---
OA_place: publisher
_id: '21021'
abstract:
- lang: eng
text: This thesis examines how geometry and topology intersect in the representation,
transformation, and analysis of complex shapes. It considers how continuous manifolds
relate to their discrete analogues, how topological structures evolve in persistence
vineyards, and how tools from topological data analysis can illuminate problems
in mathematical physics. Central to this exploration is the question of how structure,
both geometric and topological, persists or changes under approximation, sampling,
or deformation. The work develops new approaches to skeletal and grid-based representations
of surfaces, reveals the full expressive capacity of persistence vineyards, and
applies topological methods to the longstanding problem of equilibria in electrostatic
fields. These threads braid together into a broader understanding of how topology
and geometry inform one another across theory, computation, and application.
acknowledged_ssus:
- _id: M-Shop
- _id: ScienComp
acknowledgement: "The research presented in this thesis was funded by the DFG Collaborative
Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
citation:
ama: Fillmore CD. Braiding geometry and topology to study shapes and data. 2026.
doi:10.15479/AT-ISTA-21021
apa: Fillmore, C. D. (2026). Braiding geometry and topology to study shapes and
data. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-21021
chicago: Fillmore, Christopher D. “Braiding Geometry and Topology to Study Shapes
and Data.” Institute of Science and Technology Austria, 2026. https://doi.org/10.15479/AT-ISTA-21021.
ieee: C. D. Fillmore, “Braiding geometry and topology to study shapes and data,”
Institute of Science and Technology Austria, 2026.
ista: Fillmore CD. 2026. Braiding geometry and topology to study shapes and data.
Institute of Science and Technology Austria.
mla: Fillmore, Christopher D. Braiding Geometry and Topology to Study Shapes
and Data. Institute of Science and Technology Austria, 2026, doi:10.15479/AT-ISTA-21021.
short: C.D. Fillmore, Braiding Geometry and Topology to Study Shapes and Data, Institute
of Science and Technology Austria, 2026.
corr_author: '1'
date_created: 2026-01-20T21:38:40Z
date_published: 2026-01-21T00:00:00Z
date_updated: 2026-04-07T11:42:49Z
day: '21'
ddc:
- '514'
- '516'
degree_awarded: PhD
department:
- _id: GradSch
- _id: HeEd
- _id: UlWa
doi: 10.15479/AT-ISTA-21021
file:
- access_level: open_access
checksum: 4c0889130095c31d4e5088c5b8dfd607
content_type: application/pdf
creator: cfillmor
date_created: 2026-01-26T19:44:46Z
date_updated: 2026-01-30T11:40:09Z
file_id: '21046'
file_name: 2025_Fillmore_Christopher_Thesis.pdf
file_size: 55954297
relation: main_file
- access_level: closed
checksum: d69afb71d82ab98f856886126ee7303a
content_type: application/x-zip-compressed
creator: cfillmor
date_created: 2026-01-26T19:46:20Z
date_updated: 2026-01-26T19:46:20Z
file_id: '21047'
file_name: Thesis.zip
file_size: 166080788
relation: source_file
file_date_updated: 2026-01-30T11:40:09Z
has_accepted_license: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: '122'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '20260'
relation: part_of_dissertation
status: public
- id: '21050'
relation: part_of_dissertation
status: public
- id: '21051'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
title: Braiding geometry and topology to study shapes and data
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '21766'
abstract:
- lang: eng
text: We provide a new characterisation of the decades old open problem of extending
bilipschitz mappings given on a Euclidean separated net. In particular, this allows
for the complete positive solution of the open problem in dimension two. Along
the way, we develop a set of tools for bilipschitz extensions of mappings between
subsets of Euclidean spaces.
acknowledgement: "The present work developed from a research visit of M.D. to V.K.
at IST Austria, funded by\r\na London Mathematical Society Research in Pairs grant.
This work was done while V.K. was fully funded by the Austria Science Fund (FWF)
[M 3100-N]."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Michael
full_name: Dymond, Michael
last_name: Dymond
- first_name: Vojtech
full_name: Kaluza, Vojtech
id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
last_name: Kaluza
orcid: 0000-0002-2512-8698
citation:
ama: Dymond M, Kaluza V. Extending bilipschitz mappings between separated nets.
Annales Fennici Mathematici. 2026;51(1):237-260. doi:10.54330/afm.181562
apa: Dymond, M., & Kaluza, V. (2026). Extending bilipschitz mappings between
separated nets. Annales Fennici Mathematici. Finnish Mathematical Society.
https://doi.org/10.54330/afm.181562
chicago: Dymond, Michael, and Vojtech Kaluza. “Extending Bilipschitz Mappings between
Separated Nets.” Annales Fennici Mathematici. Finnish Mathematical Society,
2026. https://doi.org/10.54330/afm.181562.
ieee: M. Dymond and V. Kaluza, “Extending bilipschitz mappings between separated
nets,” Annales Fennici Mathematici, vol. 51, no. 1. Finnish Mathematical
Society, pp. 237–260, 2026.
ista: Dymond M, Kaluza V. 2026. Extending bilipschitz mappings between separated
nets. Annales Fennici Mathematici. 51(1), 237–260.
mla: Dymond, Michael, and Vojtech Kaluza. “Extending Bilipschitz Mappings between
Separated Nets.” Annales Fennici Mathematici, vol. 51, no. 1, Finnish Mathematical
Society, 2026, pp. 237–60, doi:10.54330/afm.181562.
short: M. Dymond, V. Kaluza, Annales Fennici Mathematici 51 (2026) 237–260.
corr_author: '1'
date_created: 2026-04-26T22:01:47Z
date_published: 2026-04-17T00:00:00Z
date_updated: 2026-04-28T12:06:00Z
day: '17'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.54330/afm.181562
external_id:
arxiv:
- '2507.22007'
file:
- access_level: open_access
checksum: 442023926a3803d5d6ca8db8dbc4af1c
content_type: application/pdf
creator: dernst
date_created: 2026-04-28T12:03:13Z
date_updated: 2026-04-28T12:03:13Z
file_id: '21772'
file_name: 2026_AnnalesFenniciMath_Dymond.pdf
file_size: 342082
relation: main_file
success: 1
file_date_updated: 2026-04-28T12:03:13Z
has_accepted_license: '1'
intvolume: ' 51'
issue: '1'
keyword:
- Lipschitz
- bilipschitz
- extension
- separated net.
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 237-260
project:
- _id: fc35eaa2-9c52-11eb-aca3-88501ab155e9
grant_number: M03100
name: Spectra and topology of graphs and of simplicial complexes
publication: Annales Fennici Mathematici
publication_identifier:
eissn:
- 2737-114X
issn:
- 2737-0690
publication_status: published
publisher: Finnish Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Extending bilipschitz mappings between separated nets
tmp:
image: /images/cc_by_nc.png
legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode
name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
short: CC BY-NC (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '21704'
abstract:
- lang: eng
text: How functional protein sequences are distributed in sequence space is fundamentally
important for evolutionary theory and protein design, particularly if a large
diversity of protein functions are hidden in evolutionarily unexplored areas of
the sequence space. However, this question is understudied in part because experimental
and computational studies use extant sequences as a starting point to study sequence
space. Here, we study whether extant sequences are representative of the entire
functional sequence space. Across thousands of protein families from vertebrates
and bacteria we calculate the dimensionality and the volume of sequence space
occupied by extant homologs. We find that the observed dimensionality and volume
of extant sequence space are minuscule, many orders of magnitude smaller than
what we estimated using a model of protein evolution. Simulating sequence evolution
we then quantify the impact of phylogeny, selection, and epistasis on restricting
the evolutionary exploration of sequence space. We find that sequence evolution
from a single common ancestor, or a single point of origin in sequence space,
is by far the largest limiting factor that reduces the dimensionality and volume
of extant sequence space. These results indicate that there are vast areas of
functional sequence space that have not been explored in evolution because of
the excessive restrictions on natural exploration of the protein sequence space
imposed by the point of origin effect. We suggest that protein design methods
that rely on extant sequences may be limited in their ability to discover truly
novel functions.
acknowledgement: We thank Olga Kalinina for feedback on our manuscript, Vsevolod Kuksin
for fruitful discussions and Lev Tsarin for participation in the design of our models.
This work was supported by Japan Science and Technology Agency as part of Adopting
Sustainable Partnerships for Innovative Research Ecosystem, Grant No. JPMJAP24B2
(F.A.K. and L.H.I.), and Fonds Zur Förderung der Wissenschaftlichen Forschung Grant
ESP253-B (O.O.B.)
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Lada H.
full_name: Isakova, Lada H.
last_name: Isakova
- first_name: Elizaveta
full_name: Streltsova, Elizaveta
id: 57a170da-dc96-11ea-b7c8-ab3565071bf7
last_name: Streltsova
- first_name: Olga
full_name: Bochkareva, Olga
id: C4558D3C-6102-11E9-A62E-F418E6697425
last_name: Bochkareva
orcid: 0000-0003-1006-6639
- first_name: Peter K.
full_name: Vlasov, Peter K.
last_name: Vlasov
- first_name: Fyodor
full_name: Kondrashov, Fyodor
id: 44FDEF62-F248-11E8-B48F-1D18A9856A87
last_name: Kondrashov
orcid: 0000-0001-8243-4694
citation:
ama: Isakova LH, Streltsova E, Bochkareva O, Vlasov PK, Kondrashov F. Descent from
a common ancestor restricts exploration of protein sequence space. Proceedings
of the National Academy of Sciences. 2026;123(14):e2532018123. doi:10.1073/pnas.2532018123
apa: Isakova, L. H., Streltsova, E., Bochkareva, O., Vlasov, P. K., & Kondrashov,
F. (2026). Descent from a common ancestor restricts exploration of protein sequence
space. Proceedings of the National Academy of Sciences. National Academy
of Sciences. https://doi.org/10.1073/pnas.2532018123
chicago: Isakova, Lada H., Elizaveta Streltsova, Olga Bochkareva, Peter K. Vlasov,
and Fyodor Kondrashov. “Descent from a Common Ancestor Restricts Exploration of
Protein Sequence Space.” Proceedings of the National Academy of Sciences.
National Academy of Sciences, 2026. https://doi.org/10.1073/pnas.2532018123.
ieee: L. H. Isakova, E. Streltsova, O. Bochkareva, P. K. Vlasov, and F. Kondrashov,
“Descent from a common ancestor restricts exploration of protein sequence space,”
Proceedings of the National Academy of Sciences, vol. 123, no. 14. National
Academy of Sciences, p. e2532018123, 2026.
ista: Isakova LH, Streltsova E, Bochkareva O, Vlasov PK, Kondrashov F. 2026. Descent
from a common ancestor restricts exploration of protein sequence space. Proceedings
of the National Academy of Sciences. 123(14), e2532018123.
mla: Isakova, Lada H., et al. “Descent from a Common Ancestor Restricts Exploration
of Protein Sequence Space.” Proceedings of the National Academy of Sciences,
vol. 123, no. 14, National Academy of Sciences, 2026, p. e2532018123, doi:10.1073/pnas.2532018123.
short: L.H. Isakova, E. Streltsova, O. Bochkareva, P.K. Vlasov, F. Kondrashov, Proceedings
of the National Academy of Sciences 123 (2026) e2532018123.
date_created: 2026-04-12T22:01:47Z
date_published: 2026-04-07T00:00:00Z
date_updated: 2026-05-04T06:57:31Z
day: '07'
ddc:
- '570'
department:
- _id: UlWa
doi: 10.1073/pnas.2532018123
external_id:
pmid:
- '41915737'
file:
- access_level: open_access
checksum: 11b7a13a359e302498b2367906093a6b
content_type: application/pdf
creator: dernst
date_created: 2026-05-04T06:46:31Z
date_updated: 2026-05-04T06:46:31Z
file_id: '21783'
file_name: 2026_PNAS_Isakova.pdf
file_size: 3355016
relation: main_file
success: 1
file_date_updated: 2026-05-04T06:46:31Z
has_accepted_license: '1'
intvolume: ' 123'
issue: '14'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: e2532018123
pmid: 1
publication: Proceedings of the National Academy of Sciences
publication_identifier:
eissn:
- 1091-6490
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Descent from a common ancestor restricts exploration of protein sequence space
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 123
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '21778'
abstract:
- lang: eng
text: "We prove that every \U0001D43F-bilipschitz mapping ℤ 2 → ℝ2 canbe extended
to a \U0001D436(\U0001D43F)-bilipschitz mapping ℝ2 → ℝ2,and we provide a polynomial
upper bound for \U0001D436(\U0001D43F).Moreover, we extend the result to every
separated netin ℝ2 instead of ℤ 2, with the upper bound gaininga polynomial dependence
on the separation and netconstants associated to the given separated net. Thisanswers
an Oberwolfach question of Navas from 2015and is also a positive solution of the
two-dimensionalform of a decades old open (in all dimensions at leasttwo) problem
due to Alestalo Trotsenko and Väisälä."
acknowledgement: The authors wish to thank Professor Leonid Kovalev for a valuable
observation on the first versionof this work, which led to improved estimates and
cleaner proofs in Section 6. The present workdeveloped from a research visit of
Michael Dymond to Vojtěch Kaluža at IST Austria, funded by aLondon Mathematical
Society Research in Pairs grant. This work was done whilst Vojtěch Kalužawas fully
funded by the Austria Science Fund (FWF) [M 3100-N].
article_number: e70540
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Michael
full_name: Dymond, Michael
last_name: Dymond
- first_name: Vojtech
full_name: Kaluza, Vojtech
id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
last_name: Kaluza
orcid: 0000-0002-2512-8698
citation:
ama: Dymond M, Kaluza V. Planar bilipschitz extension from separated nets. Journal
of the London Mathematical Society. 2026;113(4). doi:10.1112/jlms.70540
apa: Dymond, M., & Kaluza, V. (2026). Planar bilipschitz extension from separated
nets. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.70540
chicago: Dymond, Michael, and Vojtech Kaluza. “Planar Bilipschitz Extension from
Separated Nets.” Journal of the London Mathematical Society. Wiley, 2026.
https://doi.org/10.1112/jlms.70540.
ieee: M. Dymond and V. Kaluza, “Planar bilipschitz extension from separated nets,”
Journal of the London Mathematical Society, vol. 113, no. 4. Wiley, 2026.
ista: Dymond M, Kaluza V. 2026. Planar bilipschitz extension from separated nets.
Journal of the London Mathematical Society. 113(4), e70540.
mla: Dymond, Michael, and Vojtech Kaluza. “Planar Bilipschitz Extension from Separated
Nets.” Journal of the London Mathematical Society, vol. 113, no. 4, e70540,
Wiley, 2026, doi:10.1112/jlms.70540.
short: M. Dymond, V. Kaluza, Journal of the London Mathematical Society 113 (2026).
date_created: 2026-05-03T22:01:37Z
date_published: 2026-04-01T00:00:00Z
date_updated: 2026-05-07T08:29:18Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1112/jlms.70540
external_id:
arxiv:
- '2410.22294'
file:
- access_level: open_access
checksum: 6dbfc7134f732d17c5c8467843a73e90
content_type: application/pdf
creator: dernst
date_created: 2026-05-07T08:27:43Z
date_updated: 2026-05-07T08:27:43Z
file_id: '21836'
file_name: 2026_JourLondonMathSoc_Dymond.pdf
file_size: 617569
relation: main_file
success: 1
file_date_updated: 2026-05-07T08:27:43Z
has_accepted_license: '1'
intvolume: ' 113'
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: fc35eaa2-9c52-11eb-aca3-88501ab155e9
grant_number: M03100
name: Spectra and topology of graphs and of simplicial complexes
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Planar bilipschitz extension from separated nets
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: 113
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18157'
abstract:
- lang: eng
text: "Interest in sliding block puzzles dates back to the 15-puzzle, seemingly
invented by Noyes Chapman in 1874 (see [23] for an account of the fascinating
history of the puzzle). The game consists of fifteen movable square blocks numbered
\r\n and arranged within a \r\n square box, leaving one empty space (see Figure
1). The task at hand is to start from a given configuration of the numbered blocks
and reach the desired target configuration, where the only allowed move is to
slide a numbered block into an adjacent empty space. This task seemed to be unpredictably
either very easy to accomplish, or completely impossible, and the puzzle turned
into a worldwide sensation in the spring of 1880. A particularly challenging instance,
known as the 13-15-14 puzzle, consisted of initial and target configurations that
differed by a single swap (historically this swap involved the blocks labeled
14 and 15). The craze of this puzzle was such that it consistently made newspaper
headlines in 1880, with an article in the New York Times lamenting that it was
“threatening our free institutions” [23, p. 9]. Various prizes were offered for
anyone who could solve this challenge, beginning with a $25 set of teeth and culminating
with Sam Loyd’s famous $1,000 cash prize."
acknowledgement: Open access funding provided by Copenhagen University.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Florestan R
full_name: Brunck, Florestan R
id: 6ab6e556-f394-11eb-9cf6-9dfb78f00d8d
last_name: Brunck
- first_name: Matthew Alan
full_name: Kwan, Matthew Alan
id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
last_name: Kwan
orcid: 0000-0002-4003-7567
citation:
ama: 'Brunck FR, Kwan MA. Books, Hallways, and social butterflies: A note on sliding
block puzzles. Mathematical Intelligencer. 2025;47:52-65. doi:10.1007/s00283-024-10358-x'
apa: 'Brunck, F. R., & Kwan, M. A. (2025). Books, Hallways, and social butterflies:
A note on sliding block puzzles. Mathematical Intelligencer. Springer Nature.
https://doi.org/10.1007/s00283-024-10358-x'
chicago: 'Brunck, Florestan R, and Matthew Alan Kwan. “Books, Hallways, and Social
Butterflies: A Note on Sliding Block Puzzles.” Mathematical Intelligencer.
Springer Nature, 2025. https://doi.org/10.1007/s00283-024-10358-x.'
ieee: 'F. R. Brunck and M. A. Kwan, “Books, Hallways, and social butterflies: A
note on sliding block puzzles,” Mathematical Intelligencer, vol. 47. Springer
Nature, pp. 52–65, 2025.'
ista: 'Brunck FR, Kwan MA. 2025. Books, Hallways, and social butterflies: A note
on sliding block puzzles. Mathematical Intelligencer. 47, 52–65.'
mla: 'Brunck, Florestan R., and Matthew Alan Kwan. “Books, Hallways, and Social
Butterflies: A Note on Sliding Block Puzzles.” Mathematical Intelligencer,
vol. 47, Springer Nature, 2025, pp. 52–65, doi:10.1007/s00283-024-10358-x.'
short: F.R. Brunck, M.A. Kwan, Mathematical Intelligencer 47 (2025) 52–65.
date_created: 2024-09-29T22:01:38Z
date_published: 2025-03-01T00:00:00Z
date_updated: 2025-05-19T14:00:09Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: MaKw
doi: 10.1007/s00283-024-10358-x
external_id:
arxiv:
- '2303.09459'
isi:
- '001318056000001'
file:
- access_level: open_access
checksum: c932ebe45c460d4a73f5b2dcca643db1
content_type: application/pdf
creator: dernst
date_created: 2025-04-08T11:17:45Z
date_updated: 2025-04-08T11:17:45Z
file_id: '19530'
file_name: 2025_MathIntelligencer_Brunck.pdf
file_size: 1760643
relation: main_file
success: 1
file_date_updated: 2025-04-08T11:17:45Z
has_accepted_license: '1'
intvolume: ' 47'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 52-65
publication: Mathematical Intelligencer
publication_identifier:
issn:
- 0343-6993
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Books, Hallways, and social butterflies: A note on sliding block puzzles'
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: 47
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18580'
abstract:
- lang: eng
text: Motivated by the study of recurrent orbits and dynamics within a Morse set
of a Morse decomposition we introduce the concept of Morse predecomposition of
an isolated invariant set within the setting of both combinatorial and classical
dynamical systems. While Morse decomposition summarizes solely the gradient part
of a dynamical system, the developed generalization extends to the recurrent component
as well. In particular, a chain recurrent set, which is indecomposable in terms
of Morse decomposition, can be represented more finely in the Morse predecomposition
framework. This generalization is achieved by forgoing the poset structure inherent
to Morse decomposition and relaxing the notion of connection between Morse sets
(elements of Morse decomposition) in favor of what we term ’links’. We prove that
a Morse decomposition is a special case of Morse predecomposition indexed by a
poset. Additionally, we show how a Morse predecomposition may be condensed back
to retrieve a Morse decomposition.
acknowledgement: 'M.L. acknowledge support by the Dioscuri program initiated by the
Max Planck Society, jointly managed with the National Science Centre (Poland), and
mutually funded by the Polish Ministry of Science and Higher Education and the German
Federal Ministry of Education and Research. M.L. also acknowledges that this project
has received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Research
of M.M. is partially supported by the Polish National Science Center under Opus
Grant No. 2019/35/B/ST1/00874. The work of K.M. was partially supported by the National
Science Foundation under awards DMS-1839294 and HDR TRIPODS award CCF-1934924, DARPA
contract HR0011-16-2-0033, National Institutes of Health award R01 GM126555, Air
Force Office of Scientific Research under award numbers FA9550-23-1-0011, AWD00010853-MOD002
and MURI FA9550-23-1-0400. K.M. was also supported by a grant from the Simons Foundation.
Open access funding provided by Institute of Science and Technology (IST Austria). '
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Michał
full_name: Lipiński, Michał
id: dfffb474-4317-11ee-8f5c-fe3fc95a425e
last_name: Lipiński
orcid: 0000-0001-9789-9750
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
- first_name: Marian
full_name: Mrozek, Marian
last_name: Mrozek
citation:
ama: Lipiński M, Mischaikow K, Mrozek M. Morse predecomposition of an invariant
set. Qualitative Theory of Dynamical Systems. 2025;24(1). doi:10.1007/s12346-024-01144-3
apa: Lipiński, M., Mischaikow, K., & Mrozek, M. (2025). Morse predecomposition
of an invariant set. Qualitative Theory of Dynamical Systems. Springer
Nature. https://doi.org/10.1007/s12346-024-01144-3
chicago: Lipiński, Michał, Konstantin Mischaikow, and Marian Mrozek. “Morse Predecomposition
of an Invariant Set.” Qualitative Theory of Dynamical Systems. Springer
Nature, 2025. https://doi.org/10.1007/s12346-024-01144-3.
ieee: M. Lipiński, K. Mischaikow, and M. Mrozek, “Morse predecomposition of an invariant
set,” Qualitative Theory of Dynamical Systems, vol. 24, no. 1. Springer
Nature, 2025.
ista: Lipiński M, Mischaikow K, Mrozek M. 2025. Morse predecomposition of an invariant
set. Qualitative Theory of Dynamical Systems. 24(1), 5.
mla: Lipiński, Michał, et al. “Morse Predecomposition of an Invariant Set.” Qualitative
Theory of Dynamical Systems, vol. 24, no. 1, 5, Springer Nature, 2025, doi:10.1007/s12346-024-01144-3.
short: M. Lipiński, K. Mischaikow, M. Mrozek, Qualitative Theory of Dynamical Systems
24 (2025).
corr_author: '1'
date_created: 2024-11-24T23:01:47Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-04-14T07:54:56Z
day: '01'
ddc:
- '514'
- '510'
department:
- _id: UlWa
doi: 10.1007/s12346-024-01144-3
ec_funded: 1
external_id:
arxiv:
- '2312.08013'
isi:
- '001356000500005'
file:
- access_level: open_access
checksum: 73309a57cc798d696caa57b6aa1467d8
content_type: application/pdf
creator: mlipinsk
date_created: 2024-11-28T06:52:38Z
date_updated: 2024-11-28T06:52:38Z
file_id: '18595'
file_name: 2025_predecomposition.pdf
file_size: 1483668
relation: main_file
success: 1
file_date_updated: 2024-11-28T06:52:38Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
issue: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Qualitative Theory of Dynamical Systems
publication_identifier:
eissn:
- 1662-3592
issn:
- 1575-5460
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Morse predecomposition of an invariant set
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: 24
year: '2025'
...
---
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: 2025-09-30T12:52:15Z
day: '26'
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2025'
...
---
OA_place: publisher
OA_type: gold
_id: '20004'
abstract:
- lang: eng
text: "A long-standing conjecture of Eckhoff, Linhart, and Welzl, which would generalize
McMullen’s Upper Bound Theorem for polytopes and refine asymptotic bounds due
to Clarkson, asserts that for k ⩽ ⌊(n-d-2)/2⌋, the complexity of the (⩽ k)-level
in a simple arrangement of n hemispheres in S^d is maximized for arrangements
that are polar duals of neighborly d-polytopes. We prove this conjecture in the
case n = d+4. By Gale duality, this implies the following result about crossing
numbers: In every spherical arc drawing of K_n in S² (given by a set V ⊂ S² of
n unit vectors connected by spherical arcs), the number of crossings is at least
1/4 ⌊n/2⌋ ⌊(n-1)/2⌋ ⌊(n-2)/2⌋ ⌊(n-3)/2⌋. This lower bound is attained if every
open linear halfspace contains at least ⌊(n-2)/2⌋ of the vectors in V.\r\nMoreover,
we determine the space of all linear and affine relations that hold between the
face numbers of levels in simple arrangements of n hemispheres in S^d. This completes
a long line of research on such relations, answers a question posed by Andrzejak
and Welzl in 2003, and generalizes the classical fact that the Dehn-Sommerville
relations generate all linear relations between the face numbers of simple polytopes
(which correspond to the 0-level).\r\nTo prove these results, we introduce the
notion of the g-matrix, which encodes the face numbers of levels in an arrangement
and generalizes the classical g-vector of a polytope."
alternative_title:
- LIPIcs
article_number: '75'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Elizaveta
full_name: Streltsova, Elizaveta
id: 57a170da-dc96-11ea-b7c8-ab3565071bf7
last_name: Streltsova
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Streltsova E, Wagner U. Levels in arrangements: Linear relations, the g-matrix,
and applications to crossing numbers. In: 41st International Symposium on
Computational Geometry. Vol 332. Schloss Dagstuhl - Leibniz-Zentrum für Informatik;
2025. doi:10.4230/LIPIcs.SoCG.2025.75'
apa: 'Streltsova, E., & Wagner, U. (2025). Levels in arrangements: Linear relations,
the g-matrix, and applications to crossing numbers. In 41st International
Symposium on Computational Geometry (Vol. 332). Kanazawa, Japan: Schloss Dagstuhl
- Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2025.75'
chicago: 'Streltsova, Elizaveta, and Uli Wagner. “Levels in Arrangements: Linear
Relations, the g-Matrix, and Applications to Crossing Numbers.” In 41st International
Symposium on Computational Geometry, Vol. 332. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2025. https://doi.org/10.4230/LIPIcs.SoCG.2025.75.'
ieee: 'E. Streltsova and U. Wagner, “Levels in arrangements: Linear relations, the
g-matrix, and applications to crossing numbers,” in 41st International Symposium
on Computational Geometry, Kanazawa, Japan, 2025, vol. 332.'
ista: 'Streltsova E, Wagner U. 2025. Levels in arrangements: Linear relations, the
g-matrix, and applications to crossing numbers. 41st International Symposium
on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs,
vol. 332, 75.'
mla: 'Streltsova, Elizaveta, and Uli Wagner. “Levels in Arrangements: Linear Relations,
the g-Matrix, and Applications to Crossing Numbers.” 41st International Symposium
on Computational Geometry, vol. 332, 75, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2025, doi:10.4230/LIPIcs.SoCG.2025.75.'
short: E. Streltsova, U. Wagner, in:, 41st International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.
conference:
end_date: 2025-06-27
location: Kanazawa, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2025-06-23
corr_author: '1'
date_created: 2025-07-13T22:01:22Z
date_published: 2025-06-20T00:00:00Z
date_updated: 2025-07-14T07:19:19Z
day: '20'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2025.75
external_id:
arxiv:
- '2504.07752'
- '2504.07770'
file:
- access_level: open_access
checksum: a8f7feb1aa3b896e31195841a989d622
content_type: application/pdf
creator: dernst
date_created: 2025-07-14T07:11:04Z
date_updated: 2025-07-14T07:11:04Z
file_id: '20015'
file_name: 2025_LIPIcs.SoCG_Streltsova.pdf
file_size: 952807
relation: main_file
success: 1
file_date_updated: 2025-07-14T07:11:04Z
has_accepted_license: '1'
intvolume: ' 332'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: ' 41st International Symposium on Computational Geometry'
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959773706'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Levels in arrangements: Linear relations, the g-matrix, and applications to
crossing numbers'
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: 332
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: 2025-09-30T14:44:53Z
day: '15'
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '20008'
abstract:
- lang: eng
text: 'We study the complexity of a class of promise graph homomorphism problems.
For a fixed graph H, the H-colouring problem is to decide whether a given graph
has a homomorphism to H. By a result of Hell and Nešetřil, this problem is NP-hard
for any non-bipartite loop-less graph H. Brakensiek and Guruswami [SODA 2018]
conjectured the hardness extends to promise graph homomorphism problems as follows:
fix a pair of non-bipartite loop-less graphs G, H such that there is a homomorphism
from G to H, it is NP-hard to distinguish between graphs that are G-colourable
and those that are not H-colourable. We confirm this conjecture in the cases when
both G and H are 4-colourable. This is a common generalisation of previous results
of Khanna, Linial, and Safra [Comb. 20(3): 393-415 (2000)] and of Krokhin and
Opršal [FOCS 2019]. The result is obtained by combining the algebraic approach
to promise constraint satisfaction with methods of topological combinatorics and
equivariant obstruction theory.'
acknowledgement: This research was supported by the Austrian Science Fund (FWF project
P31312-N35) and by project MSCAfellow5_MUNI (CZ.02.01.01/00/22_010/0003229) financed
by the Ministry of Education, Youth and Sports of the Czech Republic. This project
has also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No 101034413.
article_processing_charge: Yes (in subscription journal)
author:
- first_name: Sergey
full_name: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
orcid: 0000-0002-7840-5062
- first_name: Marek
full_name: Filakovský, Marek
id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87
last_name: Filakovský
- first_name: Jakub
full_name: Opršal, Jakub
id: ec596741-c539-11ec-b829-c79322a91242
last_name: Opršal
orcid: 0000-0003-1245-3456
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Avvakumov S, Filakovský M, Opršal J, Tasinato G, Wagner U. Hardness of 4-colouring
G-colourable graphs. In: Proceedings of the 57th Annual ACM Symposium on Theory
of Computing. Association for Computing Machinery; 2025:72-83. doi:10.1145/3717823.3718154'
apa: 'Avvakumov, S., Filakovský, M., Opršal, J., Tasinato, G., & Wagner, U.
(2025). Hardness of 4-colouring G-colourable graphs. In Proceedings of the
57th Annual ACM Symposium on Theory of Computing (pp. 72–83). Prague, Czechia:
Association for Computing Machinery. https://doi.org/10.1145/3717823.3718154'
chicago: Avvakumov, Sergey, Marek Filakovský, Jakub Opršal, Gianluca Tasinato, and
Uli Wagner. “Hardness of 4-Colouring G-Colourable Graphs.” In Proceedings of
the 57th Annual ACM Symposium on Theory of Computing, 72–83. Association for
Computing Machinery, 2025. https://doi.org/10.1145/3717823.3718154.
ieee: S. Avvakumov, M. Filakovský, J. Opršal, G. Tasinato, and U. Wagner, “Hardness
of 4-colouring G-colourable graphs,” in Proceedings of the 57th Annual ACM
Symposium on Theory of Computing, Prague, Czechia, 2025, pp. 72–83.
ista: 'Avvakumov S, Filakovský M, Opršal J, Tasinato G, Wagner U. 2025. Hardness
of 4-colouring G-colourable graphs. Proceedings of the 57th Annual ACM Symposium
on Theory of Computing. STOC: Symposium on Theory of Computing, 72–83.'
mla: Avvakumov, Sergey, et al. “Hardness of 4-Colouring G-Colourable Graphs.” Proceedings
of the 57th Annual ACM Symposium on Theory of Computing, Association for Computing
Machinery, 2025, pp. 72–83, doi:10.1145/3717823.3718154.
short: S. Avvakumov, M. Filakovský, J. Opršal, G. Tasinato, U. Wagner, in:, Proceedings
of the 57th Annual ACM Symposium on Theory of Computing, Association for Computing
Machinery, 2025, pp. 72–83.
conference:
end_date: 2025-06-27
location: Prague, Czechia
name: 'STOC: Symposium on Theory of Computing'
start_date: 2025-06-23
corr_author: '1'
date_created: 2025-07-13T22:01:23Z
date_published: 2025-06-15T00:00:00Z
date_updated: 2026-04-07T12:36:50Z
day: '15'
ddc:
- '000'
department:
- _id: UlWa
doi: 10.1145/3717823.3718154
ec_funded: 1
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language:
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oa: 1
oa_version: Published Version
page: 72-83
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P31312
name: Algorithms for Embeddings and Homotopy Theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Proceedings of the 57th Annual ACM Symposium on Theory of Computing
publication_identifier:
isbn:
- '9798400715105'
issn:
- 0737-8017
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
record:
- id: '20339'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Hardness of 4-colouring G-colourable graphs
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
year: '2025'
...
---
OA_place: publisher
_id: '20339'
abstract:
- lang: eng
text: "This thesis investigates the interplay between algebraic and topological
methods and combinatorial problems, focusing on approximate graph colourings and
mass partitioning. The unifying theme throughout the dissertation is the use of
continuous maps and symmetry constraints to extract combinatorial insights.\r\n\r\nWe
first explore approximate graph colouring problems and more generally promise
constraint satisfaction problems. Using tools from equivariant topology in combination
with the general theory of polymorphism of a promise constraint satisfaction problem,
we establish hardness for specific types of approximations.\r\n\r\nIn the second
part, we address mass partitioning problems, where one seeks to divide geometric
objects or measures in Euclidean space into parts of equal size using hyperplanes.
Employing techniques from topological combinatorics (configuration space/test
map setup and Borsuk–Ulam type theorems), we both obtain a new equipartitioning
result in the and provide a fast algorithm for computing equipartitioning of point
sets in 3D.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
citation:
ama: 'Tasinato G. Topological methods in discrete geometry and theoretical computer
science : Measure partitioning and constraint satisfaction problems. 2025. doi:10.15479/AT-ISTA-20339'
apa: 'Tasinato, G. (2025). Topological methods in discrete geometry and theoretical
computer science : Measure partitioning and constraint satisfaction problems.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-20339'
chicago: 'Tasinato, Gianluca. “Topological Methods in Discrete Geometry and Theoretical
Computer Science : Measure Partitioning and Constraint Satisfaction Problems.”
Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20339.'
ieee: 'G. Tasinato, “Topological methods in discrete geometry and theoretical computer
science : Measure partitioning and constraint satisfaction problems,” Institute
of Science and Technology Austria, 2025.'
ista: 'Tasinato G. 2025. Topological methods in discrete geometry and theoretical
computer science : Measure partitioning and constraint satisfaction problems.
Institute of Science and Technology Austria.'
mla: 'Tasinato, Gianluca. Topological Methods in Discrete Geometry and Theoretical
Computer Science : Measure Partitioning and Constraint Satisfaction Problems.
Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-20339.'
short: 'G. Tasinato, Topological Methods in Discrete Geometry and Theoretical Computer
Science : Measure Partitioning and Constraint Satisfaction Problems, Institute
of Science and Technology Austria, 2025.'
corr_author: '1'
date_created: 2025-09-10T12:17:55Z
date_published: 2025-09-10T00:00:00Z
date_updated: 2026-04-07T12:36:51Z
day: '10'
ddc:
- '516'
degree_awarded: PhD
department:
- _id: GradSch
- _id: UlWa
doi: 10.15479/AT-ISTA-20339
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date_updated: 2025-09-11T12:24:12Z
file_id: '20344'
file_name: thesis-source.zip
file_size: 2218562
relation: source_file
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checksum: 04b2e016409e52167ce42b0eef839fbf
content_type: application/pdf
creator: gtasinat
date_created: 2025-09-11T12:26:14Z
date_updated: 2025-09-11T12:26:14Z
file_id: '20345'
file_name: 2025_Tasinato_Gianluca_Thesis.pdf
file_size: 10071982
relation: main_file
success: 1
file_date_updated: 2025-09-11T12:26:14Z
has_accepted_license: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '106'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '20008'
relation: part_of_dissertation
status: public
- id: '15168'
relation: part_of_dissertation
status: public
- id: '19860'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
title: 'Topological methods in discrete geometry and theoretical computer science
: Measure partitioning and constraint satisfaction problems'
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19860'
abstract:
- lang: eng
text: "An eight-partition of a finite set of points (respectively, of a continuous
mass distribution) in R^3\r\n consists of three planes that divide the space into
8 octants, such that each open octant contains at most 1/8 of the points (respectively,
of the mass). In 1966, Hadwiger showed that any mass distribution in R^3 admits
an eight-partition; moreover, one can prescribe the normal direction of one of
the three planes. The analogous result for finite point sets follows by a standard
limit argument. We prove the following variant of this result: any mass distribution
(or point set) in R^3 admits an eight-partition for which the intersection of
two of the planes is a line with a prescribed direction. Moreover, we present
an efficient algorithm for calculating an eight-partition of a set of n points
in R^3 (with prescribed normal direction of one of the planes) in time O(n^7/3).
A preliminary version of this work appeared in SoCG’24 (Aronov et al., 40th International
Symposium on Computational Geometry, 2024)."
acknowledgement: BA and AB would like to thank William Steiger for insightful initial
discussions of the problems addressed in this work. Open Access funding enabled
and organized by CAUL and its Member Institutions.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Boris
full_name: Aronov, Boris
last_name: Aronov
- first_name: Abdul
full_name: Basit, Abdul
last_name: Basit
- first_name: Indu
full_name: Ramesh, Indu
last_name: Ramesh
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Aronov B, Basit A, Ramesh I, Tasinato G, Wagner U. Eight-partitioning points
in 3D, and efficiently too. Discrete & Computational Geometry. 2025.
doi:10.1007/s00454-025-00739-0
apa: Aronov, B., Basit, A., Ramesh, I., Tasinato, G., & Wagner, U. (2025). Eight-partitioning
points in 3D, and efficiently too. Discrete & Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-025-00739-0
chicago: Aronov, Boris, Abdul Basit, Indu Ramesh, Gianluca Tasinato, and Uli Wagner.
“Eight-Partitioning Points in 3D, and Efficiently Too.” Discrete & Computational
Geometry. Springer Nature, 2025. https://doi.org/10.1007/s00454-025-00739-0.
ieee: B. Aronov, A. Basit, I. Ramesh, G. Tasinato, and U. Wagner, “Eight-partitioning
points in 3D, and efficiently too,” Discrete & Computational Geometry.
Springer Nature, 2025.
ista: Aronov B, Basit A, Ramesh I, Tasinato G, Wagner U. 2025. Eight-partitioning
points in 3D, and efficiently too. Discrete & Computational Geometry.
mla: Aronov, Boris, et al. “Eight-Partitioning Points in 3D, and Efficiently Too.”
Discrete & Computational Geometry, Springer Nature, 2025, doi:10.1007/s00454-025-00739-0.
short: B. Aronov, A. Basit, I. Ramesh, G. Tasinato, U. Wagner, Discrete & Computational
Geometry (2025).
date_created: 2025-06-22T22:02:07Z
date_published: 2025-06-12T00:00:00Z
date_updated: 2026-04-07T12:36:50Z
day: '12'
department:
- _id: UlWa
doi: 10.1007/s00454-025-00739-0
external_id:
arxiv:
- '2403.02627'
isi:
- '001506904300001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00454-025-00739-0
month: '06'
oa: 1
oa_version: Published Version
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1007/s00454-025-00759-w
record:
- id: '18917'
relation: earlier_version
status: public
- id: '20339'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Eight-partitioning points in 3D, and efficiently too
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '13974'
abstract:
- lang: eng
text: The Tverberg theorem is one of the cornerstones of discrete geometry. It states
that, given a set X of at least (d+1)(r−1)+1 points in Rd, one can find a partition
X=X1∪⋯∪Xr of X, such that the convex hulls of the Xi, i=1,…,r, all share a common
point. In this paper, we prove a trengthening of this theorem that guarantees
a partition which, in addition to the above, has the property that the boundaries
of full-dimensional convex hulls have pairwise nonempty intersections. Possible
generalizations and algorithmic aspects are also discussed. As a concrete application,
we show that any n points in the plane in general position span ⌊n/3⌋ vertex-disjoint
triangles that are pairwise crossing, meaning that their boundaries have pairwise
nonempty intersections; this number is clearly best possible. A previous result
of Álvarez-Rebollar et al. guarantees ⌊n/6⌋pairwise crossing triangles. Our result
generalizes to a result about simplices in Rd, d≥2.
acknowledgement: "Part of the research leading to this paper was done during the 16th
Gremo Workshop on Open Problems (GWOP), Waltensburg, Switzerland, June 12–16, 2018.
We thank Patrick Schnider for suggesting the problem, and Stefan Felsner, Malte
Milatz, and Emo Welzl for fruitful discussions during the workshop. We also thank
Stefan Felsner and Manfred Scheucher for finding, communicating the example from
Sect. 3.3, and the kind permission to include their visualization of the point set.
We thank Dömötör Pálvölgyi, the SoCG reviewers, and DCG reviewers for various helpful
comments.\r\nR. Fulek gratefully acknowledges support from Austrian Science Fund
(FWF), Project M2281-N35. A. Kupavskii was supported by the Advanced Postdoc.Mobility
Grant no. P300P2_177839 of the Swiss National Science Foundation. Research by P.
Valtr was supported by the Grant no. 18-19158 S of the Czech Science Foundation
(GAČR)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Radoslav
full_name: Fulek, Radoslav
id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87
last_name: Fulek
orcid: 0000-0001-8485-1774
- first_name: Bernd
full_name: Gärtner, Bernd
last_name: Gärtner
- first_name: Andrey
full_name: Kupavskii, Andrey
last_name: Kupavskii
- first_name: Pavel
full_name: Valtr, Pavel
last_name: Valtr
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem.
Discrete and Computational Geometry. 2024;72:831-848. doi:10.1007/s00454-023-00532-x
apa: Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., & Wagner, U. (2024).
The crossing Tverberg theorem. Discrete and Computational Geometry. Springer
Nature. https://doi.org/10.1007/s00454-023-00532-x
chicago: Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli
Wagner. “The Crossing Tverberg Theorem.” Discrete and Computational Geometry.
Springer Nature, 2024. https://doi.org/10.1007/s00454-023-00532-x.
ieee: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing
Tverberg theorem,” Discrete and Computational Geometry, vol. 72. Springer
Nature, pp. 831–848, 2024.
ista: Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2024. The crossing Tverberg
theorem. Discrete and Computational Geometry. 72, 831–848.
mla: Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” Discrete and Computational
Geometry, vol. 72, Springer Nature, 2024, pp. 831–48, doi:10.1007/s00454-023-00532-x.
short: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, Discrete and Computational
Geometry 72 (2024) 831–848.
date_created: 2023-08-06T22:01:12Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2025-04-14T13:52:36Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/s00454-023-00532-x
external_id:
arxiv:
- '1812.04911'
isi:
- '001038546500001'
intvolume: ' 72'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1812.04911
month: '09'
oa: 1
oa_version: Preprint
page: 831-848
project:
- _id: 261FA626-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02281
name: Eliminating intersections in drawings of graphs
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '6647'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The crossing Tverberg theorem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 72
year: '2024'
...
---
_id: '14660'
abstract:
- lang: eng
text: "The classical Steinitz theorem states that if the origin belongs to the interior
of the convex hull of a set \U0001D446⊂ℝ\U0001D451, then there are at most 2\U0001D451
points of \U0001D446 whose convex hull contains the origin in the interior. Bárány,
Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem.
Let \U0001D444 be a convex polytope in ℝ\U0001D451 containing the standard Euclidean
unit ball \U0001D401\U0001D451. Then there exist at most 2\U0001D451 vertices
of \U0001D444 whose convex hull \U0001D444′ satisfies \U0001D45F\U0001D401\U0001D451⊂\U0001D444′
with \U0001D45F⩾\U0001D451−2\U0001D451. They conjectured that \U0001D45F⩾\U0001D450\U0001D451−1∕2
holds with a universal constant \U0001D450>0. We prove \U0001D45F⩾15\U0001D4512,
the first polynomial lower bound on \U0001D45F. Furthermore, we show that \U0001D45F
is not greater than 2/√\U0001D451."
acknowledgement: M.N. was supported by the János Bolyai Scholarship of the Hungarian
Academy of Sciences aswell as the National Research, Development and Innovation
Fund (NRDI) grants K119670 andK131529, and the ÚNKP-22-5 New National Excellence
Program of the Ministry for Innovationand Technology from the source of the NRDI
as well as the ELTE TKP 2021-NKTA-62 fundingscheme
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Márton
full_name: Naszódi, Márton
last_name: Naszódi
citation:
ama: 'Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. Bulletin
of the London Mathematical Society. 2024;56(2):796-802. doi:10.1112/blms.12965'
apa: 'Ivanov, G., & Naszódi, M. (2024). Quantitative Steinitz theorem: A polynomial
bound. Bulletin of the London Mathematical Society. London Mathematical
Society. https://doi.org/10.1112/blms.12965'
chicago: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A
Polynomial Bound.” Bulletin of the London Mathematical Society. London
Mathematical Society, 2024. https://doi.org/10.1112/blms.12965.'
ieee: 'G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,”
Bulletin of the London Mathematical Society, vol. 56, no. 2. London Mathematical
Society, pp. 796–802, 2024.'
ista: 'Ivanov G, Naszódi M. 2024. Quantitative Steinitz theorem: A polynomial bound.
Bulletin of the London Mathematical Society. 56(2), 796–802.'
mla: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial
Bound.” Bulletin of the London Mathematical Society, vol. 56, no. 2, London
Mathematical Society, 2024, pp. 796–802, doi:10.1112/blms.12965.'
short: G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society 56 (2024)
796–802.
corr_author: '1'
date_created: 2023-12-10T23:00:58Z
date_published: 2024-02-01T00:00:00Z
date_updated: 2025-09-04T11:31:49Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1112/blms.12965
external_id:
arxiv:
- '2212.04308'
isi:
- '001113277100001'
file:
- access_level: open_access
checksum: 30ea0694757bc668cf7cd15ae357b35e
content_type: application/pdf
creator: dernst
date_created: 2024-07-16T10:35:10Z
date_updated: 2024-07-16T10:35:10Z
file_id: '17259'
file_name: 2024_BulletinLondonMathSoc_Ivanov.pdf
file_size: 111756
relation: main_file
success: 1
file_date_updated: 2024-07-16T10:35:10Z
has_accepted_license: '1'
intvolume: ' 56'
isi: 1
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 796-802
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- 1469-2120
issn:
- 0024-6093
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Quantitative Steinitz theorem: A polynomial bound'
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
year: '2024'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '18604'
abstract:
- lang: eng
text: 'A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an arrangement
by inserting a single additional curve. This turns out to be NP-hard; however,
it becomes tractable when the number of popular faces is small: We present a randomized
FPT-time algorithm where the parameter is the number of popular faces.'
acknowledgement: "This work was initiated at the 16th European Research Week on Geometric
Graphs in Strobl in 2019. A.W. has been supported by the Austrian Science Fund (FWF):
W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035]
and by the NWO Gravitation project NETWORKS under grant no. 024.002.003. Part of
the work was done while A.W. was emplyed at Graz University of Technology. Preliminary
versions of this work have been presented at the 38th European Workshop on Computational
Geometry (EuroCG\r\n2022) in Perugia [10] and at the 31st International Symposium
on Graph Drawing and Network Visualization (GD 2023) in Isola delle Femmine [11]."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Phoebe
full_name: De Nooijer, Phoebe
last_name: De Nooijer
- first_name: Soeren
full_name: Terziadis, Soeren
last_name: Terziadis
- first_name: Alexandra
full_name: Weinberger, Alexandra
last_name: Weinberger
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tamara
full_name: Mchedlidze, Tamara
last_name: Mchedlidze
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve
arrangements. Journal of Graph Algorithms and Applications. 2024;28(2):47-82.
doi:10.7155/jgaa.v28i2.2988
apa: De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T.,
Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements.
Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.v28i2.2988
chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová,
Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in
Curve Arrangements.” Journal of Graph Algorithms and Applications. Brown
University, 2024. https://doi.org/10.7155/jgaa.v28i2.2988.
ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,”
Journal of Graph Algorithms and Applications, vol. 28, no. 2. Brown University,
pp. 47–82, 2024.
ista: De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler
M, Rote G. 2024. Removing popular faces in curve arrangements. Journal of Graph
Algorithms and Applications. 28(2), 47–82.
mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.”
Journal of Graph Algorithms and Applications, vol. 28, no. 2, Brown University,
2024, pp. 47–82, doi:10.7155/jgaa.v28i2.2988.
short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M.
Löffler, G. Rote, Journal of Graph Algorithms and Applications 28 (2024) 47–82.
corr_author: '1'
date_created: 2024-12-01T23:01:54Z
date_published: 2024-11-03T00:00:00Z
date_updated: 2024-12-03T09:49:18Z
day: '03'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.7155/jgaa.v28i2.2988
external_id:
arxiv:
- '2202.12175'
file:
- access_level: open_access
checksum: be611da6f9d790dc980d6fb7283fe889
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date_updated: 2024-12-03T09:45:00Z
file_id: '18609'
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file_size: 1582493
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intvolume: ' 28'
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 47-82
publication: Journal of Graph Algorithms and Applications
publication_identifier:
issn:
- 1526-1719
publication_status: published
publisher: Brown University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Removing popular faces in curve arrangements
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: 28
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18617'
abstract:
- lang: eng
text: "Any complex-valued polynomial on (Rn)k decomposes into an algebraic combination
of O(n)-invariant polynomials and harmonic polynomials. This decomposition, separation
of variables, is granted to be unique if n≥2k−1. We prove that the condition n≥2k−1
is not only sufficient, but also necessary for uniqueness of the separation. Moreover,
we describe the structure of non-uniqueness of the separation in the boundary
cases when n=2k−2 and n=2k−3.\r\nFormally, we study the kernel of a multiplication
map ϕ carrying out separation of variables. We devise a general algorithmic procedure
for describing Ker ϕ in the restricted non-stable range k≤n<2k−1. In the full
non-stable range n<2k−1, we give formulas for highest weights of generators of
the kernel as well as formulas for its Hilbert series. Using the developed methods,
we obtain a list of highest weight vectors generating Ker ϕ."
acknowledgement: The author is sincerely grateful for guidance, advice and valuable
feedback from Roman Lávička.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Beďatš, Daniel
id: 78ea3cc9-31e7-11ee-aa02-a6169bbfe1f1
last_name: Beďatš
orcid: 0009-0004-1828-0044
citation:
ama: Beďatš D. Separation of variables for scalar-valued polynomials in the non-stable
range. Journal of Algebra. 2024;651:281-304. doi:10.1016/j.jalgebra.2024.04.013
apa: Beďatš, D. (2024). Separation of variables for scalar-valued polynomials in
the non-stable range. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2024.04.013
chicago: Beďatš, Daniel. “Separation of Variables for Scalar-Valued Polynomials
in the Non-Stable Range.” Journal of Algebra. Elsevier, 2024. https://doi.org/10.1016/j.jalgebra.2024.04.013.
ieee: D. Beďatš, “Separation of variables for scalar-valued polynomials in the non-stable
range,” Journal of Algebra, vol. 651. Elsevier, pp. 281–304, 2024.
ista: Beďatš D. 2024. Separation of variables for scalar-valued polynomials in the
non-stable range. Journal of Algebra. 651, 281–304.
mla: Beďatš, Daniel. “Separation of Variables for Scalar-Valued Polynomials in the
Non-Stable Range.” Journal of Algebra, vol. 651, Elsevier, 2024, pp. 281–304,
doi:10.1016/j.jalgebra.2024.04.013.
short: D. Beďatš, Journal of Algebra 651 (2024) 281–304.
corr_author: '1'
date_created: 2024-12-04T07:58:45Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T14:57:00Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1016/j.jalgebra.2024.04.013
external_id:
arxiv:
- '2309.11154'
isi:
- '001232775600001'
file:
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checksum: 7b01c89128ba16d5334dfab389a03878
content_type: application/pdf
creator: dernst
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date_updated: 2024-12-09T13:56:26Z
file_id: '18638'
file_name: 2024_JourAlgebra_Bedats.pdf
file_size: 486969
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isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 281-304
publication: Journal of Algebra
publication_identifier:
issn:
- 0021-8693
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Separation of variables for scalar-valued polynomials in the non-stable range
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 651
year: '2024'
...
---
OA_place: publisher
OA_type: gold
_id: '18917'
abstract:
- lang: eng
text: "An eight-partition of a finite set of points (respectively, of a continuous
mass distribution) in ℝ³ consists of three planes that divide the space into 8
octants, such that each open octant contains at most 1/8 of the points (respectively,
of the mass). In 1966, Hadwiger showed that any mass distribution in ℝ³ admits
an eight-partition; moreover, one can prescribe the normal direction of one of
the three planes. The analogous result for finite point sets follows by a standard
limit argument.\r\nWe prove the following variant of this result: Any mass distribution
(or point set) in ℝ³ admits an eight-partition for which the intersection of two
of the planes is a line with a prescribed direction.\r\nMoreover, we present an
efficient algorithm for calculating an eight-partition of a set of n points in
ℝ³ (with prescribed normal direction of one of the planes) in time O^*(n^{5/2})."
acknowledgement: "Aronov, Boris: Work has been supported by NSF grants CCF 15-40656
and CCF 20-08551, and by grant 2014/170 from the US-Israel Binational Science Foundation.
Part of this research was conducted while BA was visiting ISTA in the summers of
2022 and 2023. The visit of BA to ISTA in the summer of 2022 was supported by an
ISTA Visiting Professorship.\r\nBasit, Abdul: Work has been supported by Australian
Research Council grant DP220102212.\r\nRamesh, Indu: Work supported by a Tandon
School of Engineering Fellowship and by NSF Grant CCF-20-08551.\r\nBA and AB would
like to thank William Steiger for insightful initial discussions of the problems
addressed in this work."
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Boris
full_name: Aronov, Boris
last_name: Aronov
- first_name: Abdul
full_name: Basit, Abdul
last_name: Basit
- first_name: Indu
full_name: Ramesh, Indu
last_name: Ramesh
- first_name: Gianluca
full_name: Tasinato, Gianluca
id: 0433290C-AF8F-11E9-A4C7-F729E6697425
last_name: Tasinato
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Aronov B, Basit A, Ramesh I, Tasinato G, Wagner U. Eight-partitioning points
in 3D, and efficiently too. In: 40th International Symposium on Computational
Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024:8:1-8:15.
doi:10.4230/LIPIcs.SoCG.2024.8'
apa: 'Aronov, B., Basit, A., Ramesh, I., Tasinato, G., & Wagner, U. (2024).
Eight-partitioning points in 3D, and efficiently too. In 40th International
Symposium on Computational Geometry (Vol. 293, p. 8:1-8:15). Athens, Greece:
Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.8'
chicago: Aronov, Boris, Abdul Basit, Indu Ramesh, Gianluca Tasinato, and Uli Wagner.
“Eight-Partitioning Points in 3D, and Efficiently Too.” In 40th International
Symposium on Computational Geometry, 293:8:1-8:15. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.8.
ieee: B. Aronov, A. Basit, I. Ramesh, G. Tasinato, and U. Wagner, “Eight-partitioning
points in 3D, and efficiently too,” in 40th International Symposium on Computational
Geometry, Athens, Greece, 2024, vol. 293, p. 8:1-8:15.
ista: 'Aronov B, Basit A, Ramesh I, Tasinato G, Wagner U. 2024. Eight-partitioning
points in 3D, and efficiently too. 40th International Symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry vol. 293, 8:1-8:15.'
mla: Aronov, Boris, et al. “Eight-Partitioning Points in 3D, and Efficiently Too.”
40th International Symposium on Computational Geometry, vol. 293, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 8:1-8:15, doi:10.4230/LIPIcs.SoCG.2024.8.
short: B. Aronov, A. Basit, I. Ramesh, G. Tasinato, U. Wagner, in:, 40th International
Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2024, p. 8:1-8:15.
conference:
end_date: 2024-06-14
location: Athens, Greece
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2024-06-11
corr_author: '1'
date_created: 2025-01-27T14:19:17Z
date_published: 2024-06-06T00:00:00Z
date_updated: 2026-02-16T12:19:08Z
day: '06'
ddc:
- '510'
department:
- _id: UlWa
- _id: GradSch
doi: 10.4230/LIPIcs.SoCG.2024.8
external_id:
arxiv:
- '2403.02627'
file:
- access_level: open_access
checksum: 443aa29ea5d948e917cfccd681dcf176
content_type: application/pdf
creator: dernst
date_created: 2025-01-27T14:17:37Z
date_updated: 2025-01-27T14:17:37Z
file_id: '18918'
file_name: 2024_LIPICs_Aronov.pdf
file_size: 880725
relation: main_file
success: 1
file_date_updated: 2025-01-27T14:17:37Z
has_accepted_license: '1'
intvolume: ' 293'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 8:1-8:15
publication: 40th International Symposium on Computational Geometry
publication_identifier:
isbn:
- '9783959773164'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '19860'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Eight-partitioning points in 3D, and efficiently too
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: 293
year: '2024'
...
---
_id: '14888'
abstract:
- lang: eng
text: 'A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an arrangement
by inserting a single additional curve. This turns out to be NP-hard; however,
it becomes tractable when the number of popular faces is small: We present a probabilistic
FPT-approach in the number of popular faces.'
acknowledgement: 'This work was initiated at the 16th European Research Week on Geometric
Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF):
W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035].
A preliminary version of this work has been presented at the 38th European Workshop
on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper,
which includes appendices but is otherwise identical, is available as a technical
report [10].'
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Phoebe
full_name: De Nooijer, Phoebe
last_name: De Nooijer
- first_name: Soeren
full_name: Terziadis, Soeren
last_name: Terziadis
- first_name: Alexandra
full_name: Weinberger, Alexandra
last_name: Weinberger
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tamara
full_name: Mchedlidze, Tamara
last_name: Mchedlidze
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: 'De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve
arrangements. In: 31st International Symposium on Graph Drawing and Network
Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2'
apa: 'De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T.,
Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements.
In 31st International Symposium on Graph Drawing and Network Visualization
(Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature.
https://doi.org/10.1007/978-3-031-49275-4_2'
chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová,
Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve
Arrangements.” In 31st International Symposium on Graph Drawing and Network
Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2.
ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,”
in 31st International Symposium on Graph Drawing and Network Visualization,
Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.
ista: 'De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler
M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International
Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network
Visualization, LNCS, vol. 14466, 18–33.'
mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.”
31st International Symposium on Graph Drawing and Network Visualization,
vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2.
short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M.
Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network
Visualization, Springer Nature, 2024, pp. 18–33.
conference:
end_date: 2023-09-22
location: Isola delle Femmine, Palermo, Italy
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2023-09-20
date_created: 2024-01-28T23:01:43Z
date_published: 2024-01-06T00:00:00Z
date_updated: 2025-09-04T11:52:35Z
day: '06'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-031-49275-4_2
external_id:
arxiv:
- '2202.12175'
isi:
- '001207942000002'
intvolume: ' 14466'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2202.12175
month: '01'
oa: 1
oa_version: Preprint
page: 18-33
publication: 31st International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783031492747'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Removing popular faces in curve arrangements
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14466
year: '2024'
...
---
_id: '15296'
abstract:
- lang: eng
text: In this paper we build a constructive algorithm that returns a rectifiable
curve that connects two points in a weakly convex set in a Hilbert space. We have
proven that this algorithm converges and obtained an estimate on the curve’s length
and compare the length of the curve obtained to known results.
article_number: '080002'
article_processing_charge: No
author:
- first_name: Mariana
full_name: Lopushanski, Mariana
last_name: Lopushanski
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
citation:
ama: 'Lopushanski M, Ivanov G. A constructive algorithm for building rectifiable
curves in weakly convex sets. In: AIP Conference Proceedings. Vol 3030.
AIP Publishing; 2024. doi:10.1063/5.0195908'
apa: 'Lopushanski, M., & Ivanov, G. (2024). A constructive algorithm for building
rectifiable curves in weakly convex sets. In AIP Conference Proceedings
(Vol. 3030). Virtual: AIP Publishing. https://doi.org/10.1063/5.0195908'
chicago: Lopushanski, Mariana, and Grigory Ivanov. “A Constructive Algorithm for
Building Rectifiable Curves in Weakly Convex Sets.” In AIP Conference Proceedings,
Vol. 3030. AIP Publishing, 2024. https://doi.org/10.1063/5.0195908.
ieee: M. Lopushanski and G. Ivanov, “A constructive algorithm for building rectifiable
curves in weakly convex sets,” in AIP Conference Proceedings, Virtual,
2024, vol. 3030, no. 1.
ista: 'Lopushanski M, Ivanov G. 2024. A constructive algorithm for building rectifiable
curves in weakly convex sets. AIP Conference Proceedings. ICCMSE: International
Conference of Computational Methods in Sciences and Engiineering vol. 3030, 080002.'
mla: Lopushanski, Mariana, and Grigory Ivanov. “A Constructive Algorithm for Building
Rectifiable Curves in Weakly Convex Sets.” AIP Conference Proceedings,
vol. 3030, no. 1, 080002, AIP Publishing, 2024, doi:10.1063/5.0195908.
short: M. Lopushanski, G. Ivanov, in:, AIP Conference Proceedings, AIP Publishing,
2024.
conference:
end_date: 2022-10-29
location: Virtual
name: 'ICCMSE: International Conference of Computational Methods in Sciences and
Engiineering'
start_date: 2022-10-26
date_created: 2024-04-07T22:00:55Z
date_published: 2024-03-14T00:00:00Z
date_updated: 2024-04-08T07:40:53Z
day: '14'
department:
- _id: UlWa
doi: 10.1063/5.0195908
intvolume: ' 3030'
issue: '1'
language:
- iso: eng
month: '03'
oa_version: None
publication: AIP Conference Proceedings
publication_identifier:
eissn:
- 1551-7616
issn:
- 0094-243X
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: A constructive algorithm for building rectifiable curves in weakly convex sets
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3030
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '9651'
abstract:
- lang: eng
text: We introduce a hierachy of equivalence relations on the set of separated nets
of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞).
Two separated nets are called ϕ-displacement equivalent if, roughly speaking,
there is a bijection between them which, for large radii R, displaces points of
norm at most R by something of order at most ϕ(R). We show that the spectrum of
ϕ-displacement equivalence spans from the established notion of bounded displacement
equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation,
coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between
the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown
to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞.
We further undertake a comparison of our notion of ϕ-displacement equivalence
with previously studied relations on separated nets. Particular attention is given
to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz
equivalence.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). This work was started while both authors were employed at the University
of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.
It was continued when the first named author was employed at University of Leipzig
and the second named author was employed at Institute of Science and Technology
of Austria, where he was supported by an IST Fellowship.'
article_number: '15'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Michael
full_name: Dymond, Michael
last_name: Dymond
- first_name: Vojtech
full_name: Kaluza, Vojtech
id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
last_name: Kaluza
orcid: 0000-0002-2512-8698
citation:
ama: Dymond M, Kaluza V. Divergence of separated nets with respect to displacement
equivalence. Geometriae Dedicata. 2024;218. doi:10.1007/s10711-023-00862-3
apa: Dymond, M., & Kaluza, V. (2024). Divergence of separated nets with respect
to displacement equivalence. Geometriae Dedicata. Springer Nature. https://doi.org/10.1007/s10711-023-00862-3
chicago: Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with
Respect to Displacement Equivalence.” Geometriae Dedicata. Springer Nature,
2024. https://doi.org/10.1007/s10711-023-00862-3.
ieee: M. Dymond and V. Kaluza, “Divergence of separated nets with respect to displacement
equivalence,” Geometriae Dedicata, vol. 218. Springer Nature, 2024.
ista: Dymond M, Kaluza V. 2024. Divergence of separated nets with respect to displacement
equivalence. Geometriae Dedicata. 218, 15.
mla: Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect
to Displacement Equivalence.” Geometriae Dedicata, vol. 218, 15, Springer
Nature, 2024, doi:10.1007/s10711-023-00862-3.
short: M. Dymond, V. Kaluza, Geometriae Dedicata 218 (2024).
corr_author: '1'
date_created: 2021-07-14T07:01:27Z
date_published: 2024-02-01T00:00:00Z
date_updated: 2025-04-23T07:37:26Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s10711-023-00862-3
external_id:
arxiv:
- '2102.13046'
isi:
- '001105681500001'
pmid:
- '38021107'
file:
- access_level: open_access
checksum: 9418534ac2f3d6f1f091a8b8ccaed01e
content_type: application/pdf
creator: dernst
date_created: 2024-07-16T10:14:13Z
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publication: Geometriae Dedicata
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title: Divergence of separated nets with respect to displacement equivalence
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