}, DOI={10.1016/j.dam.2023.05.008},
journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen,
Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }'
chicago: 'Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic
Index of Signed Multigraphs.” Discrete Applied Mathematics 337 (2023):
185–89. https://doi.org/10.1016/j.dam.2023.05.008.'
ieee: 'E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,”
Discrete Applied Mathematics, vol. 337, pp. 185–189, 2023, doi: 10.1016/j.dam.2023.05.008.'
mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index
of Signed Multigraphs.” Discrete Applied Mathematics, vol. 337, Elsevier
BV, 2023, pp. 185–89, doi:10.1016/j.dam.2023.05.008.
short: E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.
date_created: 2024-02-14T17:33:29Z
date_updated: 2024-02-14T17:33:59Z
department:
- _id: '542'
doi: 10.1016/j.dam.2023.05.008
intvolume: ' 337'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 185-189
publication: Discrete Applied Mathematics
publication_identifier:
issn:
- 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Bounds for the chromatic index of signed multigraphs
type: journal_article
user_id: '15540'
volume: 337
year: '2023'
...
---
_id: '45190'
author:
- first_name: Chiara
full_name: Cappello, Chiara
id: '72874'
last_name: Cappello
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: 'Cappello C, Steffen E. Graph-Theoretical Models for the Analysis and Design
of Socio-Technical Networks. In: The Digital Twin of Humans. Springer International
Publishing; 2023:93--110. doi:10.1007/978-3-031-26104-6_5'
apa: Cappello, C., & Steffen, E. (2023). Graph-Theoretical Models for the Analysis
and Design of Socio-Technical Networks. In The Digital Twin of Humans (pp.
93--110). Springer International Publishing. https://doi.org/10.1007/978-3-031-26104-6_5
bibtex: '@inbook{Cappello_Steffen_2023, place={Cham}, title={Graph-Theoretical Models
for the Analysis and Design of Socio-Technical Networks}, DOI={10.1007/978-3-031-26104-6_5},
booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing},
author={Cappello, Chiara and Steffen, Eckhard}, year={2023}, pages={93--110} }'
chicago: 'Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the
Analysis and Design of Socio-Technical Networks.” In The Digital Twin of Humans,
93--110. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-26104-6_5.'
ieee: 'C. Cappello and E. Steffen, “Graph-Theoretical Models for the Analysis and
Design of Socio-Technical Networks,” in The Digital Twin of Humans, Cham:
Springer International Publishing, 2023, pp. 93--110.'
mla: Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis
and Design of Socio-Technical Networks.” The Digital Twin of Humans, Springer
International Publishing, 2023, pp. 93--110, doi:10.1007/978-3-031-26104-6_5.
short: 'C. Cappello, E. Steffen, in: The Digital Twin of Humans, Springer International
Publishing, Cham, 2023, pp. 93--110.'
date_created: 2023-05-22T10:22:21Z
date_updated: 2024-02-16T07:42:38Z
department:
- _id: '542'
doi: 10.1007/978-3-031-26104-6_5
language:
- iso: eng
page: 93--110
place: Cham
publication: The Digital Twin of Humans
publication_identifier:
isbn:
- '9783031261039'
- '9783031261046'
publication_status: published
publisher: Springer International Publishing
status: public
title: Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks
type: book_chapter
user_id: '15540'
year: '2023'
...
---
_id: '51357'
article_number: '113457'
author:
- 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: Steffen E, Wolf IH. Rotation r-graphs. Discrete Mathematics. Published
online 2023. doi:10.1016/j.disc.2023.113457
apa: Steffen, E., & Wolf, I. H. (2023). Rotation r-graphs. Discrete Mathematics,
Article 113457. https://doi.org/10.1016/j.disc.2023.113457
bibtex: '@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={10.1016/j.disc.2023.113457},
number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen,
Eckhard and Wolf, Isaak Hieronymus}, year={2023} }'
chicago: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” Discrete
Mathematics, 2023. https://doi.org/10.1016/j.disc.2023.113457.
ieee: 'E. Steffen and I. H. Wolf, “Rotation r-graphs,” Discrete Mathematics,
Art. no. 113457, 2023, doi: 10.1016/j.disc.2023.113457.'
mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” Discrete
Mathematics, 113457, Elsevier BV, 2023, doi:10.1016/j.disc.2023.113457.
short: E. Steffen, I.H. Wolf, Discrete Mathematics (2023).
date_created: 2024-02-16T08:44:50Z
date_updated: 2024-02-16T08:45:10Z
department:
- _id: '542'
doi: 10.1016/j.disc.2023.113457
keyword:
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
publication: Discrete Mathematics
publication_identifier:
issn:
- 0012-365X
publication_status: published
publisher: Elsevier BV
status: public
title: Rotation r-graphs
type: journal_article
user_id: '15540'
year: '2023'
...
---
_id: '31210'
abstract:
- lang: eng
text: "In this paper we complete the program of relating the Laplace spectrum for\r\nrank
one compact locally symmetric spaces with the first band Ruelle-Pollicott\r\nresonances
of the geodesic flow on its sphere bundle. This program was started\r\nby Flaminio
and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and\r\nGuillarmou
for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for\r\ngeneral
rank one spaces. Except for the case of hyperbolic surfaces a countable\r\nset
of exceptional spectral parameters always left untreated since the\r\ncorresponding
Poisson transforms are neither injective nor surjective. We use\r\nvector valued
Poisson transforms to treat also the exceptional spectral\r\nparameters. For surfaces
the exceptional spectral parameters lead to discrete\r\nseries representations
of $\\mathrm{SL}(2,\\mathbb R)$. In higher dimensions the\r\nsituation is more
complicated, but can be described completely."
author:
- first_name: Christian
full_name: Arends, Christian
id: '43994'
last_name: Arends
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: 'Arends C, Hilgert J. Spectral correspondences for rank one locally symmetric
spaces: the case of exceptional parameters. Journal de l’École polytechnique
— Mathématiques. 2023;10:335-403. doi:10.5802/jep.220'
apa: 'Arends, C., & Hilgert, J. (2023). Spectral correspondences for rank one
locally symmetric spaces: the case of exceptional parameters. Journal de l’École
Polytechnique — Mathématiques, 10, 335–403. https://doi.org/10.5802/jep.220'
bibtex: '@article{Arends_Hilgert_2023, title={Spectral correspondences for rank
one locally symmetric spaces: the case of exceptional parameters}, volume={10},
DOI={10.5802/jep.220}, journal={Journal
de l’École polytechnique — Mathématiques}, author={Arends, Christian and Hilgert,
Joachim}, year={2023}, pages={335–403} }'
chicago: 'Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for
Rank One Locally Symmetric Spaces: The Case of Exceptional Parameters.” Journal
de l’École Polytechnique — Mathématiques 10 (2023): 335–403. https://doi.org/10.5802/jep.220.'
ieee: 'C. Arends and J. Hilgert, “Spectral correspondences for rank one locally
symmetric spaces: the case of exceptional parameters,” Journal de l’École polytechnique
— Mathématiques, vol. 10, pp. 335–403, 2023, doi: 10.5802/jep.220.'
mla: 'Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank
One Locally Symmetric Spaces: The Case of Exceptional Parameters.” Journal
de l’École Polytechnique — Mathématiques, vol. 10, 2023, pp. 335–403, doi:10.5802/jep.220.'
short: C. Arends, J. Hilgert, Journal de l’École Polytechnique — Mathématiques 10
(2023) 335–403.
date_created: 2022-05-11T12:27:00Z
date_updated: 2024-02-19T06:30:26Z
department:
- _id: '10'
- _id: '548'
- _id: '91'
doi: 10.5802/jep.220
external_id:
arxiv:
- '2112.11073'
intvolume: ' 10'
keyword:
- Ruelle resonances
- Poisson transforms
- locally symmetric spaces
- principal series representations
language:
- iso: eng
page: 335-403
publication: Journal de l’École polytechnique — Mathématiques
publication_identifier:
eissn:
- 2270-518X
issn:
- 2429-7100
publication_status: published
status: public
title: 'Spectral correspondences for rank one locally symmetric spaces: the case of
exceptional parameters'
type: journal_article
user_id: '49063'
volume: 10
year: '2023'
...