---
OA_place: publisher
OA_type: gold
_id: '22000'
abstract:
- lang: eng
text: 'Simplicial approximation provides a framework for constructing simplicial
complexes that are homotopy equivalent to a given manifold, provided a CW structure
is explicitly known. However, its conventional implementation quickly becomes
intractable on a computer: barycentric subdivision produces poorly shaped simplices,
and the star condition introduces many vertices. To address these limitations,
this article develops a subdivision scheme based on spherical Delaunay triangulations,
which attains better refinement properties than barycentric subdivisions. Moreover,
the star condition is reframed as two independent problems, one geometric and
the other combinatorial, respectively tackled in the language of locally equiconnected
spaces and the list homomorphism problem, allowing an exponential reduction in
the number of vertices. Via a prototype implementation, we obtain simplicial complexes
homotopy equivalent to Grassmannians and Stiefel manifolds up to dimension 5.'
article_number: 93:1-93:22
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Raphaël
full_name: Tinarrage, Raphaël
id: 40ebcc9d-905f-11ef-bf0a-dc475da8a04e
last_name: Tinarrage
orcid: 0000-0002-1404-1095
citation:
ama: 'Tinarrage R. Simplicial approximation to CW complexes with spherical Delaunay
triangulations. In: 42nd International Symposium on Computational Geometry.
Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPIcs.SoCG.2026.93'
apa: 'Tinarrage, R. (2026). Simplicial approximation to CW complexes with spherical
Delaunay triangulations. In 42nd International Symposium on Computational Geometry
(Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2026.93'
chicago: Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical
Delaunay Triangulations.” In 42nd International Symposium on Computational
Geometry, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.
https://doi.org/10.4230/LIPIcs.SoCG.2026.93.
ieee: R. Tinarrage, “Simplicial approximation to CW complexes with spherical Delaunay
triangulations,” in 42nd International Symposium on Computational Geometry,
New Brunswick, NJ, United States, 2026, vol. 367.
ista: 'Tinarrage R. 2026. Simplicial approximation to CW complexes with spherical
Delaunay triangulations. 42nd International Symposium on Computational Geometry.
SoCG: Symposium on Computational Geometry vol. 367, 93:1-93:22.'
mla: Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical
Delaunay Triangulations.” 42nd International Symposium on Computational Geometry,
vol. 367, 93:1-93:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026,
doi:10.4230/LIPIcs.SoCG.2026.93.
short: R. Tinarrage, in:, 42nd International Symposium on Computational Geometry,
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.
conference:
end_date: 2026-06-05
location: New Brunswick, NJ, United States
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2026-06-02
corr_author: '1'
das_tickbox: '0'
date_created: 2026-06-14T22:01:43Z
date_published: 2026-05-27T00:00:00Z
date_updated: 2026-06-22T11:28:26Z
day: '27'
ddc:
- '500'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2026.93
external_id:
arxiv:
- '2112.07573'
file:
- access_level: open_access
checksum: a468edad327962309688aa78678138da
content_type: application/pdf
creator: dernst
date_created: 2026-06-22T07:53:13Z
date_updated: 2026-06-22T07:53:13Z
file_id: '22111'
file_name: 2026_LIPIcSSoCG_Tinarrage.pdf
file_size: 1436035
relation: main_file
success: 1
file_date_updated: 2026-06-22T07:53:13Z
has_accepted_license: '1'
intvolume: ' 367'
keyword:
- Triangulation of manifolds
- Simplicial approximation
- CW complexes
- Delaunay complexes
- List homomorphism problem
- Topological Data Analysis
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
publication: 42nd International Symposium on Computational Geometry
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959774185'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://doi.org/10.5281/zenodo.19251455
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Simplicial approximation to CW complexes with spherical Delaunay triangulations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 367
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21954'
abstract:
- lang: eng
text: We investigate a framework for train-free MRI segmentation based on Topological
Data Analysis. The pipeline proceeds in three steps, first identifying the whole
object to segment via automatic thresholding, then detecting a distinctive subset
whose topology is known in advance, and finally deducing the various components
of the segmentation. A key ingredient is the extraction of approximate representative
cycles from persistence diagrams, which provides an interpretable link between
persistent features and anatomical components. To clarify the method’s scope,
we make the underlying topological and intensity assumptions explicit, quantify
when they hold on real data, and analyze typical failure modes. We evaluate the
approach on glioblastoma and on fetal cortical plate segmentation, with comparisons
to unsupervised and deep-learning references. By operating without large annotated
datasets, the method is well suited to scarce-data settings and provides an interpretable
baseline and practical initialization for expert refinement or learning-based
pipelines.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).
article_number: '20'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Anton
full_name: François, Anton
last_name: François
- first_name: Raphaël
full_name: Tinarrage, Raphaël
id: 40ebcc9d-905f-11ef-bf0a-dc475da8a04e
last_name: Tinarrage
orcid: 0000-0002-1404-1095
citation:
ama: François A, Tinarrage R. Train-free segmentation in MRI with cubical persistent
homology. Journal of Mathematical Imaging and Vision. 2026;68(3). doi:10.1007/s10851-026-01300-1
apa: François, A., & Tinarrage, R. (2026). Train-free segmentation in MRI with
cubical persistent homology. Journal of Mathematical Imaging and Vision.
Springer Nature. https://doi.org/10.1007/s10851-026-01300-1
chicago: François, Anton, and Raphaël Tinarrage. “Train-Free Segmentation in MRI
with Cubical Persistent Homology.” Journal of Mathematical Imaging and Vision.
Springer Nature, 2026. https://doi.org/10.1007/s10851-026-01300-1.
ieee: A. François and R. Tinarrage, “Train-free segmentation in MRI with cubical
persistent homology,” Journal of Mathematical Imaging and Vision, vol.
68, no. 3. Springer Nature, 2026.
ista: François A, Tinarrage R. 2026. Train-free segmentation in MRI with cubical
persistent homology. Journal of Mathematical Imaging and Vision. 68(3), 20.
mla: François, Anton, and Raphaël Tinarrage. “Train-Free Segmentation in MRI with
Cubical Persistent Homology.” Journal of Mathematical Imaging and Vision,
vol. 68, no. 3, 20, Springer Nature, 2026, doi:10.1007/s10851-026-01300-1.
short: A. François, R. Tinarrage, Journal of Mathematical Imaging and Vision 68
(2026).
corr_author: '1'
date_created: 2026-06-08T08:34:43Z
date_published: 2026-05-25T00:00:00Z
date_updated: 2026-06-10T08:00:52Z
day: '25'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s10851-026-01300-1
external_id:
arxiv:
- '2401.01160'
file:
- access_level: open_access
checksum: 34080653e0f9c6160856a6bbca9b5248
content_type: application/pdf
creator: dernst
date_created: 2026-06-10T07:58:58Z
date_updated: 2026-06-10T07:58:58Z
file_id: '21990'
file_name: 2026_JourMathImaging_Francois.pdf
file_size: 6070434
relation: main_file
success: 1
file_date_updated: 2026-06-10T07:58:58Z
has_accepted_license: '1'
intvolume: ' 68'
issue: '3'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
eissn:
- 1573-7683
issn:
- 0924-9907
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Train-free segmentation in MRI with cubical persistent homology
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19848'
abstract:
- lang: eng
text: 'Binding precedents (súmulas vinculantes) constitute a juridical instrument
unique to the Brazilian legal system and whose objectives include the protection
of the Federal Supreme Court against repetitive demands. Studies of the effectiveness
of these instruments in decreasing the Court’s exposure to similar cases, however,
indicate that they tend to fail in such a direction, with some of the binding
precedents seemingly creating new demands. We empirically assess the legal impact
of five binding precedents, 11, 14, 17, 26, and 37, at the highest Court level
through their effects on the legal subjects they address. This analysis is only
possible through the comparison of the Court’s ruling about the precedents’ themes
before they are created, which means that these decisions should be detected through
techniques of Similar Case Retrieval, which we tackle from the angle of Case Classification.
The contributions of this article are therefore twofold: on the mathematical side,
we compare the use of different methods of Natural Language Processing — TF-IDF,
LSTM, Longformer, and regex — for Case Classification, whereas on the legal side,
we contrast the inefficiency of these binding precedents with a set of hypotheses
that may justify their repeated usage. We observe that the TF-IDF models performed
slightly better than LSTM and Longformer when compared through common metrics;
however, the deep learning models were able to detect certain important legal
events that TF-IDF missed. On the legal side, we argue that the reasons for binding
precedents to fail in responding to repetitive demand are heterogeneous and case-dependent,
making it impossible to single out a specific cause. We identify five main hypotheses,
which are found in different combinations in each of the precedents studied.'
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Raphaël
full_name: Tinarrage, Raphaël
id: 40ebcc9d-905f-11ef-bf0a-dc475da8a04e
last_name: Tinarrage
orcid: 0000-0002-1404-1095
- first_name: Henrique
full_name: Ennes, Henrique
last_name: Ennes
- first_name: Lucas
full_name: Resck, Lucas
last_name: Resck
- first_name: Lucas T.
full_name: Gomes, Lucas T.
last_name: Gomes
- first_name: Jean R.
full_name: Ponciano, Jean R.
last_name: Ponciano
- first_name: Jorge
full_name: Poco, Jorge
last_name: Poco
citation:
ama: Tinarrage R, Ennes H, Resck L, Gomes LT, Ponciano JR, Poco J. Empirical analysis
of binding precedent efficiency in Brazilian Supreme Court via case classification.
Artificial Intelligence and Law. 2025. doi:10.1007/s10506-025-09458-6
apa: Tinarrage, R., Ennes, H., Resck, L., Gomes, L. T., Ponciano, J. R., & Poco,
J. (2025). Empirical analysis of binding precedent efficiency in Brazilian Supreme
Court via case classification. Artificial Intelligence and Law. Springer
Nature. https://doi.org/10.1007/s10506-025-09458-6
chicago: Tinarrage, Raphaël, Henrique Ennes, Lucas Resck, Lucas T. Gomes, Jean R.
Ponciano, and Jorge Poco. “Empirical Analysis of Binding Precedent Efficiency
in Brazilian Supreme Court via Case Classification.” Artificial Intelligence
and Law. Springer Nature, 2025. https://doi.org/10.1007/s10506-025-09458-6.
ieee: R. Tinarrage, H. Ennes, L. Resck, L. T. Gomes, J. R. Ponciano, and J. Poco,
“Empirical analysis of binding precedent efficiency in Brazilian Supreme Court
via case classification,” Artificial Intelligence and Law. Springer Nature,
2025.
ista: Tinarrage R, Ennes H, Resck L, Gomes LT, Ponciano JR, Poco J. 2025. Empirical
analysis of binding precedent efficiency in Brazilian Supreme Court via case classification.
Artificial Intelligence and Law.
mla: Tinarrage, Raphaël, et al. “Empirical Analysis of Binding Precedent Efficiency
in Brazilian Supreme Court via Case Classification.” Artificial Intelligence
and Law, Springer Nature, 2025, doi:10.1007/s10506-025-09458-6.
short: R. Tinarrage, H. Ennes, L. Resck, L.T. Gomes, J.R. Ponciano, J. Poco, Artificial
Intelligence and Law (2025).
corr_author: '1'
date_created: 2025-06-15T22:01:31Z
date_published: 2025-05-26T00:00:00Z
date_updated: 2026-06-18T08:34:38Z
day: '26'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s10506-025-09458-6
external_id:
arxiv:
- '2407.07004'
isi:
- '001494836700001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10506-025-09458-6
month: '05'
oa: 1
oa_version: Published Version
publication: Artificial Intelligence and Law
publication_identifier:
eissn:
- 1572-8382
issn:
- 0924-8463
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Empirical analysis of binding precedent efficiency in Brazilian Supreme Court
via case classification
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20407'
abstract:
- lang: eng
text: We suggest a new algorithm to estimate representations of compact Lie groups
from finite samples of their orbits. Different from other reported techniques,
our method allows the retrieval of the precise representation type as a direct
sum of irreducible representations. Moreover, the knowledge of the representation
type permits the reconstruction of its orbit, which is useful for identifying
the Lie group that generates the action, from a finite list of candidates. Our
algorithm is general for any compact Lie group, but only instantiations for SO(2),
T^d, SU(2), and SO(3) are considered. Theoretical guarantees of robustness in
terms of Hausdorff and Wasserstein distances are derived. Our tools are drawn
from geometric measure theory, computational geometry, and optimization on matrix
manifolds. The algorithm is tested for synthetic data up to dimension 32, as well
as real-life applications in image analysis, harmonic analysis, density estimation,
equivariant neural networks, chemical conformational spaces, and classical mechanics
systems, achieving very accurate results.
acknowledgement: The original work behind this article was developed for HE’s master’s
thesis, supervised by RT. We are mostly in debt to César Camacho, who was HE’s co-advisor,
as well as the members of the thesis jury, Clément Maria, Eduardo Mendes, and Jameson
Cahill, not only for agreeing to evaluate the original work but also for many valuable
inputs. Finally, we are indebted to the anonymous reviewers for their important
feedback and suggestions. Open access funding provided by Institute of Science and
Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Henrique
full_name: Ennes, Henrique
last_name: Ennes
- first_name: Raphaël
full_name: Tinarrage, Raphaël
id: 40ebcc9d-905f-11ef-bf0a-dc475da8a04e
last_name: Tinarrage
orcid: 0000-0002-1404-1095
citation:
ama: 'Ennes H, Tinarrage R. LieDetect: Detection of representation orbits of compact
Lie groups from point clouds. Foundations of Computational Mathematics.
2025. doi:10.1007/s10208-025-09728-4'
apa: 'Ennes, H., & Tinarrage, R. (2025). LieDetect: Detection of representation
orbits of compact Lie groups from point clouds. Foundations of Computational
Mathematics. Springer Nature. https://doi.org/10.1007/s10208-025-09728-4'
chicago: 'Ennes, Henrique, and Raphaël Tinarrage. “LieDetect: Detection of Representation
Orbits of Compact Lie Groups from Point Clouds.” Foundations of Computational
Mathematics. Springer Nature, 2025. https://doi.org/10.1007/s10208-025-09728-4.'
ieee: 'H. Ennes and R. Tinarrage, “LieDetect: Detection of representation orbits
of compact Lie groups from point clouds,” Foundations of Computational Mathematics.
Springer Nature, 2025.'
ista: 'Ennes H, Tinarrage R. 2025. LieDetect: Detection of representation orbits
of compact Lie groups from point clouds. Foundations of Computational Mathematics.'
mla: 'Ennes, Henrique, and Raphaël Tinarrage. “LieDetect: Detection of Representation
Orbits of Compact Lie Groups from Point Clouds.” Foundations of Computational
Mathematics, Springer Nature, 2025, doi:10.1007/s10208-025-09728-4.'
short: H. Ennes, R. Tinarrage, Foundations of Computational Mathematics (2025).
corr_author: '1'
date_created: 2025-09-28T22:01:27Z
date_published: 2025-09-15T00:00:00Z
date_updated: 2026-06-18T18:22:42Z
day: '15'
ddc:
- '500'
department:
- _id: UlWa
doi: 10.1007/s10208-025-09728-4
external_id:
arxiv:
- '2309.03086'
isi:
- '001571197200001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10208-025-09728-4
month: '09'
oa: 1
oa_version: Published Version
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'LieDetect: Detection of representation orbits of compact Lie groups from point
clouds'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...