---
_id: '64816'
abstract:
- lang: eng
text: "We study a block mean-field Ising model with $N$ spins split into $s_N$ blocks,
with Curie-Weiss interaction within blocks and nearest-neighbor coupling between
blocks. While previous models deal with the block magnetization for a fixed number
of blocks, we study the the simultaneous limit $N\\to\\infty$ and $s_N\\to\\infty$.
The model interpolates between Curie-Weiss model for $s_N=1$, multi-species mean
field for fixed $s_N=s$, and the 1D Ising model for each spin in its own block
at $s_N=N$.\r\n Under mild growth conditions on $s_N$, we prove a law of large
numbers and a multivariate CLT with covariance given by the lattice Green's function.
For instance, the high temperature CLT essentially covers the optimal range up
to $s_N=o(N/(\\log N)^c)$ and the low temperature regime is new even for fixed
number of blocks $s > 2$. In addition to the standard competition between entropy
and energy, a new obstacle in the proofs is a curse of dimensionality as $s_N
\\to \\infty$."
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Isabel
full_name: Lammers, Isabel
last_name: Lammers
- first_name: Matthias
full_name: Löwe, Matthias
last_name: Löwe
citation:
ama: Jalowy J, Lammers I, Löwe M. The infinite block spin Ising model. arXiv:260301994.
Published online 2026.
apa: Jalowy, J., Lammers, I., & Löwe, M. (2026). The infinite block spin Ising
model. In arXiv:2603.01994.
bibtex: '@article{Jalowy_Lammers_Löwe_2026, title={The infinite block spin Ising
model}, journal={arXiv:2603.01994}, author={Jalowy, Jonas and Lammers, Isabel
and Löwe, Matthias}, year={2026} }'
chicago: Jalowy, Jonas, Isabel Lammers, and Matthias Löwe. “The Infinite Block Spin
Ising Model.” ArXiv:2603.01994, 2026.
ieee: J. Jalowy, I. Lammers, and M. Löwe, “The infinite block spin Ising model,”
arXiv:2603.01994. 2026.
mla: Jalowy, Jonas, et al. “The Infinite Block Spin Ising Model.” ArXiv:2603.01994,
2026.
short: J. Jalowy, I. Lammers, M. Löwe, ArXiv:2603.01994 (2026).
date_created: 2026-03-03T08:49:16Z
date_updated: 2026-03-03T08:49:33Z
department:
- _id: '94'
external_id:
arxiv:
- '2603.01994'
language:
- iso: eng
publication: arXiv:2603.01994
status: public
title: The infinite block spin Ising model
type: preprint
user_id: '113768'
year: '2026'
...
---
_id: '64865'
abstract:
- lang: eng
text: We provide a method to systematically construct vector fields for which the
dynamics display transitions corresponding to a desired hierarchical connection
structure. This structure is given as a finite set of directed graphs $\mathbf{G}_1,\dotsc,\mathbf{G}_N$
(the lower level), together with another digraph $\mathbfΓ$ on $N$ vertices (the
top level). The dynamic realizations of $\mathbf{G}_1,\dotsc,\mathbf{G}_N$ are
heteroclinic networks and they can be thought of as individual connection patterns
on a given set of states. Edges in $\mathbfΓ$ correspond to transitions between
these different patterns. In our construction, the connections given through $\mathbfΓ$
are not heteroclinic, but excitable with zero threshold. This describes a dynamical
transition between two invariant sets where every $δ$-neighborhood of the first
set contains an initial condition with $ω$-limit in the second set. Thus, we prove
a theorem that allows the systematic creation of hierarchical networks that are
excitable on the top level, and heteroclinic on the lower level. Our results modify
and extend the simplex realization method by Ashwin & Postlethwaite.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Alexander
full_name: Lohse, Alexander
last_name: Lohse
citation:
ama: von der Gracht S, Lohse A. Design of Hierarchical Excitable Networks. arXiv:260306157.
Published online 2026.
apa: von der Gracht, S., & Lohse, A. (2026). Design of Hierarchical Excitable
Networks. In arXiv:2603.06157.
bibtex: '@article{von der Gracht_Lohse_2026, title={Design of Hierarchical Excitable
Networks}, journal={arXiv:2603.06157}, author={von der Gracht, Sören and Lohse,
Alexander}, year={2026} }'
chicago: Gracht, Sören von der, and Alexander Lohse. “Design of Hierarchical Excitable
Networks.” ArXiv:2603.06157, 2026.
ieee: S. von der Gracht and A. Lohse, “Design of Hierarchical Excitable Networks,”
arXiv:2603.06157. 2026.
mla: von der Gracht, Sören, and Alexander Lohse. “Design of Hierarchical Excitable
Networks.” ArXiv:2603.06157, 2026.
short: S. von der Gracht, A. Lohse, ArXiv:2603.06157 (2026).
date_created: 2026-03-09T08:22:58Z
date_updated: 2026-03-09T08:26:49Z
ddc:
- '510'
department:
- _id: '101'
- _id: '841'
external_id:
arxiv:
- '2603.06157'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2026-03-09T08:26:04Z
date_updated: 2026-03-09T08:26:04Z
file_id: '64866'
file_name: design-of-hierarchical-excitable-networks.pdf
file_size: 5179491
relation: main_file
success: 1
file_date_updated: 2026-03-09T08:26:04Z
has_accepted_license: '1'
language:
- iso: eng
publication: arXiv:2603.06157
related_material:
link:
- relation: research_paper
url: https://s-vdg.github.io/publication/design-of-hierarchical-excitable-networks/design-of-hierarchical-excitable-networks.pdf
status: public
title: Design of Hierarchical Excitable Networks
type: preprint
user_id: '97359'
year: '2026'
...
---
_id: '63435'
author:
- first_name: Leander
full_name: Claes, Leander
id: '11829'
last_name: Claes
orcid: 0000-0002-4393-268X
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: 'Claes L, Winkler M. Describing smooth small-data solutions to a quasilinear
hyperbolic-parabolic system by W 1,P energy analysis. Nonlinear Analysis: Real
World Applications. 2026;91:104580. doi:10.1016/j.nonrwa.2025.104580'
apa: 'Claes, L., & Winkler, M. (2026). Describing smooth small-data solutions
to a quasilinear hyperbolic-parabolic system by W 1,P energy analysis. Nonlinear
Analysis: Real World Applications, 91, 104580. https://doi.org/10.1016/j.nonrwa.2025.104580'
bibtex: '@article{Claes_Winkler_2026, title={Describing smooth small-data solutions
to a quasilinear hyperbolic-parabolic system by W 1,P energy analysis}, volume={91},
DOI={10.1016/j.nonrwa.2025.104580},
journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV},
author={Claes, Leander and Winkler, Michael}, year={2026}, pages={104580} }'
chicago: 'Claes, Leander, and Michael Winkler. “Describing Smooth Small-Data Solutions
to a Quasilinear Hyperbolic-Parabolic System by W 1,P Energy Analysis.” Nonlinear
Analysis: Real World Applications 91 (2026): 104580. https://doi.org/10.1016/j.nonrwa.2025.104580.'
ieee: 'L. Claes and M. Winkler, “Describing smooth small-data solutions to a quasilinear
hyperbolic-parabolic system by W 1,P energy analysis,” Nonlinear Analysis:
Real World Applications, vol. 91, p. 104580, 2026, doi: 10.1016/j.nonrwa.2025.104580.'
mla: 'Claes, Leander, and Michael Winkler. “Describing Smooth Small-Data Solutions
to a Quasilinear Hyperbolic-Parabolic System by W 1,P Energy Analysis.” Nonlinear
Analysis: Real World Applications, vol. 91, Elsevier BV, 2026, p. 104580,
doi:10.1016/j.nonrwa.2025.104580.'
short: 'L. Claes, M. Winkler, Nonlinear Analysis: Real World Applications 91 (2026)
104580.'
date_created: 2026-01-05T07:32:00Z
date_updated: 2026-01-05T07:40:49Z
department:
- _id: '49'
- _id: '90'
doi: 10.1016/j.nonrwa.2025.104580
intvolume: ' 91'
language:
- iso: eng
page: '104580'
project:
- _id: '245'
name: 'FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken
für Leistungsschallanwendungen (NEPTUN)'
publication: 'Nonlinear Analysis: Real World Applications'
publication_identifier:
issn:
- 1468-1218
publisher: Elsevier BV
status: public
title: Describing smooth small-data solutions to a quasilinear hyperbolic-parabolic
system by W 1,P energy analysis
type: journal_article
user_id: '11829'
volume: 91
year: '2026'
...
---
_id: '63557'
abstract:
- lang: eng
text: We discretise a recently proposed new Lagrangian approach to optimal control
problems with dynamics described by force-controlled Euler-Lagrange equations
(Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are
in the form of discrete Lagrangians. We show that the discrete necessary conditions
for optimality obtained provide variational integrators for the continuous problem,
akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This
approach paves the way for the use of variational error analysis to derive the
order of convergence of the resulting numerical schemes for both state and costate
variables and to apply discrete Noether’s theorem to compute conserved quantities,
distinguishing itself from existing geometric approaches. We show for a family
of low-order discretisations that the resulting numerical schemes are ‘doubly-symplectic’,
meaning they yield forced symplectic integrators for the underlying controlled
mechanical system and overall symplectic integrators in the state-adjoint space.
Multi-body dynamics examples are solved numerically using the new approach. In
addition, the new approach is compared to standard direct approaches in terms
of computational performance and error convergence. The results highlight the
advantages of the new approach, namely, better performance and convergence behaviour
of state and costate variables consistent with variational error analysis and
automatic preservation of certain first integrals.
author:
- first_name: Michael
full_name: Konopik, Michael
last_name: Konopik
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Rodrigo T.
full_name: Sato Martín de Almagro, Rodrigo T.
last_name: Sato Martín de Almagro
citation:
ama: Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martín de Almagro
RT. On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics. Multibody System Dynamics. Published online 2026.
doi:10.1007/s11044-025-10138-1
apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., & Sato Martín de Almagro,
R. T. (2026). On the variational discretisation of optimal control problems for
unconstrained Lagrangian dynamics. Multibody System Dynamics. https://doi.org/10.1007/s11044-025-10138-1
bibtex: '@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_Sato Martín de Almagro_2026,
title={On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics}, DOI={10.1007/s11044-025-10138-1},
journal={Multibody System Dynamics}, publisher={Springer Science and Business
Media LLC}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya,
Sofya and Ober-Blöbaum, Sina and Sato Martín de Almagro, Rodrigo T.}, year={2026}
}'
chicago: Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum,
and Rodrigo T. Sato Martín de Almagro. “On the Variational Discretisation of Optimal
Control Problems for Unconstrained Lagrangian Dynamics.” Multibody System Dynamics,
2026. https://doi.org/10.1007/s11044-025-10138-1.
ieee: 'M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro,
“On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics,” Multibody System Dynamics, 2026, doi: 10.1007/s11044-025-10138-1.'
mla: Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control
Problems for Unconstrained Lagrangian Dynamics.” Multibody System Dynamics,
Springer Science and Business Media LLC, 2026, doi:10.1007/s11044-025-10138-1.
short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro,
Multibody System Dynamics (2026).
date_created: 2026-01-12T11:33:54Z
date_updated: 2026-01-12T11:35:27Z
department:
- _id: '636'
doi: 10.1007/s11044-025-10138-1
language:
- iso: eng
publication: Multibody System Dynamics
publication_identifier:
issn:
- 1384-5640
- 1573-272X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics
type: journal_article
user_id: '87909'
year: '2026'
...
---
_id: '64871'
author:
- first_name: Praful
full_name: Rahangdale, Praful
id: '103300'
last_name: Rahangdale
citation:
ama: Rahangdale P. Drinfeld correspondence in infinite dimensions. Published online
2026.
apa: Rahangdale, P. (2026). Drinfeld correspondence in infinite dimensions.
bibtex: '@article{Rahangdale_2026, title={Drinfeld correspondence in infinite dimensions},
author={Rahangdale, Praful}, year={2026} }'
chicago: Rahangdale, Praful. “Drinfeld Correspondence in Infinite Dimensions,” 2026.
ieee: P. Rahangdale, “Drinfeld correspondence in infinite dimensions.” 2026.
mla: Rahangdale, Praful. Drinfeld Correspondence in Infinite Dimensions.
2026.
short: P. Rahangdale, (2026).
date_created: 2026-03-09T23:25:29Z
date_updated: 2026-03-09T23:26:46Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
arxiv:
- ' arXiv:2603.04634'
language:
- iso: eng
status: public
title: Drinfeld correspondence in infinite dimensions
type: preprint
user_id: '178'
year: '2026'
...
---
_id: '64979'
abstract:
- lang: eng
text: We investigate homogeneous coupled cell systems with high-dimensional internal
dynamics. In many studies on network dynamics, the analysis is restricted to networks
with one-dimensional internal dynamics. Here, we show how symmetry explains the
relation between dynamical behavior of systems with one-dimensional internal dynamics
and with higher dimensional internal dynamics, when the underlying network topology
is the same. Fundamental networks of homogeneous coupled cell systems (B. Rink,
J. Sanders. Coupled Cell Networks and Their Hidden Symmetries. SIAM J. Math. Anal.
46.2 (2014)) can be expressed in terms of monoid representations, which uniquely
decompose into indecomposable subrepresentations. In the high-dimensional internal
dynamics case, these subrepresentations are isomorphic to multiple copies of those
one computes in the one-dimensional internal dynamics case. This has interesting
implications for possible center subspaces in bifurcation analysis. We describe
the effect on steady state and Hopf bifurcations in l-parameter families of network
vector fields. The main results in that regard are that (1) generic one-parameter
steady state bifurcations are qualitatively independent of the dimension of the
internal dynamics and that, (2) in order to observe all generic l-parameter bifurcations
that may occur for internal dynamics of any dimension, the internal dynamics has
to be at least l-dimensional for steady state bifurcations and 2l-dimensional
for Hopf bifurcations. Furthermore, we illustrate how additional structure in
the network can be exploited to obtain even greater understanding of bifurcation
scenarios in the high-dimensional case beyond qualitative statements about the
collective dynamics. One-parameter steady state bifurcations in feedforward networks
exhibit an unusual amplification in the asymptotic growth rates of individual
cells, when these are one-dimensional (S. von der Gracht, E. Nijholt, B. Rink.
Amplified steady state bifurcations in feedforward networks. Nonlinearity 35.4
(2022)). As another main result, we prove that (3) the same cells exhibit this
amplifying effect with the same growth rates when the internal dynamics is high-dimensional.
article_number: '118196'
article_type: original
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: von der Gracht S, Nijholt E, Rink B. Homogeneous coupled cell systems with
high-dimensional internal dynamics. Chaos, Solitons & Fractals. 2026;208.
doi:10.1016/j.chaos.2026.118196
apa: von der Gracht, S., Nijholt, E., & Rink, B. (2026). Homogeneous coupled
cell systems with high-dimensional internal dynamics. Chaos, Solitons &
Fractals, 208, Article 118196. https://doi.org/10.1016/j.chaos.2026.118196
bibtex: '@article{von der Gracht_Nijholt_Rink_2026, title={Homogeneous coupled cell
systems with high-dimensional internal dynamics}, volume={208}, DOI={10.1016/j.chaos.2026.118196},
number={118196}, journal={Chaos, Solitons & Fractals}, publisher={Elsevier
BV}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2026}
}'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Homogeneous Coupled
Cell Systems with High-Dimensional Internal Dynamics.” Chaos, Solitons &
Fractals 208 (2026). https://doi.org/10.1016/j.chaos.2026.118196.
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Homogeneous coupled cell systems
with high-dimensional internal dynamics,” Chaos, Solitons & Fractals,
vol. 208, Art. no. 118196, 2026, doi: 10.1016/j.chaos.2026.118196.'
mla: von der Gracht, Sören, et al. “Homogeneous Coupled Cell Systems with High-Dimensional
Internal Dynamics.” Chaos, Solitons & Fractals, vol. 208, 118196, Elsevier
BV, 2026, doi:10.1016/j.chaos.2026.118196.
short: S. von der Gracht, E. Nijholt, B. Rink, Chaos, Solitons & Fractals 208
(2026).
date_created: 2026-03-16T08:39:07Z
date_updated: 2026-03-16T08:42:56Z
ddc:
- '510'
department:
- _id: '101'
- _id: '841'
doi: 10.1016/j.chaos.2026.118196
external_id:
arxiv:
- '2510.06740'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2026-03-16T08:40:04Z
date_updated: 2026-03-16T08:40:04Z
file_id: '64980'
file_name: homogeneous-coupled-cell-systems-with-high-dimensional-internal-dynamics.pdf
file_size: 1951746
relation: main_file
success: 1
file_date_updated: 2026-03-16T08:40:04Z
has_accepted_license: '1'
intvolume: ' 208'
keyword:
- Coupled cell systems
- Network dynamics
- Dimension reduction
- Bifurcation theory
- Symmetry
- Monoid representation theory
language:
- iso: eng
publication: Chaos, Solitons & Fractals
publication_identifier:
issn:
- 0960-0779
publication_status: published
publisher: Elsevier BV
status: public
title: Homogeneous coupled cell systems with high-dimensional internal dynamics
type: journal_article
user_id: '97359'
volume: 208
year: '2026'
...
---
_id: '64176'
author:
- first_name: Katrin
full_name: Deutschen, Katrin
id: '64894'
last_name: Deutschen
- first_name: Inga
full_name: Neufeld, Inga
id: '61635'
last_name: Neufeld
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
orcid: 0000-0001-6278-4240
citation:
ama: Deutschen K, Neufeld I, Häsel-Weide U. Lernbegleitung produktiv gestalten.
Mathematische Verstehensprozesse von Kindern anregen. Grundschule aktuell.
2026;(173):10-11.
apa: Deutschen, K., Neufeld, I., & Häsel-Weide, U. (2026). Lernbegleitung produktiv
gestalten. Mathematische Verstehensprozesse von Kindern anregen. Grundschule
aktuell, 173, 10–11.
bibtex: '@article{Deutschen_Neufeld_Häsel-Weide_2026, title={Lernbegleitung produktiv
gestalten. Mathematische Verstehensprozesse von Kindern anregen.}, number={173},
journal={Grundschule aktuell}, author={Deutschen, Katrin and Neufeld, Inga and
Häsel-Weide, Uta}, year={2026}, pages={10–11} }'
chicago: 'Deutschen, Katrin, Inga Neufeld, and Uta Häsel-Weide. “Lernbegleitung
produktiv gestalten. Mathematische Verstehensprozesse von Kindern anregen.” Grundschule
aktuell, no. 173 (2026): 10–11.'
ieee: K. Deutschen, I. Neufeld, and U. Häsel-Weide, “Lernbegleitung produktiv gestalten.
Mathematische Verstehensprozesse von Kindern anregen.,” Grundschule aktuell,
no. 173, pp. 10–11, 2026.
mla: Deutschen, Katrin, et al. “Lernbegleitung produktiv gestalten. Mathematische
Verstehensprozesse von Kindern anregen.” Grundschule aktuell, no. 173,
2026, pp. 10–11.
short: K. Deutschen, I. Neufeld, U. Häsel-Weide, Grundschule aktuell (2026) 10–11.
date_created: 2026-02-16T12:16:29Z
date_updated: 2026-03-17T10:48:56Z
department:
- _id: '543'
issue: '173'
language:
- iso: ger
page: 10-11
publication: Grundschule aktuell
status: public
title: Lernbegleitung produktiv gestalten. Mathematische Verstehensprozesse von Kindern
anregen.
type: journal_article
user_id: '44184'
year: '2026'
...
---
_id: '65026'
author:
- first_name: Inga
full_name: Neufeld, Inga
id: '61635'
last_name: Neufeld
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
orcid: 0000-0001-6278-4240
citation:
ama: 'Neufeld I, Häsel-Weide U. Lernbegleitung in der mathematischen Förderung.
Praktiken von (angehenden) Lehrkräften bei der Förderung arithmetischer Basiskompetenzen.
In: Vogelsang C, Grotegurt L, Bruns J, Riese J, Fechner S, eds. Handlungsorientierung
in Der Ausbildung von Lehrkräften Und Pädagogischen Fachkräften. Konzeptionen
Und Forschungsperspektiven. ; 2026:119-134. doi:10.31244/9783818851057 '
apa: Neufeld, I., & Häsel-Weide, U. (2026). Lernbegleitung in der mathematischen
Förderung. Praktiken von (angehenden) Lehrkräften bei der Förderung arithmetischer
Basiskompetenzen. In C. Vogelsang, L. Grotegurt, J. Bruns, J. Riese, & S.
Fechner (Eds.), Handlungsorientierung in der Ausbildung von Lehrkräften und
pädagogischen Fachkräften. Konzeptionen und Forschungsperspektiven (pp. 119–134).
https://doi.org/10.31244/9783818851057
bibtex: '@inbook{Neufeld_Häsel-Weide_2026, title={ Lernbegleitung in der mathematischen
Förderung. Praktiken von (angehenden) Lehrkräften bei der Förderung arithmetischer
Basiskompetenzen}, DOI={10.31244/9783818851057
}, booktitle={Handlungsorientierung in der Ausbildung von Lehrkräften und
pädagogischen Fachkräften. Konzeptionen und Forschungsperspektiven}, author={Neufeld,
Inga and Häsel-Weide, Uta}, editor={Vogelsang, C. and Grotegurt, L. and Bruns,
J. and Riese, J. and Fechner, S.}, year={2026}, pages={119–134} }'
chicago: Neufeld, Inga, and Uta Häsel-Weide. “ Lernbegleitung in Der Mathematischen
Förderung. Praktiken von (Angehenden) Lehrkräften Bei Der Förderung Arithmetischer
Basiskompetenzen.” In Handlungsorientierung in Der Ausbildung von Lehrkräften
Und Pädagogischen Fachkräften. Konzeptionen Und Forschungsperspektiven, edited
by C. Vogelsang, L. Grotegurt, J. Bruns, J. Riese, and S. Fechner, 119–34, 2026.
https://doi.org/10.31244/9783818851057
.
ieee: I. Neufeld and U. Häsel-Weide, “ Lernbegleitung in der mathematischen Förderung.
Praktiken von (angehenden) Lehrkräften bei der Förderung arithmetischer Basiskompetenzen,”
in Handlungsorientierung in der Ausbildung von Lehrkräften und pädagogischen
Fachkräften. Konzeptionen und Forschungsperspektiven, C. Vogelsang, L. Grotegurt,
J. Bruns, J. Riese, and S. Fechner, Eds. 2026, pp. 119–134.
mla: Neufeld, Inga, and Uta Häsel-Weide. “ Lernbegleitung in Der Mathematischen
Förderung. Praktiken von (Angehenden) Lehrkräften Bei Der Förderung Arithmetischer
Basiskompetenzen.” Handlungsorientierung in Der Ausbildung von Lehrkräften
Und Pädagogischen Fachkräften. Konzeptionen Und Forschungsperspektiven, edited
by C. Vogelsang et al., 2026, pp. 119–34, doi:10.31244/9783818851057 .
short: 'I. Neufeld, U. Häsel-Weide, in: C. Vogelsang, L. Grotegurt, J. Bruns, J.
Riese, S. Fechner (Eds.), Handlungsorientierung in Der Ausbildung von Lehrkräften
Und Pädagogischen Fachkräften. Konzeptionen Und Forschungsperspektiven, 2026,
pp. 119–134.'
date_created: 2026-03-17T10:57:17Z
date_updated: 2026-03-17T11:03:11Z
department:
- _id: '543'
doi: '10.31244/9783818851057 '
editor:
- first_name: C.
full_name: Vogelsang, C.
last_name: Vogelsang
- first_name: L.
full_name: Grotegurt, L.
last_name: Grotegurt
- first_name: J.
full_name: Bruns, J.
last_name: Bruns
- first_name: J.
full_name: Riese, J.
last_name: Riese
- first_name: S.
full_name: Fechner, S.
last_name: Fechner
language:
- iso: eng
page: 119-134
publication: Handlungsorientierung in der Ausbildung von Lehrkräften und pädagogischen
Fachkräften. Konzeptionen und Forschungsperspektiven
status: public
title: ' Lernbegleitung in der mathematischen Förderung. Praktiken von (angehenden)
Lehrkräften bei der Förderung arithmetischer Basiskompetenzen'
type: book_chapter
user_id: '44184'
year: '2026'
...
---
_id: '65036'
author:
- first_name: Tal
full_name: Cohen, Tal
last_name: Cohen
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
- first_name: Gil
full_name: Goffer, Gil
last_name: Goffer
- first_name: Waltraud
full_name: Lederle, Waltraud
last_name: Lederle
citation:
ama: Cohen T, Glöckner H, Goffer G, Lederle W. Compact invariant random subgroups.
Published online 2026.
apa: Cohen, T., Glöckner, H., Goffer, G., & Lederle, W. (2026). Compact invariant
random subgroups.
bibtex: '@article{Cohen_Glöckner_Goffer_Lederle_2026, title={Compact invariant random
subgroups}, author={Cohen, Tal and Glöckner, Helge and Goffer, Gil and Lederle,
Waltraud}, year={2026} }'
chicago: Cohen, Tal, Helge Glöckner, Gil Goffer, and Waltraud Lederle. “Compact
Invariant Random Subgroups,” 2026.
ieee: T. Cohen, H. Glöckner, G. Goffer, and W. Lederle, “Compact invariant random
subgroups.” 2026.
mla: Cohen, Tal, et al. Compact Invariant Random Subgroups. 2026.
short: T. Cohen, H. Glöckner, G. Goffer, W. Lederle, (2026).
date_created: 2026-03-18T02:49:44Z
date_updated: 2026-03-18T02:50:18Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
arxiv:
- 'arXiv:2603.16022 '
language:
- iso: eng
status: public
title: Compact invariant random subgroups
type: preprint
user_id: '178'
year: '2026'
...
---
_id: '57580'
abstract:
- lang: eng
text: We investigate dispersive and Strichartz estimates for the Schrödinger equation
involving the fractional Laplacian in real hyperbolic spaces and their discrete
analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates
on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives.
A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears
on homogeneous trees, due to the triviality of the estimates for small times.
author:
- first_name: Guendalina
full_name: Palmirotta, Guendalina
id: '109467'
last_name: Palmirotta
- first_name: Yannick
full_name: Sire, Yannick
last_name: Sire
- first_name: Jean-Philippe
full_name: Anker, Jean-Philippe
last_name: Anker
citation:
ama: Palmirotta G, Sire Y, Anker J-P. The Schrödinger equation with fractional Laplacian
on hyperbolic spaces and homogeneous trees. Journal of Differential Equations.
Published online 2026. doi:10.1016/j.jde.2025.114065
apa: Palmirotta, G., Sire, Y., & Anker, J.-P. (2026). The Schrödinger equation
with fractional Laplacian on hyperbolic spaces and homogeneous trees. Journal
of Differential Equations. https://doi.org/10.1016/j.jde.2025.114065
bibtex: '@article{Palmirotta_Sire_Anker_2026, title={The Schrödinger equation with
fractional Laplacian on hyperbolic spaces and homogeneous trees}, DOI={10.1016/j.jde.2025.114065},
journal={Journal of Differential Equations}, publisher={Elsevier}, author={Palmirotta,
Guendalina and Sire, Yannick and Anker, Jean-Philippe}, year={2026} }'
chicago: Palmirotta, Guendalina, Yannick Sire, and Jean-Philippe Anker. “The Schrödinger
Equation with Fractional Laplacian on Hyperbolic Spaces and Homogeneous Trees.”
Journal of Differential Equations, 2026. https://doi.org/10.1016/j.jde.2025.114065.
ieee: 'G. Palmirotta, Y. Sire, and J.-P. Anker, “The Schrödinger equation with fractional
Laplacian on hyperbolic spaces and homogeneous trees,” Journal of Differential
Equations, 2026, doi: 10.1016/j.jde.2025.114065.'
mla: Palmirotta, Guendalina, et al. “The Schrödinger Equation with Fractional Laplacian
on Hyperbolic Spaces and Homogeneous Trees.” Journal of Differential Equations,
Elsevier, 2026, doi:10.1016/j.jde.2025.114065.
short: G. Palmirotta, Y. Sire, J.-P. Anker, Journal of Differential Equations (2026).
date_created: 2024-12-04T16:21:38Z
date_updated: 2026-03-30T12:03:37Z
department:
- _id: '10'
- _id: '548'
doi: 10.1016/j.jde.2025.114065
external_id:
arxiv:
- '2412.00780'
keyword:
- Schrödinger equation
- Fractional Laplacian
- Dispersive estimates
- Strichartz estimates
- Real hyperbolic spaces
- Homogeneous trees
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.jde.2025.114065
oa: '1'
project:
- _id: '356'
name: 'TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem
Volumen (Teilprojekt B02)'
publication: Journal of Differential Equations
publication_status: published
publisher: Elsevier
related_material:
link:
- relation: confirmation
url: https://www.sciencedirect.com/science/article/pii/S0022039625010927?via%3Dihub
status: public
title: The Schrödinger equation with fractional Laplacian on hyperbolic spaces and
homogeneous trees
type: journal_article
user_id: '109467'
year: '2026'
...
---
_id: '65232'
abstract:
- lang: eng
text: On finite regular graphs, we construct Patterson-Sullivan distributions associated
with eigenfunctions of the discrete Laplace operator via their boundary values
on the phase space. These distributions are closely related to Wigner distributions
defined via a pseudo-differential calculus on graphs, which appear naturally in
the study of quantum chaos. Using a pairing formula, we prove that Patterson-Sullivan
distributions are also related to invariant Ruelle distributions arising from
the transfer operator of the geodesic flow on the shift space. Both relationships
provide discrete analogues of results for compact hyperbolic surfaces obtained
by Anantharaman-Zelditch and by Guillarmou-Hilgert-Weich.
author:
- first_name: Christian
full_name: Arends, Christian
last_name: Arends
- first_name: Guendalina
full_name: Palmirotta, Guendalina
id: '109467'
last_name: Palmirotta
citation:
ama: Arends C, Palmirotta G. Patterson-Sullivan distributions of finite regular
graphs. arXiv:260309779. Published online 2026.
apa: Arends, C., & Palmirotta, G. (2026). Patterson-Sullivan distributions of
finite regular graphs. In arXiv:2603.09779.
bibtex: '@article{Arends_Palmirotta_2026, title={Patterson-Sullivan distributions
of finite regular graphs}, journal={arXiv:2603.09779}, author={Arends, Christian
and Palmirotta, Guendalina}, year={2026} }'
chicago: Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions
of Finite Regular Graphs.” ArXiv:2603.09779, 2026.
ieee: C. Arends and G. Palmirotta, “Patterson-Sullivan distributions of finite regular
graphs,” arXiv:2603.09779. 2026.
mla: Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions
of Finite Regular Graphs.” ArXiv:2603.09779, 2026.
short: C. Arends, G. Palmirotta, ArXiv:2603.09779 (2026).
date_created: 2026-03-30T11:56:04Z
date_updated: 2026-03-30T12:02:56Z
department:
- _id: '548'
- _id: '10'
- _id: '34'
external_id:
arxiv:
- '2603.09779'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2603.09779
oa: '1'
page: '38'
project:
- _id: '358'
name: 'TRR 358; TP B04: Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden'
publication: arXiv:2603.09779
status: public
title: Patterson-Sullivan distributions of finite regular graphs
type: preprint
user_id: '109467'
year: '2026'
...
---
_id: '64797'
alternative_title:
- Editorial
citation:
ama: Birk L, Loth G, Jotzo L, Binder K, Frischemeier D, eds. 14th IASE Satellite
Conference “Statistics and Data Science Education in STEAM.” International
Association for Statistics Education; 2026. doi:10.52041/iase25.158
apa: Birk, L., Loth, G., Jotzo, L., Binder, K., & Frischemeier, D. (Eds.). (2026).
14th IASE Satellite Conference “Statistics and Data Science Education in STEAM.”
International Association for Statistics Education. https://doi.org/10.52041/iase25.158
bibtex: '@book{Birk_Loth_Jotzo_Binder_Frischemeier_2026, title={14th IASE Satellite
Conference “Statistics and Data Science Education in STEAM”}, DOI={10.52041/iase25.158},
publisher={International Association for Statistics Education}, year={2026} }'
chicago: Birk, Lisa, Gerrit Loth, Luca Jotzo, Karin Binder, and Daniel Frischemeier,
eds. 14th IASE Satellite Conference “Statistics and Data Science Education
in STEAM.” International Association for Statistics Education, 2026. https://doi.org/10.52041/iase25.158.
ieee: L. Birk, G. Loth, L. Jotzo, K. Binder, and D. Frischemeier, Eds., 14th
IASE Satellite Conference “Statistics and Data Science Education in STEAM.”
International Association for Statistics Education, 2026.
mla: Birk, Lisa, et al., editors. 14th IASE Satellite Conference “Statistics
and Data Science Education in STEAM.” International Association for Statistics
Education, 2026, doi:10.52041/iase25.158.
short: L. Birk, G. Loth, L. Jotzo, K. Binder, D. Frischemeier, eds., 14th IASE Satellite
Conference “Statistics and Data Science Education in STEAM,” International Association
for Statistics Education, 2026.
conference:
end_date: 2025-10-02
location: Münster
name: 14th IASE Satellite Conference "Statistics and Data Science Education in STEAM"
start_date: 2025-09-30
date_created: 2026-03-01T13:18:24Z
date_updated: 2026-04-20T16:19:18Z
ddc:
- '370'
department:
- _id: '979'
doi: 10.52041/iase25.158
editor:
- first_name: Lisa
full_name: Birk, Lisa
last_name: Birk
- first_name: Gerrit
full_name: Loth, Gerrit
last_name: Loth
- first_name: Luca
full_name: Jotzo, Luca
id: '88811'
last_name: Jotzo
orcid: 0009-0003-1440-6466
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2026-04-20T16:18:30Z
date_updated: 2026-04-20T16:18:30Z
file_id: '65467'
file_name: Birk, Loth, Jotzo, Binder, Frischemeier 2025 IASE Satellite Editorial.pdf
file_size: 1447145
relation: main_file
success: 1
file_date_updated: 2026-04-20T16:18:30Z
has_accepted_license: '1'
language:
- iso: eng
publication_status: published
publisher: International Association for Statistics Education
status: public
title: 14th IASE Satellite Conference "Statistics and Data Science Education in STEAM"
type: conference_editor
user_id: '83381'
year: '2026'
...
---
_id: '63135'
abstract:
- lang: eng
text: We propose a definition of Coxeter-Dynkin algebras of canonical type generalising
the definition as a path algebra of a quiver. Moreover, we construct two tilting
objects over the squid algebra - one via generalised APR-tilting and one via one-point-extensions
and reflection functors - and identify their endomorphism algebras with the Coxeter-Dynkin
algebra. This shows that our definition gives another representative in the derived
equivalence class of the squid algebra, and hence of the corresponding canonical
algebra. Finally, we have a closer look at the Grothendieck group and the Euler
form which illustrates the connection to Saito's classification of marked extended
affine root systems. On the other hand, this enables us to prove that in the domestic
case Coxeter-Dynkin algebras are of finite representation type.
author:
- first_name: Daniel
full_name: Perniok, Daniel
id: '64242'
last_name: Perniok
citation:
ama: Perniok D. Coxeter-Dynkin algebras of canonical type. Journal of Pure and
Applied Algebra. 2026;230(5). doi:10.1016/j.jpaa.2026.108250
apa: Perniok, D. (2026). Coxeter-Dynkin algebras of canonical type. Journal of
Pure and Applied Algebra, 230(5). https://doi.org/10.1016/j.jpaa.2026.108250
bibtex: '@article{Perniok_2026, title={Coxeter-Dynkin algebras of canonical type},
volume={230}, DOI={10.1016/j.jpaa.2026.108250},
number={5}, journal={Journal of Pure and Applied Algebra}, author={Perniok, Daniel},
year={2026} }'
chicago: Perniok, Daniel. “Coxeter-Dynkin Algebras of Canonical Type.” Journal
of Pure and Applied Algebra 230, no. 5 (2026). https://doi.org/10.1016/j.jpaa.2026.108250.
ieee: 'D. Perniok, “Coxeter-Dynkin algebras of canonical type,” Journal of Pure
and Applied Algebra, vol. 230, no. 5, 2026, doi: 10.1016/j.jpaa.2026.108250.'
mla: Perniok, Daniel. “Coxeter-Dynkin Algebras of Canonical Type.” Journal of
Pure and Applied Algebra, vol. 230, no. 5, 2026, doi:10.1016/j.jpaa.2026.108250.
short: D. Perniok, Journal of Pure and Applied Algebra 230 (2026).
date_created: 2025-12-16T14:20:09Z
date_updated: 2026-04-23T13:00:59Z
department:
- _id: '602'
doi: 10.1016/j.jpaa.2026.108250
external_id:
arxiv:
- '2509.17887'
intvolume: ' 230'
issue: '5'
language:
- iso: eng
publication: Journal of Pure and Applied Algebra
status: public
title: Coxeter-Dynkin algebras of canonical type
type: journal_article
user_id: '64242'
volume: 230
year: '2026'
...
---
_id: '65512'
abstract:
- lang: eng
text: "Zusammenfassung\r\n Risikokompetenz
beinhaltet auch die Fähigkeit, stochastische Informationen, wie beispielsweise
Anteile und Wahrscheinlichkeiten, richtig zu versprachlichen. Aus der Forschung
zu bedingten Wahrscheinlichkeiten und Bayesianischen Aufgaben ist bekannt, dass
die Nutzung von Visualisierungen und sogenannten „natürlichen Häufigkeiten“ (z. B.
„80 von 100 Personen“) statt Wahrscheinlichkeiten in Prozent Verwechslungen beim
Bestimmen von Wahrscheinlichkeiten eindämmen kann. Über den umgekehrten Prozess
– das Versprachlichen von in Visualisierungen dargestellten Informationen – ist
bisher jedoch wenig bekannt, obwohl diese Versprachlichungen auch für den Aufbau
konzeptuellen Wissen als essentiell angesehen werden. In der vorliegenden Studie
wurde daher untersucht, wie gut Schüler:innen die Versprachlichung von in Visualisierungen
dargestellten Anteilen und natürlichen Häufigkeiten gelingt. Dazu wurde mit 138
Realschüler:innen aus der 9. Jahrgangsstufe ein Papier-und-Bleistift-Test durchgeführt,
bei dem den Teilnehmenden nacheinander je ein (vollständig ausgefülltes) Baumdiagramm
und ein Netzdiagramm präsentiert wurde. Die Schüler:innen sollten die inhaltliche
Bedeutung der in der Visualisierung dargestellten stochastischen Informationen
möglichst genau versprachlichen. Fokus der Studie ist der Einfluss der Visualisierung
(Baumdiagramm vs. Netzdiagramm) und des Informationsformats der Visualisierung
(Anteile in Prozent vs. natürliche Häufigkeiten) auf die richtige Versprachlichung
von verschiedenen Relationstypen (Schnittinformationen vs. bedingte Informationen).
Die Ergebnisse zeigen unter anderem, dass Informationen in natürlichen Häufigkeiten
deutlich besser versprachlicht werden als in Prozenten und dass Schnittinformationen
in Prozent besser anhand von Netzdiagrammen als von Baumdiagrammen versprachlicht
werden. Die gewonnenen Erkenntnisse geben überdies Einblicke in typische (fehlerhafte)
Versprachlichungen von Schüler:innen und könnten als Basis für die Entwicklung
eines sprachsensiblen Unterrichts zu Anteilen und Wahrscheinlichkeiten im schulischen
Stochastikunterricht dienen."
article_number: '5'
author:
- first_name: Michael
full_name: Rößner, Michael
id: '87801'
last_name: Rößner
- first_name: Karin
full_name: Binder, Karin
id: '83381'
last_name: Binder
- first_name: Julian
full_name: Albrecht, Julian
last_name: Albrecht
citation:
ama: Rößner M, Binder K, Albrecht J. Versprachlichung von Anteilen und natürlichen
Häufigkeiten anhand von Baum- und Netzdiagrammen Verbalization of proportions
and natural frequencies based on tree diagrams and net diagrams. Journal für
Mathematik-Didaktik. 2026;47(1). doi:10.1007/s13138-026-00267-1
apa: Rößner, M., Binder, K., & Albrecht, J. (2026). Versprachlichung von Anteilen
und natürlichen Häufigkeiten anhand von Baum- und Netzdiagrammen Verbalization
of proportions and natural frequencies based on tree diagrams and net diagrams.
Journal für Mathematik-Didaktik, 47(1), Article 5. https://doi.org/10.1007/s13138-026-00267-1
bibtex: '@article{Rößner_Binder_Albrecht_2026, title={Versprachlichung von Anteilen
und natürlichen Häufigkeiten anhand von Baum- und Netzdiagrammen Verbalization
of proportions and natural frequencies based on tree diagrams and net diagrams},
volume={47}, DOI={10.1007/s13138-026-00267-1},
number={15}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science
and Business Media LLC}, author={Rößner, Michael and Binder, Karin and Albrecht,
Julian}, year={2026} }'
chicago: Rößner, Michael, Karin Binder, and Julian Albrecht. “Versprachlichung von
Anteilen und natürlichen Häufigkeiten anhand von Baum- und Netzdiagrammen Verbalization
of proportions and natural frequencies based on tree diagrams and net diagrams.”
Journal für Mathematik-Didaktik 47, no. 1 (2026). https://doi.org/10.1007/s13138-026-00267-1.
ieee: 'M. Rößner, K. Binder, and J. Albrecht, “Versprachlichung von Anteilen und
natürlichen Häufigkeiten anhand von Baum- und Netzdiagrammen Verbalization of
proportions and natural frequencies based on tree diagrams and net diagrams,”
Journal für Mathematik-Didaktik, vol. 47, no. 1, Art. no. 5, 2026, doi:
10.1007/s13138-026-00267-1.'
mla: Rößner, Michael, et al. “Versprachlichung von Anteilen und natürlichen Häufigkeiten
anhand von Baum- und Netzdiagrammen Verbalization of proportions and natural frequencies
based on tree diagrams and net diagrams.” Journal für Mathematik-Didaktik,
vol. 47, no. 1, 5, Springer Science and Business Media LLC, 2026, doi:10.1007/s13138-026-00267-1.
short: M. Rößner, K. Binder, J. Albrecht, Journal für Mathematik-Didaktik 47 (2026).
date_created: 2026-04-29T08:25:18Z
date_updated: 2026-04-29T08:29:01Z
ddc:
- '370'
department:
- _id: '983'
doi: 10.1007/s13138-026-00267-1
file:
- access_level: closed
content_type: application/pdf
creator: binder
date_created: 2026-04-29T08:28:25Z
date_updated: 2026-04-29T08:28:25Z
file_id: '65514'
file_name: Rößner Binder Albrecht 2026 Versprachlichung von Anteilen und natürlichen
Häufigkeiten anhand von Baum- und Netzdiagrammen.pdf
file_size: 2993685
relation: main_file
success: 1
file_date_updated: 2026-04-29T08:28:25Z
has_accepted_license: '1'
intvolume: ' 47'
issue: '1'
language:
- iso: ger
publication: Journal für Mathematik-Didaktik
publication_identifier:
issn:
- 0173-5322
- 1869-2699
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Versprachlichung von Anteilen und natürlichen Häufigkeiten anhand von Baum-
und Netzdiagrammen Verbalization of proportions and natural frequencies based on
tree diagrams and net diagrams
type: journal_article
user_id: '83381'
volume: 47
year: '2026'
...
---
_id: '61759'
abstract:
- lang: eng
text: 'Intersection distribution and non-hitting index are concepts introduced recently
by Li and Pott as a new way to view the behaviour of a collection of finite field
polynomials. With both an algebraic interpretation via the intersection of a polynomial
with a set of lines, and a geometric interpretation via a (q+1)-set possessing
an internal nucleus, the concepts have proved their usefulness as a new way to
view various long-standing problems, and have applications in areas such as Kakeya
sets. In this paper, by exploiting connections with diverse areas including the
theory of algebraic curves, cyclotomy and the enumeration of irreducible polynomials,
we establish new results and resolve various Open Problems of Li and Pott. We
prove geometric results which shed new light on the relationship between intersection
distribution and projective equivalence of polynomials, and algebraic results
which describe and characterise the degree of Sf - the index of the largest non-zero
entry in the intersection distribution of f. We provide new insights into the
non-hitting spectrum, and show the limitations of the non-hitting index as a tool
for characterisation. Finally, the benefits provided by the connections to other
areas are evidenced in two short new proofs of the cubic case. '
article_number: '102828'
article_type: original
author:
- first_name: Lukas-André Dominik
full_name: Klawuhn, Lukas-André Dominik
id: '91965'
last_name: Klawuhn
orcid: 0009-0009-7736-4885
- first_name: Sophie
full_name: Huczynska, Sophie
last_name: Huczynska
- first_name: Maura
full_name: Paterson, Maura
last_name: Paterson
citation:
ama: 'Klawuhn L-AD, Huczynska S, Paterson M. The Intersection Distribution: New
Results and Perspectives. Finite Fields and Their Applications. 2026;114.
doi:10.1016/j.ffa.2026.102828'
apa: 'Klawuhn, L.-A. D., Huczynska, S., & Paterson, M. (2026). The Intersection
Distribution: New Results and Perspectives. Finite Fields and Their Applications,
114, Article 102828. https://doi.org/10.1016/j.ffa.2026.102828'
bibtex: '@article{Klawuhn_Huczynska_Paterson_2026, title={The Intersection Distribution:
New Results and Perspectives}, volume={114}, DOI={10.1016/j.ffa.2026.102828},
number={102828}, journal={Finite Fields and Their Applications}, publisher={Elsevier},
author={Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura},
year={2026} }'
chicago: 'Klawuhn, Lukas-André Dominik, Sophie Huczynska, and Maura Paterson. “The
Intersection Distribution: New Results and Perspectives.” Finite Fields and
Their Applications 114 (2026). https://doi.org/10.1016/j.ffa.2026.102828.'
ieee: 'L.-A. D. Klawuhn, S. Huczynska, and M. Paterson, “The Intersection Distribution:
New Results and Perspectives,” Finite Fields and Their Applications, vol.
114, Art. no. 102828, 2026, doi: 10.1016/j.ffa.2026.102828.'
mla: 'Klawuhn, Lukas-André Dominik, et al. “The Intersection Distribution: New Results
and Perspectives.” Finite Fields and Their Applications, vol. 114, 102828,
Elsevier, 2026, doi:10.1016/j.ffa.2026.102828.'
short: L.-A.D. Klawuhn, S. Huczynska, M. Paterson, Finite Fields and Their Applications
114 (2026).
date_created: 2025-10-08T14:52:20Z
date_updated: 2026-05-06T15:08:06Z
department:
- _id: '100'
doi: 10.1016/j.ffa.2026.102828
intvolume: ' 114'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S1071579726000390
oa: '1'
publication: Finite Fields and Their Applications
publisher: Elsevier
status: public
title: 'The Intersection Distribution: New Results and Perspectives'
type: journal_article
user_id: '91965'
volume: 114
year: '2026'
...
---
_id: '65631'
abstract:
- lang: eng
text: "Abstract\r\n \r\n Mathematics
textbooks used to be the key resource for students’ self-regulated learning of
mathematics. Primarily due to the digitalization of society, students have potentially
greater access to a wider range of resources such as internet search engines,
learning platforms, educational videos, and Generative AI. This study investigates
the role of the mathematics textbook in comparison to other resources within students’
self-regulated learning practices. Data were collected via a survey of 1101 German
secondary students, representing three school types (\r\n Gymnasium\r\n
\ ,\r\n Gesamtschule\r\n
\ ,\r\n Realschule\r\n
\ ) and three grade levels (6, 9, and upper secondary). The
questionnaire assessed the frequency of resource use in and outside class, reasons
and purposes of use, and resource-based strategies when facing learning challenges
outside class. Results show that the printed mathematics textbook is the most
frequently used resource both in class and outside class. The textbook remains
the most relevant resource for key purposes, such as an aid for doing homework
and preparing for tests and exams. However, its dominance diminishes with age:
in upper secondary school, students increasingly rely on self-created notes, and
online resources. Correlation analyses reveal moderate to strong links between
in-class and out-of-class use, suggesting an association between resource use
and classroom culture. The findings underscore the textbook’s enduring centrality
as a foundational, trusted resource within a dynamic and increasingly diverse
learning environment. This study calls for pedagogical approaches that integrate
textbooks more intentionally within broader resource systems, supporting students’
agency and strategic resource selection in an era of digital abundance.\r\n "
article_type: original
author:
- first_name: Lea
full_name: Stallmeister, Lea
id: '63369'
last_name: Stallmeister
- first_name: Sebastian
full_name: Rezat, Sebastian
id: '31132'
last_name: Rezat
citation:
ama: Stallmeister L, Rezat S. The role of the mathematics textbook in times of resource
diversity. Educational Studies in Mathematics. Published online 2026. doi:10.1007/s10649-026-10511-7
apa: Stallmeister, L., & Rezat, S. (2026). The role of the mathematics textbook
in times of resource diversity. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-026-10511-7
bibtex: '@article{Stallmeister_Rezat_2026, title={The role of the mathematics textbook
in times of resource diversity}, DOI={10.1007/s10649-026-10511-7},
journal={Educational Studies in Mathematics}, publisher={Springer Science and
Business Media LLC}, author={Stallmeister, Lea and Rezat, Sebastian}, year={2026}
}'
chicago: Stallmeister, Lea, and Sebastian Rezat. “The Role of the Mathematics Textbook
in Times of Resource Diversity.” Educational Studies in Mathematics, 2026.
https://doi.org/10.1007/s10649-026-10511-7.
ieee: 'L. Stallmeister and S. Rezat, “The role of the mathematics textbook in times
of resource diversity,” Educational Studies in Mathematics, 2026, doi:
10.1007/s10649-026-10511-7.'
mla: Stallmeister, Lea, and Sebastian Rezat. “The Role of the Mathematics Textbook
in Times of Resource Diversity.” Educational Studies in Mathematics, Springer
Science and Business Media LLC, 2026, doi:10.1007/s10649-026-10511-7.
short: L. Stallmeister, S. Rezat, Educational Studies in Mathematics (2026).
date_created: 2026-05-17T14:32:31Z
date_updated: 2026-05-17T14:40:54Z
ddc:
- '370'
department:
- _id: '360'
doi: 10.1007/s10649-026-10511-7
keyword:
- mathematics
- textbooks
- userstudy
- resources
- digital resources
- students
- secondary eduction
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10649-026-10511-7
oa: '1'
publication: Educational Studies in Mathematics
publication_identifier:
issn:
- 0013-1954
- 1573-0816
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: The role of the mathematics textbook in times of resource diversity
type: journal_article
user_id: '31132'
year: '2026'
...
---
_id: '65630'
abstract:
- lang: eng
text: 'Mathematics textbooks used to be the key resource for students’ self-regulated
learning of mathematics. Primarily due to the digitalization of society, students
have potentially greater access to a wider range of resources such as internet
search engines, learning platforms, educational videos, and Generative AI. This
study investigates the role of the mathematics textbook in comparison to other
resources within students’ self-regulated learning practices. Data were collected
via a survey of 1101 German secondary students, representing three school types
(Gymnasium, Gesamtschule, Realschule) and three grade levels (6, 9, and upper
secondary). The questionnaire assessed the frequency of resource use in and outside
class, reasons and purposes of use, and resource-based strategies when facing
learning challenges outside class. Results show that the printed mathematics textbook
is the most frequently used resource both in class and outside class. The textbook
remains the most relevant resource for key purposes, such as an aid for doing
homework and preparing for tests and exams. However, its dominance diminishes
with age: in upper secondary school, students increasingly rely on self-created
notes, and online resources. Correlation analyses reveal moderate to strong links
between in-class and out-of-class use, suggesting an association between resource
use and classroom culture. The findings underscore the textbook’s enduring centrality
as a foundational, trusted resource within a dynamic and increasingly diverse
learning environment. This study calls for pedagogical approaches that integrate
textbooks more intentionally within broader resource systems, supporting students’
agency and strategic resource selection in an era of digital abundance.'
author:
- first_name: Lea
full_name: Stallmeister, Lea
last_name: Stallmeister
- first_name: Sebastian
full_name: Rezat, Sebastian
last_name: Rezat
citation:
ama: Stallmeister L, Rezat S. The role of the mathematics textbook in times of resource
diversity. Educational Studies in Mathematics. Published online 2026. doi:10.1007/s10649-026-10511-7
apa: Stallmeister, L., & Rezat, S. (2026). The role of the mathematics textbook
in times of resource diversity. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-026-10511-7
bibtex: '@article{Stallmeister_Rezat_2026, title={The role of the mathematics textbook
in times of resource diversity}, DOI={10.1007/s10649-026-10511-7},
journal={Educational Studies in Mathematics}, publisher={Springer}, author={Stallmeister,
Lea and Rezat, Sebastian}, year={2026} }'
chicago: Stallmeister, Lea, and Sebastian Rezat. “The Role of the Mathematics Textbook
in Times of Resource Diversity.” Educational Studies in Mathematics, 2026.
https://doi.org/10.1007/s10649-026-10511-7.
ieee: 'L. Stallmeister and S. Rezat, “The role of the mathematics textbook in times
of resource diversity,” Educational Studies in Mathematics, 2026, doi:
10.1007/s10649-026-10511-7.'
mla: Stallmeister, Lea, and Sebastian Rezat. “The Role of the Mathematics Textbook
in Times of Resource Diversity.” Educational Studies in Mathematics, Springer,
2026, doi:10.1007/s10649-026-10511-7.
short: L. Stallmeister, S. Rezat, Educational Studies in Mathematics (2026).
date_created: 2026-05-16T14:27:57Z
date_updated: 2026-05-16T14:33:38Z
department:
- _id: '98'
doi: 10.1007/s10649-026-10511-7
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10649-026-10511-7
oa: '1'
publication: Educational Studies in Mathematics
publication_status: published
publisher: Springer
status: public
title: The role of the mathematics textbook in times of resource diversity
type: journal_article
user_id: '63369'
year: '2026'
...
---
_id: '65645'
abstract:
- lang: eng
text: Curriculum material is often designed to address content-specific
intended learning goals. However, research indicates that teachers’ personal goals
may cause misalignments between their implementation of curriculum material and
its intended learning goals. This study aims to investigate misalignments between
teachers’ implementation of curriculum material and its intended learning goals
and to which extent they are caused by teachers’ personal goals. To reach this
aim, a qualitative study was conducted to examine how eight vocational school
teachers implemented the learning activity “How many?” suggested for the initial
training of early childhood educators on the topic of set perception and determination
of cardinality. Each participant provided a lesson plan and self-recorded lesson
video on the topic of set perception and determination of cardinality. In addition,
participants were interviewed on how they used the provided curriculum material
for designing their lessons and their potential reasons to adapt or omit “How
many?”. To evaluate their lesson design’s alignment with the activity’s intended
learning goals, the participants' lesson plans were analyzed using qualitative
content analysis. Triangulation of the findings with the interview data revealed
that only one participant fully adopted the intended learning goals as her own
and implemented the activity completely in line with its intended learning goals.
Meanwhile, the remaining participants’ personal goals, such as reducing math anxiety,
seemed to cause misalignments regarding the intended learning goals. The study's
results detail further constraints and affordances to the alignment between teachers’
lesson designs and learning goals intended by curriculum material. It is followed
that it is central to support teachers in adopting intended learning goals as
their personal goals. Otherwise, teachers’ classroom implementation of curriculum
material may not suffice to reach desired outcomes.
article_number: em0883
author:
- first_name: Alix
full_name: Richter, Alix
id: '93186'
last_name: Richter
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
citation:
ama: Richter A, Bruns J. All a question of the goal? Re-tracing (mis)alignments
between teachers’ implementations of curriculum material and intended learning
goals in the context of early childhood educator training in Germany. International
Electronic Journal of Mathematics Education. 2026;21(2). doi:10.29333/iejme/18564
apa: Richter, A., & Bruns, J. (2026). All a question of the goal? Re-tracing
(mis)alignments between teachers’ implementations of curriculum material and intended
learning goals in the context of early childhood educator training in Germany.
International Electronic Journal of Mathematics Education, 21(2),
Article em0883. https://doi.org/10.29333/iejme/18564
bibtex: '@article{Richter_Bruns_2026, title={All a question of the goal? Re-tracing
(mis)alignments between teachers’ implementations of curriculum material and intended
learning goals in the context of early childhood educator training in Germany},
volume={21}, DOI={10.29333/iejme/18564},
number={2em0883}, journal={International Electronic Journal of Mathematics Education},
publisher={Modestum Ltd}, author={Richter, Alix and Bruns, Julia}, year={2026}
}'
chicago: Richter, Alix, and Julia Bruns. “All a Question of the Goal? Re-Tracing
(Mis)Alignments between Teachers’ Implementations of Curriculum Material and Intended
Learning Goals in the Context of Early Childhood Educator Training in Germany.”
International Electronic Journal of Mathematics Education 21, no. 2 (2026).
https://doi.org/10.29333/iejme/18564.
ieee: 'A. Richter and J. Bruns, “All a question of the goal? Re-tracing (mis)alignments
between teachers’ implementations of curriculum material and intended learning
goals in the context of early childhood educator training in Germany,” International
Electronic Journal of Mathematics Education, vol. 21, no. 2, Art. no. em0883,
2026, doi: 10.29333/iejme/18564.'
mla: Richter, Alix, and Julia Bruns. “All a Question of the Goal? Re-Tracing (Mis)Alignments
between Teachers’ Implementations of Curriculum Material and Intended Learning
Goals in the Context of Early Childhood Educator Training in Germany.” International
Electronic Journal of Mathematics Education, vol. 21, no. 2, em0883, Modestum
Ltd, 2026, doi:10.29333/iejme/18564.
short: A. Richter, J. Bruns, International Electronic Journal of Mathematics Education
21 (2026).
date_created: 2026-05-19T13:52:04Z
date_updated: 2026-05-19T14:00:34Z
department:
- _id: '611'
doi: 10.29333/iejme/18564
intvolume: ' 21'
issue: '2'
language:
- iso: eng
publication: International Electronic Journal of Mathematics Education
publication_identifier:
issn:
- 1306-3030
publication_status: published
publisher: Modestum Ltd
status: public
title: All a question of the goal? Re-tracing (mis)alignments between teachers’ implementations
of curriculum material and intended learning goals in the context of early childhood
educator training in Germany
type: journal_article
user_id: '72183'
volume: 21
year: '2026'
...
---
_id: '64211'
author:
- first_name: Vivien
full_name: Wiebe, Vivien
id: '77748'
last_name: Wiebe
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
orcid: 0000-0001-6278-4240
citation:
ama: 'Wiebe V, Häsel-Weide U. Initiating and establishing mathematical practices
of determining and transforming numbers as a foundational skill in fostering mathematics
teaching. In: Mosvold R, Fauskanger J, Ferretti F, Vondrová N, Charles University,
Faculty of Education and ERME, eds. Proceedings of the Nineteenth ERME Topic
Conference: Connecting the Learning of Mathematics Teaching to Practice. ;
2026:122-129.'
apa: 'Wiebe, V., & Häsel-Weide, U. (2026). Initiating and establishing mathematical
practices of determining and transforming numbers as a foundational skill in fostering
mathematics teaching. In R. Mosvold, J. Fauskanger, F. Ferretti, N. Vondrová,
& Charles University, Faculty of Education and ERME (Eds.), Proceedings
of the Nineteenth ERME Topic Conference: Connecting the Learning of Mathematics
Teaching to Practice (pp. 122–129).'
bibtex: '@inproceedings{Wiebe_Häsel-Weide_2026, place={Prag}, title={ Initiating
and establishing mathematical practices of determining and transforming numbers
as a foundational skill in fostering mathematics teaching}, booktitle={Proceedings
of the Nineteenth ERME Topic Conference: Connecting the Learning of Mathematics
Teaching to Practice}, author={Wiebe, Vivien and Häsel-Weide, Uta}, editor={Mosvold,
R. and Fauskanger, J. and Ferretti, F. and Vondrová, N. and Charles University,
Faculty of Education and ERME}, year={2026}, pages={122–129} }'
chicago: 'Wiebe, Vivien, and Uta Häsel-Weide. “ Initiating and Establishing Mathematical
Practices of Determining and Transforming Numbers as a Foundational Skill in Fostering
Mathematics Teaching.” In Proceedings of the Nineteenth ERME Topic Conference:
Connecting the Learning of Mathematics Teaching to Practice, edited by R.
Mosvold, J. Fauskanger, F. Ferretti, N. Vondrová, and Charles University, Faculty
of Education and ERME, 122–29. Prag, 2026.'
ieee: 'V. Wiebe and U. Häsel-Weide, “ Initiating and establishing mathematical practices
of determining and transforming numbers as a foundational skill in fostering mathematics
teaching,” in Proceedings of the Nineteenth ERME Topic Conference: Connecting
the Learning of Mathematics Teaching to Practice, Prag, 2026, pp. 122–129.'
mla: 'Wiebe, Vivien, and Uta Häsel-Weide. “ Initiating and Establishing Mathematical
Practices of Determining and Transforming Numbers as a Foundational Skill in Fostering
Mathematics Teaching.” Proceedings of the Nineteenth ERME Topic Conference:
Connecting the Learning of Mathematics Teaching to Practice, edited by R.
Mosvold et al., 2026, pp. 122–29.'
short: 'V. Wiebe, U. Häsel-Weide, in: R. Mosvold, J. Fauskanger, F. Ferretti, N.
Vondrová, Charles University, Faculty of Education and ERME (Eds.), Proceedings
of the Nineteenth ERME Topic Conference: Connecting the Learning of Mathematics
Teaching to Practice, Prag, 2026, pp. 122–129.'
conference:
location: Prag
name: Nineteenth ERME Topic Conference
corporate_editor:
- Charles University, Faculty of Education and ERME
date_created: 2026-02-18T10:41:23Z
date_updated: 2026-05-26T07:56:19Z
department:
- _id: '543'
editor:
- first_name: R.
full_name: Mosvold, R.
last_name: Mosvold
- first_name: J.
full_name: Fauskanger, J.
last_name: Fauskanger
- first_name: F.
full_name: Ferretti, F.
last_name: Ferretti
- first_name: N.
full_name: Vondrová, N.
last_name: Vondrová
language:
- iso: eng
page: 122-129
place: Prag
publication: 'Proceedings of the Nineteenth ERME Topic Conference: Connecting the
Learning of Mathematics Teaching to Practice'
related_material:
link:
- relation: confirmation
url: https://hal.science/hal-05463964v1
status: public
title: ' Initiating and establishing mathematical practices of determining and transforming
numbers as a foundational skill in fostering mathematics teaching'
type: conference
user_id: '44184'
year: '2026'
...
---
_id: '65745'
abstract:
- lang: eng
text: "Abstract\r\n In this work,
we address the numerical identification of entanglement in dynamical scenarios.
To this end, we consider different programs based on the restriction of the evolution
to the set of separable (i.e., non-entangled) states, together with the discretization
of the space of variables for numerical computations. As a first approach, we
apply linear splitting methods to the restricted, continuous equations of motion
derived from variational principles. We utilize an exchange interaction Hamiltonian
to confirm that the numerical and analytical solutions coincide in the limit of
small time steps. The application to different Hamiltonians shows the wide applicability
of the method to detect dynamical entanglement. To avoid the derivation of analytical
solutions for complex dynamics, we consider variational, numerical integration
schemes, introducing a variational discretization for Lagrangians linear in velocities.
Here, we examine and compare two approaches: one in which the system is discretized
before the restriction is applied, and another in which the restriction precedes
the discretization. We find that the \"first-discretize-then-restrict\" method
becomes numerically unstable, already for the example of an exchange-interaction
Hamiltonian, which can be an important consideration for the numerical analysis
of constrained quantum dynamics. Thereby, broadly applicable numerical tools,
including their limitations, for studying entanglement over time are established
for assessing the entangling power of processes that are used in quantum information
theory."
author:
- first_name: Christian
full_name: Offen, Christian
last_name: Offen
- first_name: Boris
full_name: Wembe, Boris
last_name: Wembe
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Jan
full_name: Sperling, Jan
last_name: Sperling
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
citation:
ama: 'Offen C, Wembe B, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches
to entangling dynamics from variational principles. Journal of Physics A: Mathematical
and Theoretical. Published online 2026. doi:10.1088/1751-8121/ae6d51'
apa: 'Offen, C., Wembe, B., Ares, L., Sperling, J., & Ober-Blöbaum, S. (2026).
Numerical approaches to entangling dynamics from variational principles. Journal
of Physics A: Mathematical and Theoretical. https://doi.org/10.1088/1751-8121/ae6d51'
bibtex: '@article{Offen_Wembe_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical
approaches to entangling dynamics from variational principles}, DOI={10.1088/1751-8121/ae6d51},
journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing},
author={Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and
Ober-Blöbaum, Sina}, year={2026} }'
chicago: 'Offen, Christian, Boris Wembe, Laura Ares, Jan Sperling, and Sina Ober-Blöbaum.
“Numerical Approaches to Entangling Dynamics from Variational Principles.” Journal
of Physics A: Mathematical and Theoretical, 2026. https://doi.org/10.1088/1751-8121/ae6d51.'
ieee: 'C. Offen, B. Wembe, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical
approaches to entangling dynamics from variational principles,” Journal of
Physics A: Mathematical and Theoretical, 2026, doi: 10.1088/1751-8121/ae6d51.'
mla: 'Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from
Variational Principles.” Journal of Physics A: Mathematical and Theoretical,
IOP Publishing, 2026, doi:10.1088/1751-8121/ae6d51.'
short: 'C. Offen, B. Wembe, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal of Physics
A: Mathematical and Theoretical (2026).'
date_created: 2026-06-01T09:36:09Z
date_updated: 2026-06-01T09:36:17Z
department:
- _id: '94'
doi: 10.1088/1751-8121/ae6d51
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
issn:
- 1751-8113
- 1751-8121
publication_status: published
publisher: IOP Publishing
status: public
title: Numerical approaches to entangling dynamics from variational principles
type: journal_article
user_id: '95394'
year: '2026'
...