---
_id: '27426'
abstract:
- lang: eng
text: "Regularization is used in many different areas of optimization when solutions\r\nare
sought which not only minimize a given function, but also possess a certain\r\ndegree
of regularity. Popular applications are image denoising, sparse\r\nregression
and machine learning. Since the choice of the regularization\r\nparameter is crucial
but often difficult, path-following methods are used to\r\napproximate the entire
regularization path, i.e., the set of all possible\r\nsolutions for all regularization
parameters. Due to their nature, the\r\ndevelopment of these methods requires
structural results about the\r\nregularization path. The goal of this article
is to derive these results for\r\nthe case of a smooth objective function which
is penalized by a piecewise\r\ndifferentiable regularization term. We do this
by treating regularization as a\r\nmultiobjective optimization problem. Our results
suggest that even in this\r\ngeneral case, the regularization path is piecewise
smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features
that occur in between\r\nsmooth parts. This is demonstrated in two applications,
namely support-vector\r\nmachines and exact penalty methods."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise
differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741.
doi:10.1007/s10898-022-01223-2
apa: Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization
paths for piecewise differentiable regularization terms. Journal of Global
Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2
bibtex: '@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization
paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2},
number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and
Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }'
chicago: 'Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure
of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal
of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2.'
ieee: 'B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths
for piecewise differentiable regularization terms,” Journal of Global Optimization,
vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.'
mla: Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise
Differentiable Regularization Terms.” Journal of Global Optimization, vol.
85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.
short: B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023)
709–741.
date_created: 2021-11-15T09:24:59Z
date_updated: 2023-03-11T17:16:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10898-022-01223-2
intvolume: ' 85'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf
oa: '1'
page: 709-741
publication: Journal of Global Optimization
status: public
title: On the structure of regularization paths for piecewise differentiable regularization
terms
type: journal_article
user_id: '47427'
volume: 85
year: '2023'
...
---
_id: '31849'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Hoffmann M, Biehler R. Student Teachers ’ Knowledge of Congruence before a
University Course on Geometry. In: Trigueros M, Barquero B, Hochmuth R, Peters
J, eds. Proceedings of the Fourth Conference of the International Network for
Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022).
University of Hannover and INDRUM.; 2023.'
apa: Hoffmann, M., & Biehler, R. (2023). Student Teachers ’ Knowledge of Congruence
before a University Course on Geometry. In M. Trigueros, B. Barquero, R. Hochmuth,
& J. Peters (Eds.), Proceedings of the Fourth Conference of the International
Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October
2022). University of Hannover and INDRUM.
bibtex: '@inproceedings{Hoffmann_Biehler_2023, place={Hannover}, title={Student
Teachers ’ Knowledge of Congruence before a University Course on Geometry}, booktitle={Proceedings
of the Fourth Conference of the International Network for Didactic Research in
University Mathematics (INDRUM 2022, 19-22 October 2022)}, publisher={University
of Hannover and INDRUM.}, author={Hoffmann, Max and Biehler, Rolf}, editor={Trigueros,
Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023}
}'
chicago: 'Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence
before a University Course on Geometry.” In Proceedings of the Fourth Conference
of the International Network for Didactic Research in University Mathematics (INDRUM
2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard
Hochmuth, and Jana Peters. Hannover: University of Hannover and INDRUM., 2023.'
ieee: M. Hoffmann and R. Biehler, “Student Teachers ’ Knowledge of Congruence before
a University Course on Geometry,” in Proceedings of the Fourth Conference of
the International Network for Didactic Research in University Mathematics (INDRUM
2022, 19-22 October 2022), 2023.
mla: Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence
before a University Course on Geometry.” Proceedings of the Fourth Conference
of the International Network for Didactic Research in University Mathematics (INDRUM
2022, 19-22 October 2022), edited by Marı́a Trigueros et al., University of
Hannover and INDRUM., 2023.
short: 'M. Hoffmann, R. Biehler, in: M. Trigueros, B. Barquero, R. Hochmuth, J.
Peters (Eds.), Proceedings of the Fourth Conference of the International Network
for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022),
University of Hannover and INDRUM., Hannover, 2023.'
date_created: 2022-06-12T11:07:34Z
date_updated: 2023-03-25T10:11:35Z
ddc:
- '370'
- '510'
department:
- _id: '97'
editor:
- first_name: Marı́a
full_name: Trigueros, Marı́a
last_name: Trigueros
- first_name: Berta
full_name: Barquero, Berta
last_name: Barquero
- first_name: Reinhard
full_name: Hochmuth, Reinhard
last_name: Hochmuth
- first_name: Jana
full_name: Peters, Jana
last_name: Peters
file:
- access_level: closed
content_type: application/pdf
creator: maxh
date_created: 2023-03-25T10:01:03Z
date_updated: 2023-03-25T10:01:03Z
file_id: '43096'
file_name: HoffmannBiehler2022_indrum_congruence.pdf
file_size: 201942
relation: main_file
success: 1
file_date_updated: 2023-03-25T10:01:03Z
has_accepted_license: '1'
keyword:
- Teaching and learning of specific topics in university mathematics
- Transition to
- across and from university mathematics
- Student Teachers
- Geometry
- Congruence
- Double Discontinuity.
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.univ-reims.fr/INDRUM2022/
oa: '1'
place: Hannover
publication: Proceedings of the Fourth Conference of the International Network for
Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)
publication_status: published
publisher: University of Hannover and INDRUM.
quality_controlled: '1'
status: public
title: Student Teachers ’ Knowledge of Congruence before a University Course on Geometry
type: conference
user_id: '32202'
year: '2023'
...
---
_id: '43097'
author:
- first_name: Ignasio
full_name: Florensa, Ignasio
last_name: Florensa
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
- first_name: Avenilde
full_name: Romo Vázquez, Avenilde
last_name: Romo Vázquez
- first_name: Michelle
full_name: Zandieh, Michelle
last_name: Zandieh
- first_name: Rafael
full_name: Martínez-Planell, Rafael
last_name: Martínez-Planell
citation:
ama: 'Florensa I, Hoffmann M, Romo Vázquez A, Zandieh M, Martínez-Planell R. Innovations
in university teaching based on mathematic education research. In: Trigueros M,
Barquero B, Hochmuth R, Peters J, eds. Proceedings of the Fourth Conference
of the International Network for Didactic Research in University Mathematics (INDRUM
2022, 19-22 October 2022). ; 2023.'
apa: Florensa, I., Hoffmann, M., Romo Vázquez, A., Zandieh, M., & Martínez-Planell,
R. (2023). Innovations in university teaching based on mathematic education research.
In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings
of the Fourth Conference of the International Network for Didactic Research in
University Mathematics (INDRUM 2022, 19-22 October 2022).
bibtex: '@inproceedings{Florensa_Hoffmann_Romo Vázquez_Zandieh_Martínez-Planell_2023,
place={Hannover}, title={Innovations in university teaching based on mathematic
education research}, booktitle={Proceedings of the Fourth Conference of the International
Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October
2022)}, author={Florensa, Ignasio and Hoffmann, Max and Romo Vázquez, Avenilde
and Zandieh, Michelle and Martínez-Planell, Rafael}, editor={Trigueros, Marı́a
and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }'
chicago: Florensa, Ignasio, Max Hoffmann, Avenilde Romo Vázquez, Michelle Zandieh,
and Rafael Martínez-Planell. “Innovations in University Teaching Based on Mathematic
Education Research.” In Proceedings of the Fourth Conference of the International
Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October
2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and
Jana Peters. Hannover, 2023.
ieee: I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, and R. Martínez-Planell,
“Innovations in university teaching based on mathematic education research,” in
Proceedings of the Fourth Conference of the International Network for Didactic
Research in University Mathematics (INDRUM 2022, 19-22 October 2022), 2023.
mla: Florensa, Ignasio, et al. “Innovations in University Teaching Based on Mathematic
Education Research.” Proceedings of the Fourth Conference of the International
Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October
2022), edited by Marı́a Trigueros et al., 2023.
short: 'I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, R. Martínez-Planell,
in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the
Fourth Conference of the International Network for Didactic Research in University
Mathematics (INDRUM 2022, 19-22 October 2022), Hannover, 2023.'
date_created: 2023-03-25T10:09:06Z
date_updated: 2023-03-25T10:10:58Z
ddc:
- '370'
- '510'
department:
- _id: '97'
editor:
- first_name: Marı́a
full_name: Trigueros, Marı́a
last_name: Trigueros
- first_name: Berta
full_name: Barquero, Berta
last_name: Barquero
- first_name: Reinhard
full_name: Hochmuth, Reinhard
last_name: Hochmuth
- first_name: Jana
full_name: Peters, Jana
last_name: Peters
file:
- access_level: closed
content_type: application/pdf
creator: maxh
date_created: 2023-03-25T10:07:54Z
date_updated: 2023-03-25T10:07:54Z
file_id: '43098'
file_name: 2022_FlorensaEtAl_indrum_panelInnovations.pdf
file_size: 642388
relation: main_file
success: 1
file_date_updated: 2023-03-25T10:07:54Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.univ-reims.fr/INDRUM2022/
oa: '1'
place: Hannover
publication: Proceedings of the Fourth Conference of the International Network for
Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)
quality_controlled: '1'
status: public
title: Innovations in university teaching based on mathematic education research
type: conference
user_id: '32202'
year: '2023'
...
---
_id: '43504'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: A.
full_name: Schmitz, A.
last_name: Schmitz
citation:
ama: Biehler R, Liebendörfer M, Schmitz A. Lernvideos und ihre Erstellung - Das
Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für Didaktik der Mathematik.
2023;114:8-12.
apa: Biehler, R., Liebendörfer, M., & Schmitz, A. (2023). Lernvideos und ihre
Erstellung - Das Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für
Didaktik der Mathematik, 114, 8–12.
bibtex: '@article{Biehler_Liebendörfer_Schmitz_2023, title={Lernvideos und ihre
Erstellung - Das Projekt studiVEMINTvideos}, volume={114}, journal={Mitteilungen
der Gesellschaft für Didaktik der Mathematik}, author={Biehler, Rolf and Liebendörfer,
Michael and Schmitz, A.}, year={2023}, pages={8–12} }'
chicago: 'Biehler, Rolf, Michael Liebendörfer, and A. Schmitz. “Lernvideos und ihre
Erstellung - Das Projekt studiVEMINTvideos.” Mitteilungen der Gesellschaft
für Didaktik der Mathematik 114 (2023): 8–12.'
ieee: R. Biehler, M. Liebendörfer, and A. Schmitz, “Lernvideos und ihre Erstellung
- Das Projekt studiVEMINTvideos,” Mitteilungen der Gesellschaft für Didaktik
der Mathematik, vol. 114, pp. 8–12, 2023.
mla: Biehler, Rolf, et al. “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos.”
Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 114, 2023,
pp. 8–12.
short: R. Biehler, M. Liebendörfer, A. Schmitz, Mitteilungen der Gesellschaft für
Didaktik der Mathematik 114 (2023) 8–12.
date_created: 2023-04-14T09:25:18Z
date_updated: 2023-04-14T09:25:27Z
department:
- _id: '34'
- _id: '10'
- _id: '97'
- _id: '363'
intvolume: ' 114'
language:
- iso: ger
page: 8-12
publication: Mitteilungen der Gesellschaft für Didaktik der Mathematik
status: public
title: Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos
type: journal_article
user_id: '37888'
volume: 114
year: '2023'
...
---
_id: '43105'
article_number: '103868'
author:
- first_name: Tobias
full_name: Black, Tobias
id: '23686'
last_name: Black
orcid: 0000-0001-9963-0800
- first_name: Mario
full_name: Fuest, Mario
last_name: Fuest
- first_name: Johannes
full_name: Lankeit, Johannes
last_name: Lankeit
- first_name: Masaaki
full_name: Mizukami, Masaaki
last_name: Mizukami
citation:
ama: 'Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis
systems with spatially heterogeneous logistic source. Nonlinear Analysis: Real
World Applications. 2023;73. doi:10.1016/j.nonrwa.2023.103868'
apa: 'Black, T., Fuest, M., Lankeit, J., & Mizukami, M. (2023). Possible points
of blow-up in chemotaxis systems with spatially heterogeneous logistic source.
Nonlinear Analysis: Real World Applications, 73, Article 103868.
https://doi.org/10.1016/j.nonrwa.2023.103868'
bibtex: '@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up
in chemotaxis systems with spatially heterogeneous logistic source}, volume={73},
DOI={10.1016/j.nonrwa.2023.103868},
number={103868}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier
BV}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami,
Masaaki}, year={2023} }'
chicago: 'Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible
Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic
Source.” Nonlinear Analysis: Real World Applications 73 (2023). https://doi.org/10.1016/j.nonrwa.2023.103868.'
ieee: 'T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up
in chemotaxis systems with spatially heterogeneous logistic source,” Nonlinear
Analysis: Real World Applications, vol. 73, Art. no. 103868, 2023, doi: 10.1016/j.nonrwa.2023.103868.'
mla: 'Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with
Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications,
vol. 73, 103868, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2023.103868.'
short: 'T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World
Applications 73 (2023).'
date_created: 2023-03-27T07:25:58Z
date_updated: 2023-03-27T07:27:03Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1016/j.nonrwa.2023.103868
intvolume: ' 73'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Economics
- Econometrics and Finance
- General Engineering
- General Medicine
- Analysis
language:
- iso: eng
publication: 'Nonlinear Analysis: Real World Applications'
publication_identifier:
issn:
- 1468-1218
publication_status: published
publisher: Elsevier BV
status: public
title: Possible points of blow-up in chemotaxis systems with spatially heterogeneous
logistic source
type: journal_article
user_id: '23686'
volume: 73
year: '2023'
...
---
_id: '43227'
author:
- first_name: Vivian
full_name: Vitt, Vivian
last_name: Vitt
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: 'Vitt V, Häsel-Weide U. Reziprokes Peer-Tutoring zur Förderung von Schüler*innen
mit Schwierigkeiten beim Mathematiklernen. In: Mathematica Didactica, 46.
; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1671'
apa: Vitt, V., & Häsel-Weide, U. (2023). Reziprokes Peer-Tutoring zur Förderung
von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In Mathematica
Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1671
bibtex: '@inbook{Vitt_Häsel-Weide_2023, title={Reziprokes Peer-Tutoring zur Förderung
von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}, DOI={https://doi.org/10.18716/ojs/md/2023.1671},
booktitle={Mathematica Didactica, 46}, author={Vitt, Vivian and Häsel-Weide, Uta},
year={2023} }'
chicago: Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung
von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” In Mathematica
Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1671.
ieee: V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen
mit Schwierigkeiten beim Mathematiklernen.,” in Mathematica Didactica, 46,
2023.
mla: Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung
von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” Mathematica Didactica,
46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1671.
short: 'V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023.'
date_created: 2023-03-30T10:06:24Z
date_updated: 2023-03-30T10:06:53Z
department:
- _id: '543'
doi: https://doi.org/10.18716/ojs/md/2023.1671
language:
- iso: eng
publication: Mathematica Didactica, 46
status: public
title: Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten
beim Mathematiklernen.
type: book_chapter
user_id: '44184'
year: '2023'
...
---
_id: '43226'
author:
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: M.
full_name: Nührenbörger, M.
last_name: Nührenbörger
citation:
ama: 'Häsel-Weide U, Nührenbörger M. Inklusive Praktiken unterrichtsintegrierter
Förderung im Mathematikunterricht. In: Mathematica Didactica, 46. ; 2023.
doi:https://doi.org/10.18716/ojs/md/2023.1670'
apa: Häsel-Weide, U., & Nührenbörger, M. (2023). Inklusive Praktiken unterrichtsintegrierter
Förderung im Mathematikunterricht. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1670
bibtex: '@inbook{Häsel-Weide_Nührenbörger_2023, title={Inklusive Praktiken unterrichtsintegrierter
Förderung im Mathematikunterricht.}, DOI={https://doi.org/10.18716/ojs/md/2023.1670},
booktitle={Mathematica Didactica, 46}, author={Häsel-Weide, Uta and Nührenbörger,
M.}, year={2023} }'
chicago: Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter
Förderung Im Mathematikunterricht.” In Mathematica Didactica, 46, 2023.
https://doi.org/10.18716/ojs/md/2023.1670.
ieee: U. Häsel-Weide and M. Nührenbörger, “Inklusive Praktiken unterrichtsintegrierter
Förderung im Mathematikunterricht.,” in Mathematica Didactica, 46, 2023.
mla: Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter
Förderung Im Mathematikunterricht.” Mathematica Didactica, 46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1670.
short: 'U. Häsel-Weide, M. Nührenbörger, in: Mathematica Didactica, 46, 2023.'
date_created: 2023-03-30T10:04:31Z
date_updated: 2023-03-30T10:06:49Z
department:
- _id: '543'
doi: https://doi.org/10.18716/ojs/md/2023.1670
language:
- iso: eng
publication: Mathematica Didactica, 46
status: public
title: Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.
type: book_chapter
user_id: '44184'
year: '2023'
...
---
_id: '34832'
author:
- first_name: Maximilian
full_name: Hanusch, Maximilian
id: '30905'
last_name: Hanusch
citation:
ama: Hanusch M. The Lax Equation and Weak Regularity of Asymptotic Estimate Lie
Groups. Annals of Global Analysis and Geometry. 2023;63(21). doi:10.1007/s10455-023-09888-y
apa: Hanusch, M. (2023). The Lax Equation and Weak Regularity of Asymptotic Estimate
Lie Groups. Annals of Global Analysis and Geometry, 63(21). https://doi.org/10.1007/s10455-023-09888-y
bibtex: '@article{Hanusch_2023, title={The Lax Equation and Weak Regularity of Asymptotic
Estimate Lie Groups}, volume={63}, DOI={10.1007/s10455-023-09888-y},
number={21}, journal={Annals of Global Analysis and Geometry}, author={Hanusch,
Maximilian}, year={2023} }'
chicago: Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic
Estimate Lie Groups.” Annals of Global Analysis and Geometry 63, no. 21
(2023). https://doi.org/10.1007/s10455-023-09888-y.
ieee: 'M. Hanusch, “The Lax Equation and Weak Regularity of Asymptotic Estimate
Lie Groups,” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023,
doi: 10.1007/s10455-023-09888-y.'
mla: Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate
Lie Groups.” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023,
doi:10.1007/s10455-023-09888-y.
short: M. Hanusch, Annals of Global Analysis and Geometry 63 (2023).
date_created: 2022-12-22T09:45:34Z
date_updated: 2023-04-05T18:18:24Z
department:
- _id: '93'
doi: 10.1007/s10455-023-09888-y
intvolume: ' 63'
issue: '21'
keyword:
- Lax equation
- generalized Baker-Campbell-Dynkin-Hausdorff formula
- regularity of Lie groups
language:
- iso: eng
project:
- _id: '161'
name: 'RegLie: Regularität von Lie-Gruppen und Lie''s Dritter Satz (RegLie)'
publication: Annals of Global Analysis and Geometry
publication_status: published
status: public
title: The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups
type: journal_article
user_id: '30905'
volume: 63
year: '2023'
...
---
_id: '44501'
abstract:
- lang: eng
text: "Extending the notion of maxcut, the study of the frustration index of signed
graphs is one of the basic questions in the theory of signed graphs. Recently
two of the authors initiated the study of critically frustrated signed graphs.
That is a signed graph whose frustration index decreases with the removal of any
edge. The main focus of this study is on critical signed graphs which are not
edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable
signed graphs) and which are not built from other critically frustrated signed
graphs by subdivision. We conjecture that for any given k there are only finitely
many critically k-frustrated signed graphs of this kind.\r\nProviding support
for this conjecture we show that there are only two of such critically 3-frustrated
signed graphs where there is no pair of edge-disjoint negative cycles. Similarly,
we show that there are exactly ten critically 3-frustrated signed planar graphs
that are neither decomposable nor subdivisions of other critically frustrated
signed graphs. We present a method for building non-decomposable critically frustrated
signed graphs based on two given such signed graphs. We also show that the condition
of being non-decomposable is necessary for our conjecture. "
author:
- first_name: Chiara
full_name: Cappello, Chiara
id: '72874'
last_name: Cappello
- first_name: Reza
full_name: Naserasr, Reza
last_name: Naserasr
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Zhouningxin
full_name: Wang, Zhouningxin
last_name: Wang
citation:
ama: Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs.
arXiv:230410243. Published online 2023.
apa: Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically
3-frustrated signed graphs. In arXiv:2304.10243.
bibtex: '@article{Cappello_Naserasr_Steffen_Wang_2023, title={Critically 3-frustrated
signed graphs}, journal={arXiv:2304.10243}, author={Cappello, Chiara and Naserasr,
Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2023} }'
chicago: Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang.
“Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.
ieee: C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated
signed graphs,” arXiv:2304.10243. 2023.
mla: Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243,
2023.
short: C. Cappello, R. Naserasr, E. Steffen, Z. Wang, ArXiv:2304.10243 (2023).
date_created: 2023-05-05T06:52:39Z
date_updated: 2023-05-05T06:53:47Z
department:
- _id: '542'
external_id:
arxiv:
- '2304.10243'
language:
- iso: eng
publication: arXiv:2304.10243
status: public
title: Critically 3-frustrated signed graphs
type: preprint
user_id: '15540'
year: '2023'
...
---
_id: '44857'
abstract:
- lang: eng
text: Ancestral reconstruction is a classic task in comparative genomics. Here,
we study the genome median problem, a related computational problem which, given
a set of three or more genomes, asks to find a new genome that minimizes the sum
of pairwise distances between it and the given genomes. The distance stands for
the amount of evolution observed at the genome level, for which we determine the
minimum number of rearrangement operations necessary to transform one genome into
the other. For almost all rearrangement operations the median problem is NP-hard,
with the exception of the breakpoint median that can be constructed efficiently
for multichromosomal circular and mixed genomes. In this work, we study the median
problem under a restricted rearrangement measure called c4-distance, which is
closely related to the breakpoint and the DCJ distance. We identify tight bounds
and decomposers of the c4-median and develop algorithms for its construction,
one exact ILP-based and three combinatorial heuristics. Subsequently, we perform
experiments on simulated data sets. Our results suggest that the c4-distance is
useful for the study the genome median problem, from theoretical and practical
perspectives.
author:
- first_name: Helmuth O.M.
full_name: Silva, Helmuth O.M.
last_name: Silva
- first_name: Diego P.
full_name: Rubert, Diego P.
last_name: Rubert
- first_name: Eloi
full_name: Araujo, Eloi
last_name: Araujo
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Daniel
full_name: Doerr, Daniel
last_name: Doerr
- first_name: Fábio V.
full_name: Martinez, Fábio V.
last_name: Martinez
citation:
ama: Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms
for the genome median under a restricted measure of rearrangement. RAIRO -
Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052
apa: Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez,
F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement.
RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052
bibtex: '@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms
for the genome median under a restricted measure of rearrangement}, volume={57},
DOI={10.1051/ro/2023052}, number={3},
journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva,
Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr,
Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }'
chicago: 'Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel
Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted
Measure of Rearrangement.” RAIRO - Operations Research 57, no. 3 (2023):
1045–58. https://doi.org/10.1051/ro/2023052.'
ieee: 'H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V.
Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,”
RAIRO - Operations Research, vol. 57, no. 3, pp. 1045–1058, 2023, doi:
10.1051/ro/2023052.'
mla: Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted
Measure of Rearrangement.” RAIRO - Operations Research, vol. 57, no. 3,
EDP Sciences, 2023, pp. 1045–58, doi:10.1051/ro/2023052.
short: H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez,
RAIRO - Operations Research 57 (2023) 1045–1058.
date_created: 2023-05-16T08:48:22Z
date_updated: 2023-05-16T08:49:30Z
department:
- _id: '542'
doi: 10.1051/ro/2023052
intvolume: ' 57'
issue: '3'
keyword:
- Management Science and Operations Research
- Computer Science Applications
- Theoretical Computer Science
language:
- iso: eng
page: 1045-1058
publication: RAIRO - Operations Research
publication_identifier:
issn:
- 0399-0559
- 2804-7303
publication_status: published
publisher: EDP Sciences
status: public
title: Algorithms for the genome median under a restricted measure of rearrangement
type: journal_article
user_id: '15540'
volume: 57
year: '2023'
...