---
_id: '1584'
abstract:
- lang: eng
text: We investigate weighted straight skeletons from a geometric, graph-theoretical,
and combinatorial point of view. We start with a thorough definition and shed
light on some ambiguity issues in the procedural definition. We investigate the
geometry, combinatorics, and topology of faces and the roof model, and we discuss
in which cases a weighted straight skeleton is connected. Finally, we show that
the weighted straight skeleton of even a simple polygon may be non-planar and
may contain cycles, and we discuss under which restrictions on the weights and/or
the input polygon the weighted straight skeleton still behaves similar to its
unweighted counterpart. In particular, we obtain a non-procedural description
and a linear-time construction algorithm for the straight skeleton of strictly
convex polygons with arbitrary weights.
article_processing_charge: No
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Dominik
full_name: Kaaser, Dominik
last_name: Kaaser
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight
skeletons in the plane. Computational Geometry: Theory and Applications.
2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004'
apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint
of: Weighted straight skeletons in the plane. Computational Geometry: Theory
and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004'
chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry:
Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.'
ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted
straight skeletons in the plane,” Computational Geometry: Theory and Applications,
vol. 48, no. 5. Elsevier, pp. 429–442, 2015.'
ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted
straight skeletons in the plane. Computational Geometry: Theory and Applications.
48(5), 429–442.'
mla: 'Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.”
Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier,
2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.'
short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry:
Theory and Applications 48 (2015) 429–442.'
date_created: 2018-12-11T11:52:51Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2025-09-29T11:06:25Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.01.004
external_id:
isi:
- '000351967400008'
file:
- access_level: open_access
checksum: 5b33719a86f7f4c8e5dc62c1b6893f49
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:17:36Z
date_updated: 2020-07-14T12:45:03Z
file_id: '5292'
file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf
file_size: 508379
relation: main_file
file_date_updated: 2020-07-14T12:45:03Z
has_accepted_license: '1'
intvolume: ' 48'
isi: 1
issue: '5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 429 - 442
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5587'
pubrep_id: '475'
quality_controlled: '1'
related_material:
record:
- id: '1582'
relation: other
status: public
scopus_import: '1'
status: public
title: 'Reprint of: Weighted straight skeletons in the plane'
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: 48
year: '2015'
...
---
_id: '1590'
abstract:
- lang: eng
text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing
the vertices during a mitered offsetting process. It is known that the straight
skeleton of a simple polygon is a tree, and one can naturally derive directions
on the edges of the tree from the propagation of the shrinking process. In this
paper, we ask the reverse question: Given a tree with directed edges, can it be
the straight skeleton of a polygon? And if so, can we find a suitable simple polygon?
We answer these questions for all directed trees where the order of edges around
each node is fixed.'
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Thomas
full_name: Hackl, Thomas
last_name: Hackl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight
skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer
Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28'
apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P.,
& Vogtenhuber, B. (2015). Representing directed trees as straight skeletons.
In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los
Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28'
chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber,
Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight
Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer
Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28.
ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,”
in Graph Drawing and Network Visualization, vol. 9411, Springer Nature,
2015, pp. 335–347.
ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber
B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and
Network Visualization. LNCS, vol. 9411, 335–347.'
mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.”
Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015,
pp. 335–47, doi:10.1007/978-3-319-27261-0_28.
short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber,
in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.
conference:
end_date: 2015-09-26
location: Los Angeles, CA, United States
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:54Z
date_published: 2015-11-27T00:00:00Z
date_updated: 2025-09-23T10:35:07Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-27261-0_28
external_id:
arxiv:
- '1508.01076'
isi:
- '000373628600028'
intvolume: ' 9411'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1508.01076
month: '11'
oa: 1
oa_version: Preprint
page: 335 - 347
publication: Graph Drawing and Network Visualization
publication_identifier:
eisbn:
- 978-3-319-27261-0
isbn:
- 978-3-319-27260-3
publication_status: published
publisher: Springer Nature
publist_id: '5581'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Representing directed trees as straight skeletons
type: book_chapter
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 9411
year: '2015'
...
---
_id: '1682'
abstract:
- lang: eng
text: 'We study the problem of robust satisfiability of systems of nonlinear equations,
namely, whether for a given continuous function f:K→ ℝn on a finite simplicial
complex K and α > 0, it holds that each function g: K → ℝn such that ||g -
f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps
into a sphere, we particularly show that this problem is decidable in polynomial
time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension
of previous computational applications of topological degree and related concepts
in numerical and interval analysis. Via a reverse reduction, we prove that the
problem is undecidable when dim K > 2n - 2, where the threshold comes from
the stable range in homotopy theory. For the lucidity of our exposition, we focus
on the setting when f is simplexwise linear. Such functions can approximate general
continuous functions, and thus we get approximation schemes and undecidability
of the robust satisfiability in other possible settings.'
article_number: '26'
article_processing_charge: No
arxiv: 1
author:
- first_name: Peter
full_name: Franek, Peter
last_name: Franek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
citation:
ama: Franek P, Krcál M. Robust satisfiability of systems of equations. Journal
of the ACM. 2015;62(4). doi:10.1145/2751524
apa: Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations.
Journal of the ACM. ACM. https://doi.org/10.1145/2751524
chicago: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.”
Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524.
ieee: P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal
of the ACM, vol. 62, no. 4. ACM, 2015.
ista: Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal
of the ACM. 62(4), 26.
mla: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.”
Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524.
short: P. Franek, M. Krcál, Journal of the ACM 62 (2015).
corr_author: '1'
date_created: 2018-12-11T11:53:27Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-09-23T10:38:46Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2751524
external_id:
arxiv:
- '1402.0858'
isi:
- '000361200500001'
intvolume: ' 62'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1402.0858
month: '08'
oa: 1
oa_version: Preprint
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '5466'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Robust satisfiability of systems of equations
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 62
year: '2015'
...
---
_id: '1710'
abstract:
- lang: eng
text: 'We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by
a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles
incident on the hollow. It is assumed that u satisfies the so-called single impact
condition (SIC): each incident particle is elastically reflected by graph(u) and
goes away without hitting the graph of u anymore. We solve the problem: find the
function u minimizing the force of resistance created by the flow. We show that
the graph of the minimizer is formed by two arcs of parabolas symmetric to each
other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals
1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This
result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014),
pp. 2730-2742] stating in particular that the minimal resistance of a hollow in
higher dimensions equals 0.5. We additionally consider a similar problem of minimal
resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1
is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x =
(x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow
is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides
with 0.6435 when d = 1) and converges to 0.5 as d → ∞.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexander
full_name: Plakhov, Alexander
last_name: Plakhov
citation:
ama: Akopyan A, Plakhov A. Minimal resistance of curves under the single impact
assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769.
doi:10.1137/140993843
apa: Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the
single impact assumption. Society for Industrial and Applied Mathematics.
SIAM. https://doi.org/10.1137/140993843
chicago: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves
under the Single Impact Assumption.” Society for Industrial and Applied Mathematics.
SIAM, 2015. https://doi.org/10.1137/140993843.
ieee: A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single
impact assumption,” Society for Industrial and Applied Mathematics, vol.
47, no. 4. SIAM, pp. 2754–2769, 2015.
ista: Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single
impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769.
mla: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under
the Single Impact Assumption.” Society for Industrial and Applied Mathematics,
vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843.
short: A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47
(2015) 2754–2769.
date_created: 2018-12-11T11:53:36Z
date_published: 2015-07-14T00:00:00Z
date_updated: 2025-09-23T09:35:36Z
day: '14'
department:
- _id: HeEd
doi: 10.1137/140993843
ec_funded: 1
external_id:
arxiv:
- '1410.3736'
isi:
- '000360691500009'
intvolume: ' 47'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1410.3736
month: '07'
oa: 1
oa_version: Preprint
page: 2754 - 2769
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Society for Industrial and Applied Mathematics
publication_status: published
publisher: SIAM
publist_id: '5423'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Minimal resistance of curves under the single impact assumption
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 47
year: '2015'
...
---
_id: '1938'
abstract:
- lang: eng
text: 'We numerically investigate the distribution of extrema of ''chaotic'' Laplacian
eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a)
we count extrema on grid graphs with a small number of randomly added edges and
show the behavior to coincide with the 1957 prediction of Longuet-Higgins for
the continuous case and (b) we compute the regularity of their spatial distribution
using discrepancy, which is a classical measure from the theory of Monte Carlo
integration. The first part suggests that grid graphs with randomly added edges
should behave like two-dimensional surfaces with ergodic geodesic flow; in the
second part we show that the extrema are more regularly distributed in space than
the grid Z2.'
acknowledgement: "F.P. was supported by the Graduate School of IST Austria. S.S. was
partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and
Michael Kerber for sharing their implementation of the persistence algorithm. "
article_processing_charge: No
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
- first_name: Stefan
full_name: Steinerberger, Stefan
last_name: Steinerberger
citation:
ama: Pausinger F, Steinerberger S. On the distribution of local extrema in quantum
chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010
apa: Pausinger, F., & Steinerberger, S. (2015). On the distribution of local
extrema in quantum chaos. Physics Letters, Section A. Elsevier. https://doi.org/10.1016/j.physleta.2014.12.010
chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
Extrema in Quantum Chaos.” Physics Letters, Section A. Elsevier, 2015.
https://doi.org/10.1016/j.physleta.2014.12.010.
ieee: F. Pausinger and S. Steinerberger, “On the distribution of local extrema in
quantum chaos,” Physics Letters, Section A, vol. 379, no. 6. Elsevier,
pp. 535–541, 2015.
ista: Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in
quantum chaos. Physics Letters, Section A. 379(6), 535–541.
mla: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6,
Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010.
short: F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.
corr_author: '1'
date_created: 2018-12-11T11:54:49Z
date_published: 2015-03-06T00:00:00Z
date_updated: 2025-09-23T09:44:12Z
day: '06'
department:
- _id: HeEd
doi: 10.1016/j.physleta.2014.12.010
external_id:
isi:
- '000349586000006'
intvolume: ' 379'
isi: 1
issue: '6'
language:
- iso: eng
month: '03'
oa_version: None
page: 535 - 541
publication: Physics Letters, Section A
publication_status: published
publisher: Elsevier
publist_id: '5152'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the distribution of local extrema in quantum chaos
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 379
year: '2015'
...
---
_id: '2035'
abstract:
- lang: eng
text: "Considering a continuous self-map and the induced endomorphism on homology,
we study the eigenvalues and eigenspaces of the latter. Taking a filtration of
representations, we define the persistence of the eigenspaces, effectively introducing
a hierarchical organization of the map. The algorithm that computes this information
for a finite sample is proved to be stable, and to give the correct answer for
a sufficiently dense sample. Results computed with an implementation of the algorithm
provide evidence of its practical utility.\r\n"
acknowledgement: This research is partially supported by the Toposys project FP7-ICT-318493-STREP,
by ESF under the ACAT Research Network Programme, by the Russian Government under
mega project 11.G34.31.0053, and by the Polish National Science Center under Grant
No. N201 419639.
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Grzegorz
full_name: Jablonski, Grzegorz
id: 4483EF78-F248-11E8-B48F-1D18A9856A87
last_name: Jablonski
orcid: 0000-0002-3536-9866
- first_name: Marian
full_name: Mrozek, Marian
last_name: Mrozek
citation:
ama: Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map.
Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y
apa: Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology
of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y
chicago: Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent
Homology of a Self-Map.” Foundations of Computational Mathematics. Springer,
2015. https://doi.org/10.1007/s10208-014-9223-y.
ieee: H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of
a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5.
Springer, pp. 1213–1244, 2015.
ista: Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a
self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.
mla: Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations
of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44,
doi:10.1007/s10208-014-9223-y.
short: H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics
15 (2015) 1213–1244.
date_created: 2018-12-11T11:55:20Z
date_published: 2015-10-01T00:00:00Z
date_updated: 2025-09-23T14:08:54Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10208-014-9223-y
ec_funded: 1
external_id:
isi:
- '000360862900004'
file:
- access_level: open_access
checksum: 3566f3a8b0c1bc550e62914a88c584ff
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:10Z
date_updated: 2020-07-14T12:45:26Z
file_id: '4670'
file_name: IST-2016-486-v1+1_s10208-014-9223-y.pdf
file_size: 1317546
relation: main_file
file_date_updated: 2020-07-14T12:45:26Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
issue: '5'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1213 - 1244
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Foundations of Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '5022'
pubrep_id: '486'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The persistent homology of a self-map
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: 15
year: '2015'
...
---
_id: '1792'
abstract:
- lang: eng
text: Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop
a new concept of variation of multivariate functions on a compact Hausdorff space
with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka
theorem that holds for this notion of variation and discrepancy with respect to
D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions,
such as extreme or isotropic discrepancy. For extreme discrepancy, our result
coincides with the usual Koksma-Hlawka theorem. We show that the space of functions
of bounded D-variation contains important discontinuous functions and is closed
under natural algebraic operations. Finally, we illustrate the results on concrete
integration problems from integral geometry and stereology.
acknowledgement: F.P. is supported by the Graduate School of IST Austria, A.M.S is
supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by
a grant from the Villum Foundation.
article_processing_charge: No
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
- first_name: Anne
full_name: Svane, Anne
last_name: Svane
citation:
ama: Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems.
Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002
apa: Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general
discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002
chicago: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002.
ieee: F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy
systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797,
2015.
ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy
systems. Journal of Complexity. 31(6), 773–797.
mla: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press,
2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002.
short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.
corr_author: '1'
date_created: 2018-12-11T11:54:02Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2026-04-09T14:26:05Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.06.002
external_id:
isi:
- '000362926900001'
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isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa_version: None
page: 773 - 797
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5320'
quality_controlled: '1'
related_material:
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scopus_import: '1'
status: public
title: A Koksma-Hlawka inequality for general discrepancy systems
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 31
year: '2015'
...
---
_id: '1793'
abstract:
- lang: eng
text: We present a software platform for reconstructing and analyzing the growth
of a plant root system from a time-series of 3D voxelized shapes. It aligns the
shapes with each other, constructs a geometric graph representation together with
the function that records the time of growth, and organizes the branches into
a hierarchy that reflects the order of creation. The software includes the automatic
computation of structural and dynamic traits for each root in the system enabling
the quantification of growth on fine-scale. These are important advances in plant
phenotyping with applications to the study of genetic and environmental influences
on growth.
article_number: e0127657
article_processing_charge: No
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
orcid: 0000-0003-2012-9947
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for
the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6).
doi:10.1371/journal.pone.0127657'
apa: 'Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software
platform for the reconstruction and analysis of growing plant roots. PLoS One.
Public Library of Science. https://doi.org/10.1371/journal.pone.0127657'
chicago: 'Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots:
A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.”
PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.'
ieee: 'O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots,” PLoS One,
vol. 10, no. 6. Public Library of Science, 2015.'
ista: 'Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.'
mla: 'Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction
and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657,
Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.'
short: O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).
corr_author: '1'
date_created: 2018-12-11T11:54:02Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2025-09-23T08:30:43Z
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ddc:
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department:
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- _id: HeEd
doi: 10.1371/journal.pone.0127657
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publication: PLoS One
publication_status: published
publisher: Public Library of Science
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pubrep_id: '454'
quality_controlled: '1'
related_material:
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relation: research_data
status: public
scopus_import: '1'
status: public
title: 'DynamicRoots: A software platform for the reconstruction and analysis of growing
plant roots'
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
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volume: 10
year: '2015'
...
---
OA_place: publisher
OA_type: free access
_id: '1805'
abstract:
- lang: eng
text: 'We consider the problem of deciding whether the persistent homology group
of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex
X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded
in double-struck R3. As a consequence, we show that it is NP-hard to simplify
level and sublevel sets of scalar functions on double-struck S3 within a given
tolerance constraint. This problem has relevance to the visualization of medical
images by isosurfaces. We also show an implication to the theory of well groups
of scalar functions: not every well group can be realized by some level set, and
deciding whether a well group can be realized is NP-hard.'
article_processing_charge: No
article_type: original
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Olivier
full_name: Devillers, Olivier
last_name: Devillers
- first_name: Marc
full_name: Glisse, Marc
last_name: Glisse
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
citation:
ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications.
2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010'
apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015).
Homological reconstruction and simplification in R3. Computational Geometry:
Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010'
chicago: 'Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André
Lieutier. “Homological Reconstruction and Simplification in R3.” Computational
Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.'
ieee: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological
reconstruction and simplification in R3,” Computational Geometry: Theory and
Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.'
ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications. 48(8),
606–621.'
mla: 'Attali, Dominique, et al. “Homological Reconstruction and Simplification in
R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier,
2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.'
short: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational
Geometry: Theory and Applications 48 (2015) 606–621.'
corr_author: '1'
date_created: 2018-12-11T11:54:06Z
date_published: 2015-06-03T00:00:00Z
date_updated: 2026-06-18T17:57:28Z
day: '03'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.010
ec_funded: 1
external_id:
isi:
- '000357353200006'
intvolume: ' 48'
isi: 1
issue: '8'
language:
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main_file_link:
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url: https://doi.org/10.1016/j.comgeo.2014.08.010
month: '06'
oa: 1
oa_version: Published Version
page: 606 - 621
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5305'
quality_controlled: '1'
related_material:
record:
- id: '2812'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Homological reconstruction and simplification in R3
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2015'
...
---
_id: '1828'
abstract:
- lang: eng
text: We construct a non-linear Markov process connected with a biological model
of a bacterial genome recombination. The description of invariant measures of
this process gives us the solution of one problem in elementary probability theory.
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Sergey
full_name: Pirogov, Sergey
last_name: Pirogov
- first_name: Aleksandr
full_name: Rybko, Aleksandr
last_name: Rybko
citation:
ama: Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination
process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5
apa: Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic
recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5
chicago: Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures
of Genetic Recombination Process.” Journal of Statistical Physics. Springer,
2015. https://doi.org/10.1007/s10955-015-1238-5.
ieee: A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination
process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp.
163–167, 2015.
ista: Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination
process. Journal of Statistical Physics. 160(1), 163–167.
mla: Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.”
Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67,
doi:10.1007/s10955-015-1238-5.
short: A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015)
163–167.
corr_author: '1'
date_created: 2018-12-11T11:54:14Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2025-09-23T09:23:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10955-015-1238-5
ec_funded: 1
external_id:
arxiv:
- '1406.5313'
isi:
- '000356579000009'
intvolume: ' 160'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1406.5313
month: '07'
oa: 1
oa_version: Preprint
page: 163 - 167
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '5276'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Invariant measures of genetic recombination process
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 160
year: '2015'
...
---
_id: '9737'
article_processing_charge: No
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
orcid: 0000-0003-2012-9947
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for
the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001
apa: Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed
by DynamicRoots for the maize root shown in fig 2. Public Library of Science.
https://doi.org/10.1371/journal.pone.0127657.s001
chicago: Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits
Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of
Science, 2015. https://doi.org/10.1371/journal.pone.0127657.s001.
ieee: O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots
for the maize root shown in fig 2.” Public Library of Science, 2015.
ista: Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots
for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001.
mla: Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize
Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001.
short: O. Symonova, C. Topp, H. Edelsbrunner, (2015).
date_created: 2021-07-28T06:20:13Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2025-09-23T08:30:43Z
day: '01'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657.s001
month: '06'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '1793'
relation: used_in_publication
status: public
status: public
title: Root traits computed by DynamicRoots for the maize root shown in fig 2
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2015'
...
---
_id: '10817'
abstract:
- lang: eng
text: The Morse-Smale complex can be either explicitly or implicitly represented.
Depending on the type of representation, the simplification of the Morse-Smale
complex works differently. In the explicit representation, the Morse-Smale complex
is directly simplified by explicitly reconnecting the critical points during the
simplification. In the implicit representation, on the other hand, the Morse-Smale
complex is given by a combinatorial gradient field. In this setting, the simplification
changes the combinatorial flow, which yields an indirect simplification of the
Morse-Smale complex. The topological complexity of the Morse-Smale complex is
reduced in both representations. However, the simplifications generally yield
different results. In this chapter, we emphasize properties of the two representations
that cause these differences. We also provide a complexity analysis of the two
schemes with respect to running time and memory consumption.
acknowledgement: This research is supported and funded by the Digiteo unTopoVis project,
the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.
article_processing_charge: No
author:
- first_name: David
full_name: Günther, David
last_name: Günther
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hans-Peter
full_name: Seidel, Hans-Peter
last_name: Seidel
- first_name: Tino
full_name: Weinkauf, Tino
last_name: Weinkauf
citation:
ama: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification
of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds.
Topological Methods in Data Analysis and Visualization III. Mathematics
and Visualization. Cham: Springer Nature; 2014:135-150. doi:10.1007/978-3-319-04099-8_9'
apa: 'Günther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes
on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V.
Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and
Visualization III. (pp. 135–150). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-04099-8_9'
chicago: 'Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf.
“Notes on the Simplification of the Morse-Smale Complex.” In Topological Methods
in Data Analysis and Visualization III., edited by Peer-Timo Bremer, Ingrid
Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization.
Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-04099-8_9.'
ieee: 'D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the
simplification of the Morse-Smale complex,” in Topological Methods in Data
Analysis and Visualization III., P.-T. Bremer, I. Hotz, V. Pascucci, and R.
Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.'
ista: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification
of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization
III. , 135–150.'
mla: Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.”
Topological Methods in Data Analysis and Visualization III., edited by
Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:10.1007/978-3-319-04099-8_9.
short: D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer,
I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis
and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.
date_created: 2022-03-04T08:33:57Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_9
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
language:
- iso: eng
month: '03'
oa_version: None
page: 135-150
place: Cham
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Topological Methods in Data Analysis and Visualization III.
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Notes on the simplification of the Morse-Smale complex
type: book_chapter
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2014'
...
---
_id: '10886'
abstract:
- lang: eng
text: We propose a method for visualizing two-dimensional symmetric positive definite
tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the
heat kernel and was originally introduced as an isometry invariant shape signature.
Each positive definite tensor field defines a Riemannian manifold by considering
the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply
the definition of the HKS. The resulting scalar quantity is used for the visualization
of tensor fields. The HKS is closely related to the Gaussian curvature of the
Riemannian manifold and the time parameter of the heat kernel allows a multiscale
analysis in a natural way. In this way, the HKS represents field related scale
space properties, enabling a level of detail analysis of tensor fields. This makes
the HKS an interesting new scalar quantity for tensor fields, which differs significantly
from usual tensor invariants like the trace or the determinant. A method for visualization
and a numerical realization of the HKS for tensor fields is proposed in this chapter.
To validate the approach we apply it to some illustrating simple examples as isolated
critical points and to a medical diffusion tensor data set.
acknowledgement: This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.
alternative_title:
- Mathematics and Visualization
article_processing_charge: No
author:
- first_name: Valentin
full_name: Zobel, Valentin
last_name: Zobel
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
citation:
ama: 'Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature. In: Topological
Methods in Data Analysis and Visualization III . Springer; 2014:249-262. doi:10.1007/978-3-319-04099-8_16'
apa: Zobel, V., Reininghaus, J., & Hotz, I. (2014). Visualization of two-dimensional
symmetric positive definite tensor fields using the heat kernel signature. In
Topological Methods in Data Analysis and Visualization III (pp. 249–262).
Springer. https://doi.org/10.1007/978-3-319-04099-8_16
chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional
Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In
Topological Methods in Data Analysis and Visualization III , 249–62. Springer,
2014. https://doi.org/10.1007/978-3-319-04099-8_16.
ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature,” in Topological
Methods in Data Analysis and Visualization III , 2014, pp. 249–262.
ista: Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric
positive definite tensor fields using the heat kernel signature. Topological Methods
in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.
mla: Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive
Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods
in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16.
short: V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis
and Visualization III , Springer, 2014, pp. 249–262.
date_created: 2022-03-18T13:05:39Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2023-09-05T14:13:16Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_16
language:
- iso: eng
month: '03'
oa_version: None
page: 249-262
publication: 'Topological Methods in Data Analysis and Visualization III '
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visualization of two-dimensional symmetric positive definite tensor fields
using the heat kernel signature
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2014'
...
---
_id: '10892'
abstract:
- lang: eng
text: "In this paper, we introduce planar matchings on directed pseudo-line arrangements,
which yield a planar set of pseudo-line segments such that only matching-partners
are adjacent. By translating the planar matching problem into a corresponding
stable roommates problem we show that such matchings always exist.\r\nUsing our
new framework, we establish, for the first time, a complete, rigorous definition
of weighted straight skeletons, which are based on a so-called wavefront propagation
process. We present a generalized and unified approach to treat structural changes
in the wavefront that focuses on the restoration of weak planarity by finding
planar matchings."
acknowledgement: 'T. Biedl was supported by NSERC and the Ross and Muriel Cheriton
Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
citation:
ama: 'Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons.
In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature;
2014:117-127. doi:10.1007/978-3-319-13075-0_10'
apa: 'Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted
straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889,
pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10'
chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for
Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014,
8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10.
ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight
skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea,
2014, vol. 8889, pp. 117–127.
ista: 'Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight
skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium
on Algorithms and Computation, LNCS, vol. 8889, 117–127.'
mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.”
25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014,
pp. 117–27, doi:10.1007/978-3-319-13075-0_10.
short: T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC
2014, Springer Nature, 2014, pp. 117–127.
conference:
end_date: 2014-12-17
location: Jeonju, Korea
name: 'ISAAC: International Symposium on Algorithms and Computation'
start_date: 2014-12-15
corr_author: '1'
date_created: 2022-03-21T07:09:03Z
date_published: 2014-11-08T00:00:00Z
date_updated: 2025-09-29T13:22:55Z
day: '08'
department:
- _id: HeEd
doi: 10.1007/978-3-319-13075-0_10
external_id:
isi:
- '000354865900010'
intvolume: ' 8889'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 117-127
publication: 25th International Symposium, ISAAC 2014
publication_identifier:
eisbn:
- '9783319130750'
eissn:
- 1611-3349
isbn:
- '9783319130743'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '481'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Planar matchings for weighted straight skeletons
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 8889
year: '2014'
...
---
_id: '10893'
abstract:
- lang: eng
text: Saddle periodic orbits are an essential and stable part of the topological
skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm
to robustly extract these features. In this chapter, we present a novel technique
to extract saddle periodic orbits. Exploiting the analytic properties of such
an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent
(FTLE) that indicates its presence. Using persistent homology, we can then extract
the robust cycles of this field. These cycles thereby represent the saddle periodic
orbits of the given vector field. We discuss the different existing FTLE approximation
schemes regarding their applicability to this specific problem and propose an
adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate
our method using simple analytic vector field data.
acknowledgement: First, we thank the reviewers of this paper for their ideas and critical
comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions.
This research is supported by the European Commission under the TOPOSYS project
FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the
European Science Foundation under the ACAT Research Network Program.
article_processing_charge: No
author:
- first_name: Jens
full_name: Kasten, Jens
last_name: Kasten
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Wieland
full_name: Reich, Wieland
last_name: Reich
- first_name: Gerik
full_name: Scheuermann, Gerik
last_name: Scheuermann
citation:
ama: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of
saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization.
Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4'
apa: 'Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward
the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci,
& R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization
III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4'
chicago: 'Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward
the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis
and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014.
https://doi.org/10.1007/978-3-319-04099-8_4.'
ieee: 'J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction
of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization
III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham:
Springer, 2014, pp. 55–69.'
ista: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction
of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization
III . vol. 1, 55–69.'
mla: Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological
Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer
et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4.
short: J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I.
Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and
Visualization III , Springer, Cham, 2014, pp. 55–69.
date_created: 2022-03-21T07:11:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_4
ec_funded: 1
editor:
- first_name: Peer-Timo
full_name: Bremer, Peer-Timo
last_name: Bremer
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Valerio
full_name: Pascucci, Valerio
last_name: Pascucci
- first_name: Ronald
full_name: Peikert, Ronald
last_name: Peikert
intvolume: ' 1'
language:
- iso: eng
month: '03'
oa_version: None
page: 55-69
place: Cham
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Topological Methods in Data Analysis and Visualization III '
publication_identifier:
eisbn:
- '9783319040998'
eissn:
- 2197-666X
isbn:
- '9783319040981'
issn:
- 1612-3786
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
series_title: Mathematics and Visualization
status: public
title: Toward the extraction of saddle periodic orbits
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2014'
...
---
_id: '10894'
abstract:
- lang: eng
text: PHAT is a C++ library for the computation of persistent homology by matrix
reduction. We aim for a simple generic design that decouples algorithms from data
structures without sacrificing efficiency or user-friendliness. This makes PHAT
a versatile platform for experimenting with algorithmic ideas and comparing them
to state of the art implementations.
article_processing_charge: No
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hubert
full_name: Wagner, Hubert
last_name: Wagner
citation:
ama: 'Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms
Toolbox. In: ICMS 2014: International Congress on Mathematical Software.
Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143.
doi:10.1007/978-3-662-44199-2_24'
apa: 'Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent
Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical
Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-662-44199-2_24'
chicago: 'Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT
– Persistent Homology Algorithms Toolbox.” In ICMS 2014: International Congress
on Mathematical Software, 8592:137–43. LNCS. Berlin, Heidelberg: Springer
Berlin Heidelberg, 2014. https://doi.org/10.1007/978-3-662-44199-2_24.'
ieee: 'U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology
Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software,
Seoul, South Korea, 2014, vol. 8592, pp. 137–143.'
ista: 'Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology
Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software.
ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.'
mla: 'Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” ICMS
2014: International Congress on Mathematical Software, vol. 8592, Springer
Berlin Heidelberg, 2014, pp. 137–43, doi:10.1007/978-3-662-44199-2_24.'
short: 'U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International
Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg,
2014, pp. 137–143.'
conference:
end_date: 2014-08-09
location: Seoul, South Korea
name: 'ICMS: International Congress on Mathematical Software'
start_date: 2014-08-05
date_created: 2022-03-21T07:12:16Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2026-06-18T17:35:15Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-662-44199-2_24
intvolume: ' 8592'
language:
- iso: eng
month: '09'
oa_version: None
page: 137-143
place: Berlin, Heidelberg
publication: 'ICMS 2014: International Congress on Mathematical Software'
publication_identifier:
eisbn:
- '9783662441992'
eissn:
- 1611-3349
isbn:
- '9783662441985'
issn:
- 0302-9743
publication_status: published
publisher: Springer Berlin Heidelberg
quality_controlled: '1'
related_material:
record:
- id: '1433'
relation: later_version
status: public
scopus_import: '1'
series_title: LNCS
status: public
title: PHAT – Persistent Homology Algorithms Toolbox
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 8592
year: '2014'
...
---
_id: '2255'
abstract:
- lang: eng
text: Motivated by applications in biology, we present an algorithm for estimating
the length of tube-like shapes in 3-dimensional Euclidean space. In a first step,
we combine the tube formula of Weyl with integral geometric methods to obtain
an integral representation of the length, which we approximate using a variant
of the Koksma-Hlawka Theorem. In a second step, we use tools from computational
topology to decrease the dependence on small perturbations of the shape. We present
computational experiments that shed light on the stability and the convergence
rate of our algorithm.
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal
of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x
apa: Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like
shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer,
2014. https://doi.org/10.1007/s10851-013-0468-x.
ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp.
164–177, 2014.
ista: Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes.
Journal of Mathematical Imaging and Vision. 50(1), 164–177.
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer,
2014, pp. 164–77, doi:10.1007/s10851-013-0468-x.
short: H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision
50 (2014) 164–177.
corr_author: '1'
date_created: 2018-12-11T11:56:36Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2026-04-16T10:09:04Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10851-013-0468-x
ec_funded: 1
external_id:
isi:
- '000339823000012'
file:
- access_level: open_access
checksum: 2f93f3e63a38a85cd4404d7953913b14
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:18Z
date_updated: 2020-07-14T12:45:35Z
file_id: '5204'
file_name: IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf
file_size: 3941391
relation: main_file
file_date_updated: 2020-07-14T12:45:35Z
has_accepted_license: '1'
intvolume: ' 50'
isi: 1
issue: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
page: 164 - 177
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
issn:
- 0924-9907
publication_status: published
publisher: Springer
publist_id: '4691'
pubrep_id: '549'
quality_controlled: '1'
related_material:
record:
- id: '2843'
relation: earlier_version
status: public
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Stable length estimates of tube-like shapes
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 50
year: '2014'
...
---
_id: '2905'
abstract:
- lang: eng
text: "Persistent homology is a recent grandchild of homology that has found use
in\r\nscience and engineering as well as in mathematics. This paper surveys the
method as well\r\nas the applications, neglecting completeness in favor of highlighting
ideas and directions."
acknowledgement: This research is partially supported by NSF under grant DBI-0820624,
by ESF under the Research Networking Programme, and by the Russian Government Project
11.G34.31.0053.
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Dmitriy
full_name: Morozovy, Dmitriy
last_name: Morozovy
citation:
ama: 'Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In:
European Mathematical Society; 2014:31-50. doi:10.4171/120-1/3'
apa: 'Edelsbrunner, H., & Morozovy, D. (2014). Persistent homology: Theory and
practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics,
Kraków, Poland: European Mathematical Society. https://doi.org/10.4171/120-1/3'
chicago: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory
and Practice,” 31–50. European Mathematical Society, 2014. https://doi.org/10.4171/120-1/3.'
ieee: 'H. Edelsbrunner and D. Morozovy, “Persistent homology: Theory and practice,”
presented at the ECM: European Congress of Mathematics, Kraków, Poland, 2014,
pp. 31–50.'
ista: 'Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice.
ECM: European Congress of Mathematics, 31–50.'
mla: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. Persistent Homology: Theory
and Practice. European Mathematical Society, 2014, pp. 31–50, doi:10.4171/120-1/3.'
short: H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society, 2014, pp.
31–50.
conference:
end_date: 2012-07-07
location: Kraków, Poland
name: 'ECM: European Congress of Mathematics'
start_date: 2012-07-02
corr_author: '1'
date_created: 2018-12-11T12:00:16Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2025-06-03T11:46:59Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.4171/120-1/3
file:
- access_level: open_access
checksum: 1d4a046f1af945c407c5c4d411d4c5e4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:43Z
date_updated: 2020-07-14T12:45:52Z
file_id: '5232'
file_name: IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf
file_size: 435320
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Submitted Version
page: 31 - 50
publication_status: published
publisher: European Mathematical Society
publist_id: '3842'
pubrep_id: '544'
quality_controlled: '1'
status: public
title: 'Persistent homology: Theory and practice'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2153'
abstract:
- lang: eng
text: 'We define a simple, explicit map sending a morphism f : M → N of pointwise
finite dimensional persistence modules to a matching between the barcodes of M
and N. Our main result is that, in a precise sense, the quality of this matching
is tightly controlled by the lengths of the longest intervals in the barcodes
of ker f and coker f . As an immediate corollary, we obtain a new proof of the
algebraic stability theorem for persistence barcodes [5, 9], a fundamental result
in the theory of persistent homology. In contrast to previous proofs, ours shows
explicitly how a δ-interleaving morphism between two persistence modules induces
a δ-matching between the barcodes of the two modules. Our main result also specializes
to a structure theorem for submodules and quotients of persistence modules. Copyright
is held by the owner/author(s).'
article_processing_charge: No
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Lesnick, Michael
last_name: Lesnick
citation:
ama: 'Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability
of persistence. In: Proceedings of the Annual Symposium on Computational Geometry.
ACM; 2014:355-364. doi:10.1145/2582112.2582168'
apa: 'Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the
algebraic stability of persistence. In Proceedings of the Annual Symposium
on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168'
chicago: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and
the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium
on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168.
ieee: U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic
stability of persistence,” in Proceedings of the Annual Symposium on Computational
Geometry, Kyoto, Japan, 2014, pp. 355–364.
ista: 'Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic
stability of persistence. Proceedings of the Annual Symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 355–364.'
mla: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the
Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on
Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.
short: U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 355–364.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2025-06-11T07:57:54Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582168
ec_funded: 1
external_id:
arxiv:
- '1311.3681'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1311.3681
month: '06'
oa: 1
oa_version: Submitted Version
page: 355 - 364
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4853'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Induced matchings of barcodes and the algebraic stability of persistence
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2155'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a positive radius, we study the Čech,
Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete
Morse theory. We prove that the latter three complexes are simple-homotopy equivalent.
Our results have applications in topological data analysis and in the reconstruction
of shapes from sampled data. Copyright is held by the owner/author(s).
acknowledgement: This research is partially supported by ESF under the ACAT Research
Network Programme, and by the Russian Government under mega project 11.G34.31.0053
article_processing_charge: No
arxiv: 1
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations.
In: Proceedings of the Annual Symposium on Computational Geometry. ACM;
2014:484-490. doi:10.1145/2582112.2582167'
apa: 'Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay
filtrations. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167'
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Filtrations.” In Proceedings of the Annual Symposium on Computational
Geometry, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167.
ieee: U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,”
in Proceedings of the Annual Symposium on Computational Geometry, Kyoto,
Japan, 2014, pp. 484–490.
ista: 'Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations.
Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium
on Computational Geometry, 484–490.'
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Filtrations.” Proceedings of the Annual Symposium on Computational Geometry,
ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167.
short: U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 484–490.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
corr_author: '1'
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2025-06-11T07:58:27Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582167
ec_funded: 1
external_id:
arxiv:
- '1312.1231'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1312.1231
month: '06'
oa: 1
oa_version: Submitted Version
page: 484 - 490
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4851'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The morse theory of Čech and Delaunay filtrations
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...