---
_id: '106'
abstract:
- lang: eng
text: The goal of this article is to introduce the reader to the theory of intrinsic
geometry of convex surfaces. We illustrate the power of the tools by proving a
theorem on convex surfaces containing an arbitrarily long closed simple geodesic.
Let us remind ourselves that a curve in a surface is called geodesic if every
sufficiently short arc of the curve is length minimizing; if, in addition, it
has no self-intersections, we call it simple geodesic. A tetrahedron with equal
opposite edges is called isosceles. The axiomatic method of Alexandrov geometry
allows us to work with the metrics of convex surfaces directly, without approximating
it first by a smooth or polyhedral metric. Such approximations destroy the closed
geodesics on the surface; therefore it is difficult (if at all possible) to apply
approximations in the proof of our theorem. On the other hand, a proof in the
smooth or polyhedral case usually admits a translation into Alexandrov’s language;
such translation makes the result more general. In fact, our proof resembles a
translation of the proof given by Protasov. Note that the main theorem implies
in particular that a smooth convex surface does not have arbitrarily long simple
closed geodesics. However we do not know a proof of this corollary that is essentially
simpler than the one presented below.
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Anton
full_name: Petrunin, Anton
last_name: Petrunin
citation:
ama: Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer.
2018;40(3):26-31. doi:10.1007/s00283-018-9795-5
apa: Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces.
Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5
chicago: Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.”
Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5.
ieee: A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical
Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.
ista: Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical
Intelligencer. 40(3), 26–31.
mla: Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.”
Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31,
doi:10.1007/s00283-018-9795-5.
short: A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.
date_created: 2018-12-11T11:44:40Z
date_published: 2018-09-01T00:00:00Z
date_updated: 2023-09-13T08:49:16Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00283-018-9795-5
external_id:
arxiv:
- '1702.05172'
isi:
- '000444141200005'
intvolume: ' 40'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1702.05172
month: '09'
oa: 1
oa_version: Preprint
page: 26 - 31
publication: Mathematical Intelligencer
publication_status: published
publisher: Springer
publist_id: '7948'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Long geodesics on convex surfaces
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 40
year: '2018'
...
---
_id: '530'
abstract:
- lang: eng
text: Inclusion–exclusion is an effective method for computing the volume of a union
of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion
formulas for the subset of Rn covered by at least k balls in a finite set. We
implement two of the formulas in dimension n=3 and report on results obtained
with our software.
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: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion.
Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014'
apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls
I: Inclusion–exclusion. Computational Geometry: Theory and Applications.
Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014'
chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications.
Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.'
ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,”
Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp.
119–133, 2018.'
ista: 'Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion.
Computational Geometry: Theory and Applications. 68, 119–133.'
mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications,
vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.'
short: 'H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications
68 (2018) 119–133.'
date_created: 2018-12-11T11:46:59Z
date_published: 2018-03-01T00:00:00Z
date_updated: 2023-09-13T08:59:00Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2017.06.014
ec_funded: 1
external_id:
isi:
- '000415778300010'
file:
- access_level: open_access
checksum: 1c8d58cd489a66cd3e2064c1141c8c5e
content_type: application/pdf
creator: dernst
date_created: 2019-02-12T06:47:52Z
date_updated: 2020-07-14T12:46:38Z
file_id: '5953'
file_name: 2018_Edelsbrunner.pdf
file_size: 708357
relation: main_file
file_date_updated: 2020-07-14T12:46:38Z
has_accepted_license: '1'
intvolume: ' 68'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Preprint
page: 119 - 133
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: '7289'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Multiple covers with balls I: Inclusion–exclusion'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 68
year: '2018'
...
---
_id: '193'
abstract:
- lang: eng
text: 'We show attacks on five data-independent memory-hard functions (iMHF) that
were submitted to the password hashing competition (PHC). Informally, an MHF is
a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly
lower hardware and/or energy cost than evaluating a single instance on a standard
single-core architecture. Data-independent means the memory access pattern of
the function is independent of the input; this makes iMHFs harder to construct
than data-dependent ones, but the latter can be attacked by various side-channel
attacks. Following [Alwen-Blocki''16], we capture the evaluation of an iMHF as
a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of
this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC.
Ideally, one would like the complexity of a DAG underlying an iMHF to be as close
to quadratic in the number of nodes of the graph as possible. Instead, we show
that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2,
TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show
that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have
exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial
property of each underlying DAG (called its depth-robustness. By establishing
upper bounds on this property we are then able to apply the general technique
of [Alwen-Block''16] for analyzing the hardware costs of an iMHF.'
acknowledgement: Leonid Reyzin was supported in part by IST Austria and by US NSF
grants 1012910, 1012798, and 1422965; this research was performed while he was visiting
IST Austria.
article_processing_charge: No
author:
- first_name: Joel F
full_name: Alwen, Joel F
id: 2A8DFA8C-F248-11E8-B48F-1D18A9856A87
last_name: Alwen
- first_name: Peter
full_name: Gazi, Peter
last_name: Gazi
- first_name: Chethan
full_name: Kamath Hosdurg, Chethan
id: 4BD3F30E-F248-11E8-B48F-1D18A9856A87
last_name: Kamath Hosdurg
- first_name: Karen
full_name: Klein, Karen
id: 3E83A2F8-F248-11E8-B48F-1D18A9856A87
last_name: Klein
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
- first_name: Krzysztof Z
full_name: Pietrzak, Krzysztof Z
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
- first_name: Lenoid
full_name: Reyzin, Lenoid
last_name: Reyzin
- first_name: Michal
full_name: Rolinek, Michal
id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87
last_name: Rolinek
- first_name: Michal
full_name: Rybar, Michal
id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87
last_name: Rybar
citation:
ama: 'Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data
independent password hashing functions. In: Proceedings of the 2018 on Asia
Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534'
apa: 'Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak,
K. Z., … Rybar, M. (2018). On the memory hardness of data independent password
hashing functions. In Proceedings of the 2018 on Asia Conference on Computer
and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534'
chicago: Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F
Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar.
“On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings
of the 2018 on Asia Conference on Computer and Communication Security, 51–65.
ACM, 2018. https://doi.org/10.1145/3196494.3196534.
ieee: J. F. Alwen et al., “On the memory hardness of data independent password
hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.
ista: 'Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin
L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password
hashing functions. Proceedings of the 2018 on Asia Conference on Computer and
Communication Security. ASIACCS: Asia Conference on Computer and Communications
Security , 51–65.'
mla: Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password
Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer
and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.
short: J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak,
L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference
on Computer and Communication Security, ACM, 2018, pp. 51–65.
conference:
end_date: 2018-06-08
location: Incheon, Republic of Korea
name: 'ASIACCS: Asia Conference on Computer and Communications Security '
start_date: 2018-06-04
date_created: 2018-12-11T11:45:07Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-13T09:13:12Z
day: '01'
department:
- _id: KrPi
- _id: HeEd
- _id: VlKo
doi: 10.1145/3196494.3196534
ec_funded: 1
external_id:
isi:
- '000516620100005'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprint.iacr.org/2016/783
month: '06'
oa: 1
oa_version: Submitted Version
page: 51 - 65
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
- _id: 258AA5B2-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '682815'
name: Teaching Old Crypto New Tricks
publication: Proceedings of the 2018 on Asia Conference on Computer and Communication
Security
publication_status: published
publisher: ACM
publist_id: '7723'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the memory hardness of data independent password hashing functions
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '312'
abstract:
- lang: eng
text: Motivated by biological questions, we study configurations of equal spheres
that neither pack nor cover. Placing their centers on a lattice, we define the
soft density of the configuration by penalizing multiple overlaps. Considering
the 1-parameter family of diagonally distorted 3-dimensional integer lattices,
we show that the soft density is maximized at the FCC lattice.
acknowledgement: This work was partially supported by the DFG Collaborative Research
Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35
of the Austrian Science Fund (FWF).
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft
sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201
apa: Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC
lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial
and Applied Mathematics . https://doi.org/10.1137/16M1097201
chicago: Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the
FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for
Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.
ieee: H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice
for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society
for Industrial and Applied Mathematics , pp. 750–782, 2018.
ista: Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice
for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.
mla: Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC
Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1,
Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.
short: H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.
date_created: 2018-12-11T11:45:46Z
date_published: 2018-03-29T00:00:00Z
date_updated: 2023-09-13T09:34:38Z
day: '29'
department:
- _id: HeEd
doi: 10.1137/16M1097201
external_id:
isi:
- '000428958900038'
intvolume: ' 32'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf
month: '03'
oa: 1
oa_version: Submitted Version
page: 750 - 782
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: SIAM J Discrete Math
publication_identifier:
issn:
- '08954801'
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7553'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the optimality of the FCC lattice for soft sphere packing
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 32
year: '2018'
...
---
_id: '409'
abstract:
- lang: eng
text: We give a simple proof of T. Stehling's result [4], whereby in any normal
tiling of the plane with convex polygons with number of sides not less than six,
all tiles except a finite number are hexagons.
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
citation:
ama: Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus
Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005
apa: Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes
Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005
chicago: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes
Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005.
ieee: A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes
Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.
ista: Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes
Rendus Mathematique. 356(4), 412–414.
mla: Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes
Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.
short: A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.
date_created: 2018-12-11T11:46:19Z
date_published: 2018-04-01T00:00:00Z
date_updated: 2023-09-13T09:34:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.crma.2018.03.005
external_id:
arxiv:
- '1805.01652'
isi:
- '000430402700009'
intvolume: ' 356'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.01652
month: '04'
oa: 1
oa_version: Preprint
page: 412-414
publication: Comptes Rendus Mathematique
publication_identifier:
issn:
- 1631073X
publication_status: published
publisher: Elsevier
publist_id: '7420'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the number of non-hexagons in a planar tiling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 356
year: '2018'
...
---
_id: '87'
abstract:
- lang: eng
text: Using the geodesic distance on the n-dimensional sphere, we study the expected
radius function of the Delaunay mosaic of a random set of points. Specifically,
we consider the partition of the mosaic into intervals of the radius function
and determine the expected number of intervals whose radii are less than or equal
to a given threshold. We find that the expectations are essentially the same as
for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the
points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to
the boundary complex of the convex hull in Rn+1, so we also get the expected number
of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in
Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric
to the standard n-simplex equipped with the Fisher information metric. It follows
that the latter space has similar stochastic properties as the n-dimensional Euclidean
space. Our results are therefore relevant in information geometry and in population
genetics.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius
functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238.
doi:10.1214/18-AAP1389
apa: Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have
similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389
chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes
Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied
Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389.
ieee: H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar
radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability,
vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.
ista: Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar
radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5),
3215–3238.
mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have
Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability,
vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.
short: H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.
date_created: 2018-12-11T11:44:33Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2023-09-15T12:10:35Z
day: '01'
department:
- _id: HeEd
doi: 10.1214/18-AAP1389
external_id:
arxiv:
- '1705.02870'
isi:
- '000442893500018'
intvolume: ' 28'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.02870
month: '10'
oa: 1
oa_version: Preprint
page: 3215 - 3238
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Annals of Applied Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7967'
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Random inscribed polytopes have similar radius functions as Poisson-Delaunay
mosaics
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 28
year: '2018'
...
---
_id: '6355'
abstract:
- lang: eng
text: We prove that any cyclic quadrilateral can be inscribed in any closed convex
C1-curve. The smoothness condition is not required if the quadrilateral is a
rectangle.
article_number: e7
article_processing_charge: No
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: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
citation:
ama: Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed
convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7
apa: Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed
in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2018.7
chicago: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be
Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma.
Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.
ieee: A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge
University Press, 2018.
ista: Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in
any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.
mla: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed
in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6,
e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.
short: A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).
date_created: 2019-04-30T06:09:57Z
date_published: 2018-05-31T00:00:00Z
date_updated: 2023-09-19T14:50:12Z
day: '31'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
- _id: JaMa
doi: 10.1017/fms.2018.7
ec_funded: 1
external_id:
arxiv:
- '1712.10205'
isi:
- '000433915500001'
file:
- access_level: open_access
checksum: 5a71b24ba712a3eb2e46165a38fbc30a
content_type: application/pdf
creator: dernst
date_created: 2019-04-30T06:14:58Z
date_updated: 2020-07-14T12:47:28Z
file_id: '6356'
file_name: 2018_ForumMahtematics_Akopyan.pdf
file_size: 249246
relation: main_file
file_date_updated: 2020-07-14T12:47:28Z
has_accepted_license: '1'
intvolume: ' 6'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Any cyclic quadrilateral can be inscribed in any closed convex smooth curve
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 6
year: '2018'
...
---
_id: '1064'
abstract:
- lang: eng
text: 'In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by
P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it
is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot
be separated into two subfamilies by a straight line disjoint from the disks.
In this note we show that essentially the same idea may work for different analogues
and generalizations of their result. In particular, we prove the following: Given
a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety
coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate
of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane
disjoint from the homothets.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Mikhail
full_name: Grigorev, Mikhail
last_name: Grigorev
citation:
ama: Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W.
Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009.
doi:10.1007/s00454-017-9883-x
apa: Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering
theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry.
Springer. https://doi.org/10.1007/s00454-017-9883-x
chicago: Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle
Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational
Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x.
ieee: A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem
by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry,
vol. 59, no. 4. Springer, pp. 1001–1009, 2018.
ista: Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by
A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.
mla: Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and
R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer,
2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.
short: A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry
59 (2018) 1001–1009.
date_created: 2018-12-11T11:49:57Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-20T12:08:51Z
day: '01'
ddc:
- '516'
- '000'
department:
- _id: HeEd
doi: 10.1007/s00454-017-9883-x
ec_funded: 1
external_id:
isi:
- '000432205500011'
file:
- access_level: open_access
content_type: application/pdf
creator: dernst
date_created: 2019-01-18T09:27:36Z
date_updated: 2019-01-18T09:27:36Z
file_id: '5844'
file_name: 2018_DiscreteComp_Akopyan.pdf
file_size: 482518
relation: main_file
success: 1
file_date_updated: 2019-01-18T09:27:36Z
has_accepted_license: '1'
intvolume: ' 59'
isi: 1
issue: '4'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1001-1009
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- '14320444'
issn:
- '01795376'
publication_status: published
publisher: Springer
publist_id: '6324'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the circle covering theorem by A.W. Goodman and R.E. Goodman
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 59
year: '2018'
...
---
_id: '75'
abstract:
- lang: eng
text: We prove that any convex body in the plane can be partitioned into m convex
parts of equal areas and perimeters for any integer m≥2; this result was previously
known for prime powers m=pk. We also give a higher-dimensional generalization.
article_number: '1804.03057'
article_processing_charge: No
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: Avvakumov, Sergey
id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
last_name: Avvakumov
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number
of pieces. 2018. doi:10.48550/arXiv.1804.03057
apa: Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions
into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057
chicago: Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions
into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.
ieee: A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary
number of pieces.” arXiv, 2018.
ista: Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary
number of pieces. 1804.03057.
mla: Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of
Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.
short: A. Akopyan, S. Avvakumov, R. Karasev, (2018).
date_created: 2018-12-11T11:44:30Z
date_published: 2018-09-13T00:00:00Z
date_updated: 2023-12-18T10:51:02Z
day: '13'
department:
- _id: HeEd
- _id: JaMa
doi: 10.48550/arXiv.1804.03057
ec_funded: 1
external_id:
arxiv:
- '1804.03057'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.03057
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication_status: published
publisher: arXiv
related_material:
record:
- id: '8156'
relation: dissertation_contains
status: public
status: public
title: Convex fair partitions into arbitrary number of pieces
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '481'
abstract:
- lang: eng
text: 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. Using 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: 'Supported by NSERC and the Ross and Muriel Cheriton Fellowship.
Research supported by Austrian Science Fund (FWF): P25816-N15.'
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.
International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229.
doi:10.1142/S0218195916600050
apa: Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted
straight skeletons. International Journal of Computational Geometry and Applications.
World Scientific Publishing. https://doi.org/10.1142/S0218195916600050
chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for
Weighted Straight Skeletons.” International Journal of Computational Geometry
and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.
ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight
skeletons,” International Journal of Computational Geometry and Applications,
vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.
ista: Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight
skeletons. International Journal of Computational Geometry and Applications. 26(3–4),
211–229.
mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.”
International Journal of Computational Geometry and Applications, vol.
26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.
short: T. Biedl, S. Huber, P. Palfrader, International Journal of Computational
Geometry and Applications 26 (2017) 211–229.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-04-13T00:00:00Z
date_updated: 2023-02-21T16:06:22Z
day: '13'
ddc:
- '004'
- '514'
- '516'
department:
- _id: HeEd
doi: 10.1142/S0218195916600050
file:
- access_level: open_access
checksum: f79e8558bfe4b368dfefeb8eec2e3a5e
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:34Z
date_updated: 2020-07-14T12:46:35Z
file_id: '4758'
file_name: IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf
file_size: 769296
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 26'
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 211 - 229
publication: International Journal of Computational Geometry and Applications
publication_status: published
publisher: World Scientific Publishing
publist_id: '7338'
pubrep_id: '949'
quality_controlled: '1'
related_material:
record:
- id: '10892'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Planar matchings for weighted straight skeletons
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 26
year: '2017'
...
---
_id: '521'
abstract:
- lang: eng
text: Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y
induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful
in showing that the classical dimension raising theorems hold in large scale;
that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and
Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely
n-to-1 maps, which include the natural quotient maps via a finite group action,
and prove that they preserve the asymptotic dimension.
author:
- first_name: Kyle
full_name: Austin, Kyle
last_name: Austin
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
citation:
ama: Austin K, Virk Z. Higson compactification and dimension raising. Topology
and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005
apa: Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005
chicago: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.
ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology
and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.
ista: Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology
and its Applications. 215, 45–57.
mla: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.
short: K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:01:21Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
intvolume: ' 215'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.03954v1
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
issn:
- '01668641'
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 215
year: '2017'
...
---
_id: '568'
abstract:
- lang: eng
text: 'We study robust properties of zero sets of continuous maps f: X → ℝn. Formally,
we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets
of all continuous maps g closer to f than r in the max-norm. All of these sets
are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined
by A and an element of a certain cohomotopy group which (by a recent result) is
computable whenever the dimension of X is at most 2n - 3. By considering all r
> 0 simultaneously, the pointed cohomotopy groups form a persistence module-a
structure leading to persistence diagrams as in the case of persistent homology
or well groups. Eventually, we get a descriptor of persistent robust properties
of zero sets that has better descriptive power (Theorem A) and better computability
status (Theorem B) than the established well diagrams. Moreover, if we endow every
point of each zero set with gradients of the perturbation, the robust description
of the zero sets by elements of cohomotopy groups is in some sense the best possible
(Theorem C).'
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
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. Persistence of zero sets. Homology, Homotopy and Applications.
2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16
apa: Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology,
Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16
chicago: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology,
Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.
ieee: P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy
and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.
ista: Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and
Applications. 19(2), 313–342.
mla: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy
and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.
short: P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.
date_created: 2018-12-11T11:47:14Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:03:12Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4310/HHA.2017.v19.n2.a16
ec_funded: 1
intvolume: ' 19'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1507.04310
month: '01'
oa: 1
oa_version: Submitted Version
page: 313 - 342
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 2590DB08-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '701309'
name: Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes
(H2020)
publication: Homology, Homotopy and Applications
publication_identifier:
issn:
- '15320073'
publication_status: published
publisher: International Press
publist_id: '7246'
quality_controlled: '1'
scopus_import: 1
status: public
title: Persistence of zero sets
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2017'
...
---
_id: '5803'
abstract:
- lang: eng
text: Different distance metrics produce Voronoi diagrams with different properties.
It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi
diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions.
In this paper, we first show that this metric produces a persistent VD on the
2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly
approximates the corresponding VD on the 2D real plane. Next, we show that on
a 3D digital plane D, the Euclidean metric spanning over its voxel set does not
guarantee a digital VD which is persistent with the real-space VD. As a solution,
we introduce a novel concept of functional-plane-convexity, which is ensured by
the Euclidean metric spanning over the pedal set of D. Necessary proofs and some
visual result have been provided to adjudge the merit and usefulness of the proposed
concept.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital
plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature;
2017:93-104. doi:10.1007/978-3-319-59108-7_8'
apa: 'Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi
diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256,
pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi
Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104.
Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.'
ieee: 'R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on
3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer
Nature, 2017, pp. 93–104.'
ista: 'Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on
3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.'
mla: Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram
on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer
Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.
short: R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature,
Cham, 2017, pp. 93–104.
conference:
end_date: 2017-06-21
location: Plovdiv, Bulgaria
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2017-06-19
date_created: 2019-01-08T20:42:56Z
date_published: 2017-05-17T00:00:00Z
date_updated: 2022-01-28T07:48:24Z
day: '17'
department:
- _id: HeEd
doi: 10.1007/978-3-319-59108-7_8
extern: '1'
intvolume: ' 10256'
language:
- iso: eng
month: '05'
oa_version: None
page: 93-104
place: Cham
publication: Combinatorial image analysis
publication_identifier:
isbn:
- 978-3-319-59107-0
- 978-3-319-59108-7
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Construction of persistent Voronoi diagram on 3D digital plane
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 10256
year: '2017'
...
---
_id: '688'
abstract:
- lang: eng
text: 'We show that the framework of topological data analysis can be extended from
metrics to general Bregman divergences, widening the scope of possible applications.
Examples are the Kullback - Leibler divergence, which is commonly used for comparing
text and images, and the Itakura - Saito divergence, popular for speech and sound.
In particular, we prove that appropriately generalized čech and Delaunay (alpha)
complexes capture the correct homotopy type, namely that of the corresponding
union of Bregman balls. Consequently, their filtrations give the correct persistence
diagram, namely the one generated by the uniformly growing Bregman balls. Moreover,
we show that unlike the metric setting, the filtration of Vietoris-Rips complexes
may fail to approximate the persistence diagram. We propose algorithms to compute
the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally
test their efficiency. Lastly, we explain their surprisingly good performance
by making a connection with discrete Morse theory. '
alternative_title:
- LIPIcs
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences.
In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916.
doi:10.4230/LIPIcs.SoCG.2017.39'
apa: 'Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with
Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational
Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2017.39'
chicago: Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with
Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39.
ieee: H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,”
presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia,
2017, vol. 77, pp. 391–3916.
ista: Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences.
Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.
mla: Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with
Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.
short: H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017, pp. 391–3916.
conference:
end_date: 2017-07-07
location: Brisbane, Australia
name: Symposium on Computational Geometry, SoCG
start_date: 2017-07-04
date_created: 2018-12-11T11:47:56Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2021-01-12T08:09:26Z
day: '01'
ddc:
- '514'
- '516'
department:
- _id: HeEd
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2017.39
file:
- access_level: open_access
checksum: 067ab0cb3f962bae6c3af6bf0094e0f3
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:03Z
date_updated: 2020-07-14T12:47:42Z
file_id: '4856'
file_name: IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf
file_size: 990546
relation: main_file
file_date_updated: 2020-07-14T12:47:42Z
has_accepted_license: '1'
intvolume: ' 77'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 391-3916
publication_identifier:
issn:
- '18688969'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7021'
pubrep_id: '895'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topological data analysis with Bregman divergences
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 77
year: '2017'
...
---
_id: '707'
abstract:
- lang: eng
text: We answer a question of M. Gromov on the waist of the unit ball.
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
citation:
ama: Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin
of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062
apa: Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the
ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062
chicago: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of
the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell,
2017. https://doi.org/10.1112/blms.12062.
ieee: A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,”
Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell,
pp. 690–693, 2017.
ista: Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin
of the London Mathematical Society. 49(4), 690–693.
mla: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the
Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley-Blackwell,
2017, pp. 690–93, doi:10.1112/blms.12062.
short: A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017)
690–693.
date_created: 2018-12-11T11:48:02Z
date_published: 2017-08-01T00:00:00Z
date_updated: 2021-01-12T08:11:41Z
day: '01'
department:
- _id: HeEd
doi: 10.1112/blms.12062
ec_funded: 1
intvolume: ' 49'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.06279
month: '08'
oa: 1
oa_version: Preprint
page: 690 - 693
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Bulletin of the London Mathematical Society
publication_identifier:
issn:
- '00246093'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6982'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'A tight estimate for the waist of the ball '
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2017'
...
---
_id: '718'
abstract:
- lang: eng
text: Mapping every simplex in the Delaunay mosaic of a discrete point set to the
radius of the smallest empty circumsphere gives a generalized discrete Morse function.
Choosing the points from a Poisson point process in ℝ n , we study the expected
number of simplices in the Delaunay mosaic as well as the expected number of critical
simplices and nonsingular intervals in the corresponding generalized discrete
gradient. Observing connections with other probabilistic models, we obtain precise
expressions for the expected numbers in low dimensions. In particular, we obtain
the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions
n ≤ 4.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
- first_name: Matthias
full_name: Reitzner, Matthias
last_name: Reitzner
citation:
ama: Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability.
2017;49(3):745-767. doi:10.1017/apr.2017.20
apa: Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes
of poisson Delaunay mosaics and their discrete Morse functions. Advances in
Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20
chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected
Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances
in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.
ieee: H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson
Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability,
vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.
ista: Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay
mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3),
745–767.
mla: Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and
Their Discrete Morse Functions.” Advances in Applied Probability, vol.
49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.
short: H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability
49 (2017) 745–767.
date_created: 2018-12-11T11:48:07Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2023-09-07T12:07:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1017/apr.2017.20
ec_funded: 1
external_id:
arxiv:
- '1607.05915'
intvolume: ' 49'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1607.05915
month: '09'
oa: 1
oa_version: Preprint
page: 745 - 767
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Advances in Applied Probability
publication_identifier:
issn:
- '00018678'
publication_status: published
publisher: Cambridge University Press
publist_id: '6962'
quality_controlled: '1'
related_material:
record:
- id: '6287'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 49
year: '2017'
...
---
_id: '6287'
abstract:
- lang: eng
text: The main objects considered in the present work are simplicial and CW-complexes
with vertices forming a random point cloud. In particular, we consider a Poisson
point process in R^n and study Delaunay and Voronoi complexes of the first and
higher orders and weighted Delaunay complexes obtained as sections of Delaunay
complexes, as well as the Čech complex. Further, we examine theDelaunay complex
of a Poisson point process on the sphere S^n, as well as of a uniform point cloud,
which is equivalent to the convex hull, providing a connection to the theory of
random polytopes. Each of the complexes in question can be endowed with a radius
function, which maps its cells to the radii of appropriately chosen circumspheres,
called the radius of the cell. Applying and developing discrete Morse theory for
these functions, joining it together with probabilistic and sometimes analytic
machinery, and developing several integral geometric tools, we aim at getting
the distributions of circumradii of typical cells. For all considered complexes,
we are able to generalize and obtain up to constants the distribution of radii
of typical intervals of all types. In low dimensions the constants can be computed
explicitly, thus providing the explicit expressions for the expected numbers of
cells. In particular, it allows to find the expected density of simplices of every
dimension for a Poisson point process in R^4, whereas the result for R^3 was known
already in 1970's.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873
apa: Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute
of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873
chicago: Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute
of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.
ieee: A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of
Science and Technology Austria, 2017.
ista: Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute
of Science and Technology Austria.
mla: Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute
of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.
short: A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science
and Technology Austria, 2017.
date_created: 2019-04-09T15:04:32Z
date_published: 2017-10-27T00:00:00Z
date_updated: 2023-09-15T12:10:34Z
day: '27'
ddc:
- '514'
- '516'
- '519'
degree_awarded: PhD
department:
- _id: HeEd
doi: 10.15479/AT:ISTA:th_873
file:
- access_level: open_access
checksum: ece7e598a2f060b263c2febf7f3fe7f9
content_type: application/pdf
creator: dernst
date_created: 2019-04-09T14:54:51Z
date_updated: 2020-07-14T12:47:26Z
file_id: '6289'
file_name: 2017_Thesis_Nikitenko.pdf
file_size: 2324870
relation: main_file
- access_level: closed
checksum: 99b7ad76e317efd447af60f91e29b49b
content_type: application/zip
creator: dernst
date_created: 2019-04-09T14:54:51Z
date_updated: 2020-07-14T12:47:26Z
file_id: '6290'
file_name: 2017_Thesis_Nikitenko_source.zip
file_size: 2863219
relation: source_file
file_date_updated: 2020-07-14T12:47:26Z
has_accepted_license: '1'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: '86'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
pubrep_id: '873'
related_material:
record:
- id: '718'
relation: part_of_dissertation
status: public
- id: '5678'
relation: part_of_dissertation
status: public
- id: '87'
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
title: 'Discrete Morse theory for random complexes '
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2017'
...
---
_id: '1433'
abstract:
- lang: eng
text: Phat is an open-source C. ++ library for the computation of persistent homology
by matrix reduction, targeted towards developers of software for topological data
analysis. We aim for a simple generic design that decouples algorithms from data
structures without sacrificing efficiency or user-friendliness. We provide numerous
different reduction strategies as well as data types to store and manipulate the
boundary matrix. We compare the different combinations through extensive experimental
evaluation and identify optimization techniques that work well in practical situations.
We also compare our software with various other publicly available libraries for
persistent homology.
article_processing_charge: No
article_type: original
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
last_name: Bauer
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Jan
full_name: Reininghaus, Jan
last_name: Reininghaus
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms
toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008
apa: Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent
homology algorithms toolbox. Journal of Symbolic Computation. Academic
Press. https://doi.org/10.1016/j.jsc.2016.03.008
chicago: Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat
- Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation.
Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.
ieee: U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology
algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic
Press, pp. 76–90, 2017.
ista: Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology
algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.
mla: Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal
of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.
short: U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation
78 (2017) 76–90.
date_created: 2018-12-11T11:51:59Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-20T09:42:40Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jsc.2016.03.008
ec_funded: 1
external_id:
isi:
- '000384396000005'
intvolume: ' 78'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.jsc.2016.03.008
month: '01'
oa: 1
oa_version: Published Version
page: 76 - 90
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Journal of Symbolic Computation
publication_identifier:
issn:
- ' 07477171'
publication_status: published
publisher: Academic Press
publist_id: '5765'
quality_controlled: '1'
related_material:
record:
- id: '10894'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Phat - Persistent homology algorithms toolbox
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 78
year: '2017'
...
---
_id: '1180'
abstract:
- lang: eng
text: In this article we define an algebraic vertex of a generalized polyhedron
and show that the set of algebraic vertices is the smallest set of points needed
to define the polyhedron. We prove that the indicator function of a generalized
polytope P is a linear combination of indicator functions of simplices whose vertices
are algebraic vertices of P. We also show that the indicator function of any generalized
polyhedron is a linear combination, with integer coefficients, of indicator functions
of cones with apices at algebraic vertices and line-cones. The concept of an algebraic
vertex is closely related to the Fourier–Laplace transform. We show that a point
v is an algebraic vertex of a generalized polyhedron P if and only if the tangent
cone of P, at v, has non-zero Fourier–Laplace transform.
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Imre
full_name: Bárány, Imre
last_name: Bárány
- first_name: Sinai
full_name: Robins, Sinai
last_name: Robins
citation:
ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026
apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex
polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026
chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of
Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.
ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,”
Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.
ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra.
Advances in Mathematics. 308, 627–644.
mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances
in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.
short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.
date_created: 2018-12-11T11:50:34Z
date_published: 2017-02-21T00:00:00Z
date_updated: 2023-09-20T11:21:27Z
day: '21'
department:
- _id: HeEd
doi: 10.1016/j.aim.2016.12.026
ec_funded: 1
external_id:
isi:
- '000409292900015'
intvolume: ' 308'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1508.07594
month: '02'
oa: 1
oa_version: Submitted Version
page: 627 - 644
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Advances in Mathematics
publication_identifier:
issn:
- '00018708'
publication_status: published
publisher: Academic Press
publist_id: '6173'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Algebraic vertices of non-convex polyhedra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 308
year: '2017'
...
---
_id: '1173'
abstract:
- lang: eng
text: We introduce the Voronoi functional of a triangulation of a finite set of
points in the Euclidean plane and prove that among all geometric triangulations
of the point set, the Delaunay triangulation maximizes the functional. This result
neither extends to topological triangulations in the plane nor to geometric triangulations
in three and higher dimensions.
acknowledgement: This research is partially supported by the Russian Government under
the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by
ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by
NSF grants DMS-1101688, DMS-1400876.
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: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
orcid: 0000-0002-0659-3201
citation:
ama: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is
maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910.
doi:10.1007/s00493-016-3308-y
apa: Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The
Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica.
Springer. https://doi.org/10.1007/s00493-016-3308-y
chicago: Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko.
“The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.”
Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.
ieee: H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional
is maximized by the Delaunay triangulation in the plane,” Combinatorica,
vol. 37, no. 5. Springer, pp. 887–910, 2017.
ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional
is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5),
887–910.
mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay
Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017,
pp. 887–910, doi:10.1007/s00493-016-3308-y.
short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017)
887–910.
date_created: 2018-12-11T11:50:32Z
date_published: 2017-10-01T00:00:00Z
date_updated: 2023-09-20T11:23:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00493-016-3308-y
ec_funded: 1
external_id:
isi:
- '000418056000005'
intvolume: ' 37'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.6337
month: '10'
oa: 1
oa_version: Submitted Version
page: 887 - 910
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Combinatorica
publication_identifier:
issn:
- '02099683'
publication_status: published
publisher: Springer
publist_id: '6182'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Voronoi functional is maximized by the Delaunay triangulation in the plane
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 37
year: '2017'
...
---
_id: '1072'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a radius parameter, we study the Čech,
Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized
discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel
sets of generalized discrete Morse functions, we prove that the four complexes
are simple-homotopy equivalent by a sequence of simplicial collapses, which are
explicitly described by a single discrete gradient field.
acknowledgement: This research has been supported by the EU project Toposys(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 DFG Collaborative Research Center SFB/TRR
109 “Discretization in Geometry and Dynamics”.
article_processing_charge: No
article_type: original
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 complexes. Transactions
of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991
apa: Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay
complexes. Transactions of the American Mathematical Society. American
Mathematical Society. https://doi.org/10.1090/tran/6991
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Complexes.” Transactions of the American Mathematical Society.
American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.
ieee: U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,”
Transactions of the American Mathematical Society, vol. 369, no. 5. American
Mathematical Society, pp. 3741–3762, 2017.
ista: Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes.
Transactions of the American Mathematical Society. 369(5), 3741–3762.
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Complexes.” Transactions of the American Mathematical Society, vol. 369,
no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991.
short: U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society
369 (2017) 3741–3762.
date_created: 2018-12-11T11:49:59Z
date_published: 2017-05-01T00:00:00Z
date_updated: 2023-09-20T12:05:56Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/6991
ec_funded: 1
external_id:
arxiv:
- '1312.1231'
isi:
- '000398030400024'
intvolume: ' 369'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1312.1231
month: '05'
oa: 1
oa_version: Preprint
page: 3741 - 3762
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '6311'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Morse theory of Čech and delaunay complexes
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 369
year: '2017'
...
---
_id: '1065'
abstract:
- lang: eng
text: 'We consider the problem of reachability in pushdown graphs. We study the
problem for pushdown graphs with constant treewidth. Even for pushdown graphs
with treewidth 1, for the reachability problem we establish the following: (i)
the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem
would contradict the k-clique conjecture and imply faster combinatorial algorithms
for cliques in graphs.'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Georg F
full_name: Osang, Georg F
id: 464B40D6-F248-11E8-B48F-1D18A9856A87
last_name: Osang
orcid: 0000-0002-8882-5116
citation:
ama: Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information
Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003
apa: Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant
treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003
chicago: Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with
Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003.
ieee: K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,”
Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.
ista: Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth.
Information Processing Letters. 122, 25–29.
mla: Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant
Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp.
25–29, doi:10.1016/j.ipl.2017.02.003.
short: K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.
date_created: 2018-12-11T11:49:57Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-20T12:08:18Z
day: '01'
ddc:
- '000'
department:
- _id: KrCh
- _id: HeEd
doi: 10.1016/j.ipl.2017.02.003
ec_funded: 1
external_id:
isi:
- '000399506600005'
file:
- access_level: open_access
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:17Z
date_updated: 2019-10-15T07:44:51Z
file_id: '4998'
file_name: IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf
file_size: 247657
relation: main_file
file_date_updated: 2019-10-15T07:44:51Z
has_accepted_license: '1'
intvolume: ' 122'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 25 - 29
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
publication: Information Processing Letters
publication_identifier:
issn:
- '00200190'
publication_status: published
publisher: Elsevier
publist_id: '6323'
pubrep_id: '991'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pushdown reachability with constant treewidth
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 122
year: '2017'
...
---
_id: '1022'
abstract:
- lang: eng
text: We introduce a multiscale topological description of the Megaparsec web-like
cosmic matter distribution. Betti numbers and topological persistence offer a
powerful means of describing the rich connectivity structure of the cosmic web
and of its multiscale arrangement of matter and galaxies. Emanating from algebraic
topology and Morse theory, Betti numbers and persistence diagrams represent an
extension and deepening of the cosmologically familiar topological genus measure
and the related geometric Minkowski functionals. In addition to a description
of the mathematical background, this study presents the computational procedure
for computing Betti numbers and persistence diagrams for density field filtrations.
The field may be computed starting from a discrete spatial distribution of galaxies
or simulation particles. The main emphasis of this study concerns an extensive
and systematic exploration of the imprint of different web-like morphologies and
different levels of multiscale clustering in the corresponding computed Betti
numbers and persistence diagrams. To this end, we use Voronoi clustering models
as templates for a rich variety of web-like configurations and the fractal-like
Soneira-Peebles models exemplify a range of multiscale configurations. We have
identified the clear imprint of cluster nodes, filaments, walls, and voids in
persistence diagrams, along with that of the nested hierarchy of structures in
multiscale point distributions. We conclude by outlining the potential of persistent
topology for understanding the connectivity structure of the cosmic web, in large
simulations of cosmic structure formation and in the challenging context of the
observed galaxy distribution in large galaxy surveys.
acknowledgement: Part of this work has been supported by the 7th Framework Programme
for Research of the European Commission, under FETOpen grant number 255827 (CGL
Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random
Systems via Algebraic Topology) number 320422.
article_processing_charge: No
author:
- first_name: Pratyush
full_name: Pranav, Pratyush
last_name: Pranav
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Rien
full_name: Van De Weygaert, Rien
last_name: Van De Weygaert
- first_name: Gert
full_name: Vegter, Gert
last_name: Vegter
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
- first_name: Bernard
full_name: Jones, Bernard
last_name: Jones
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic
web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical
Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862
apa: Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M.,
Jones, B., & Wintraecken, M. (2017). The topology of the cosmic web in terms
of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society.
Oxford University Press. https://doi.org/10.1093/mnras/stw2862
chicago: Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter,
Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic
Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical
Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.
ieee: P. Pranav et al., “The topology of the cosmic web in terms of persistent
Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4. Oxford University Press, pp. 4281–4310, 2017.
ista: Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B,
Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti
numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310.
mla: Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent
Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol.
465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.
short: P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B.
Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017)
4281–4310.
date_created: 2018-12-11T11:49:44Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-09-22T09:40:55Z
day: '01'
department:
- _id: HeEd
doi: 10.1093/mnras/stw2862
external_id:
isi:
- '000395170200039'
intvolume: ' 465'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.04519
month: '01'
oa: 1
oa_version: Submitted Version
page: 4281 - 4310
publication: Monthly Notices of the Royal Astronomical Society
publication_identifier:
issn:
- '00358711'
publication_status: published
publisher: Oxford University Press
publist_id: '6373'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The topology of the cosmic web in terms of persistent Betti numbers
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 465
year: '2017'
...
---
_id: '737'
abstract:
- lang: eng
text: We generalize Brazas’ topology on the fundamental group to the whole universal
path space X˜ i.e., to the set of homotopy classes of all based paths. We develop
basic properties of the new notion and provide a complete comparison of the obtained
topology with the established topologies, in particular with the Lasso topology
and the CO topology, i.e., the topology that is induced by the compact-open topology.
It turns out that the new topology is the finest topology contained in the CO
topology, for which the action of the fundamental group on the universal path
space is a continuous group action.
article_processing_charge: No
author:
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Andreas
full_name: Zastrow, Andreas
last_name: Zastrow
citation:
ama: Virk Z, Zastrow A. A new topology on the universal path space. Topology
and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015
apa: Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015
chicago: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path
Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.
ieee: Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology
and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.
ista: Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology
and its Applications. 231, 186–196.
mla: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.”
Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.
short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:53:01Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2017.09.015
external_id:
isi:
- '000413889100012'
intvolume: ' 231'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 186 - 196
publication: Topology and its Applications
publication_identifier:
issn:
- '01668641'
publication_status: published
publisher: Elsevier
publist_id: '6930'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new topology on the universal path space
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 231
year: '2017'
...
---
_id: '836'
abstract:
- lang: eng
text: Recent research has examined how to study the topological features of a continuous
self-map by means of the persistence of the eigenspaces, for given eigenvalues,
of the endomorphism induced in homology over a field. This raised the question
of how to select dynamically significant eigenvalues. The present paper aims to
answer this question, giving an algorithm that computes the persistence of eigenspaces
for every eigenvalue simultaneously, also expressing said eigenspaces as direct
sums of “finite” and “singular” subspaces.
alternative_title:
- PROMS
article_processing_charge: No
author:
- first_name: Marc
full_name: Ethier, Marc
last_name: Ethier
- 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: 'Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the
Kronecker canonical form. In: Special Sessions in Applications of Computer
Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8'
apa: 'Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of
self-maps with the Kronecker canonical form. In Special Sessions in Applications
of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8'
chicago: Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues
of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications
of Computer Algebra, 198:119–36. Springer, 2017. https://doi.org/10.1007/978-3-319-56932-1_8.
ieee: M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps
with the Kronecker canonical form,” in Special Sessions in Applications of
Computer Algebra, Kalamata, Greece, 2017, vol. 198, pp. 119–136.
ista: 'Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with
the Kronecker canonical form. Special Sessions in Applications of Computer Algebra.
ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.'
mla: Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical
Form.” Special Sessions in Applications of Computer Algebra, vol. 198,
Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8.
short: M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications
of Computer Algebra, Springer, 2017, pp. 119–136.
conference:
end_date: 2015-07-23
location: Kalamata, Greece
name: 'ACA: Applications of Computer Algebra'
start_date: 2015-07-20
date_created: 2018-12-11T11:48:46Z
date_published: 2017-07-27T00:00:00Z
date_updated: 2023-09-26T15:50:52Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-56932-1_8
ec_funded: 1
external_id:
isi:
- '000434088200008'
intvolume: ' 198'
isi: 1
language:
- iso: eng
month: '07'
oa_version: None
page: 119 - 136
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Special Sessions in Applications of Computer Algebra
publication_identifier:
isbn:
- 978-331956930-7
publication_status: published
publisher: Springer
publist_id: '6812'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finding eigenvalues of self-maps with the Kronecker canonical form
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 198
year: '2017'
...
---
_id: '833'
abstract:
- lang: eng
text: We present an efficient algorithm to compute Euler characteristic curves of
gray scale images of arbitrary dimension. In various applications the Euler characteristic
curve is used as a descriptor of an image. Our algorithm is the first streaming
algorithm for Euler characteristic curves. The usage of streaming removes the
necessity to store the entire image in RAM. Experiments show that our implementation
handles terabyte scale images on commodity hardware. Due to lock-free parallelism,
it scales well with the number of processor cores. Additionally, we put the concept
of the Euler characteristic curve in the wider context of computational topology.
In particular, we explain the connection with persistence diagrams.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Teresa
full_name: Heiss, Teresa
id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
last_name: Heiss
orcid: 0000-0002-1780-2689
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: 'Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of
multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer;
2017:397-409. doi:10.1007/978-3-319-64689-3_32'
apa: 'Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic
curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger
(Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of
Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32'
chicago: Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic
Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden,
and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32.
ieee: 'T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves
of multidimensional images,” presented at the CAIP: Computer Analysis of Images
and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.'
ista: 'Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves
of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS,
vol. 10424, 397–409.'
mla: Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic
Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol.
10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.
short: T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer,
2017, pp. 397–409.
conference:
end_date: 2017-08-24
location: Ystad, Sweden
name: 'CAIP: Computer Analysis of Images and Patterns'
start_date: 2017-08-22
date_created: 2018-12-11T11:48:45Z
date_published: 2017-07-28T00:00:00Z
date_updated: 2023-09-26T16:10:03Z
day: '28'
department:
- _id: HeEd
doi: 10.1007/978-3-319-64689-3_32
editor:
- first_name: Michael
full_name: Felsberg, Michael
last_name: Felsberg
- first_name: Anders
full_name: Heyden, Anders
last_name: Heyden
- first_name: Norbert
full_name: Krüger, Norbert
last_name: Krüger
external_id:
isi:
- '000432085900032'
intvolume: ' 10424'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.02045
month: '07'
oa: 1
oa_version: Submitted Version
page: 397 - 409
publication_identifier:
issn:
- '03029743'
publication_status: published
publisher: Springer
publist_id: '6815'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Streaming algorithm for Euler characteristic curves of multidimensional images
type: conference
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 10424
year: '2017'
...
---
_id: '84'
abstract:
- lang: eng
text: The advent of high-throughput technologies and the concurrent advances in
information sciences have led to a data revolution in biology. This revolution
is most significant in molecular biology, with an increase in the number and scale
of the “omics” projects over the last decade. Genomics projects, for example,
have produced impressive advances in our knowledge of the information concealed
into genomes, from the many genes that encode for the proteins that are responsible
for most if not all cellular functions, to the noncoding regions that are now
known to provide regulatory functions. Proteomics initiatives help to decipher
the role of post-translation modifications on the protein structures and provide
maps of protein-protein interactions, while functional genomics is the field that
attempts to make use of the data produced by these projects to understand protein
functions. The biggest challenge today is to assimilate the wealth of information
provided by these initiatives into a conceptual framework that will help us decipher
life. For example, the current views of the relationship between protein structure
and function remain fragmented. We know of their sequences, more and more about
their structures, we have information on their biological activities, but we have
difficulties connecting this dotted line into an informed whole. We lack the experimental
and computational tools for directly studying protein structure, function, and
dynamics at the molecular and supra-molecular levels. In this chapter, we review
some of the current developments in building the computational tools that are
needed, focusing on the role that geometry and topology play in these efforts.
One of our goals is to raise the general awareness about the importance of geometric
methods in elucidating the mysterious foundations of our very existence. Another
goal is the broadening of what we consider a geometric algorithm. There is plenty
of valuable no-man’s-land between combinatorial and numerical algorithms, and
it seems opportune to explore this land with a computational-geometric frame of
mind.
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: Patrice
full_name: Koehl, Patrice
last_name: Koehl
citation:
ama: 'Edelsbrunner H, Koehl P. Computational topology for structural molecular biology.
In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational
Geometry, Third Edition. Handbook of Discrete and Computational Geometry.
Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601'
apa: Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural
molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook
of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor
& Francis. https://doi.org/10.1201/9781315119601
chicago: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural
Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third
Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35.
Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601.
ieee: H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular
biology,” in Handbook of Discrete and Computational Geometry, Third Edition,
C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735.
ista: 'Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular
biology. In: Handbook of Discrete and Computational Geometry, Third Edition. ,
1709–1735.'
mla: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural
Molecular Biology.” Handbook of Discrete and Computational Geometry, Third
Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35,
doi:10.1201/9781315119601.
short: H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.),
Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis,
2017, pp. 1709–1735.
date_created: 2018-12-11T11:44:32Z
date_published: 2017-11-09T00:00:00Z
date_updated: 2023-10-16T11:15:22Z
day: '09'
department:
- _id: HeEd
doi: 10.1201/9781315119601
editor:
- first_name: Csaba
full_name: Toth, Csaba
last_name: Toth
- first_name: Joseph
full_name: O'Rourke, Joseph
last_name: O'Rourke
- first_name: Jacob
full_name: Goodman, Jacob
last_name: Goodman
language:
- iso: eng
month: '11'
oa_version: None
page: 1709 - 1735
publication: Handbook of Discrete and Computational Geometry, Third Edition
publication_identifier:
eisbn:
- '9781498711425'
publication_status: published
publisher: Taylor & Francis
publist_id: '7970'
quality_controlled: '1'
scopus_import: '1'
series_title: Handbook of Discrete and Computational Geometry
status: public
title: Computational topology for structural molecular biology
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2017'
...
---
_id: '909'
abstract:
- lang: eng
text: We study the lengths of curves passing through a fixed number of points on
the boundary of a convex shape in the plane. We show that, for any convex shape
K, there exist four points on the boundary of K such that the length of any curve
passing through these points is at least half of the perimeter of K. It is also
shown that the same statement does not remain valid with the additional constraint
that the points are extreme points of K. Moreover, the factor ½ cannot
be achieved with any fixed number of extreme points. We conclude the paper with
a few other inequalities related to the perimeter of a convex shape.
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Vladislav
full_name: Vysotsky, Vladislav
last_name: Vysotsky
citation:
ama: Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points
of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596.
doi:10.4169/amer.math.monthly.124.7.588
apa: Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through
boundary points of a planar convex shape. The American Mathematical Monthly.
Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588
chicago: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.
ieee: A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary
points of a planar convex shape,” The American Mathematical Monthly, vol.
124, no. 7. Mathematical Association of America, pp. 588–596, 2017.
ista: Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary
points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.
mla: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing
through Boundary Points of a Planar Convex Shape.” The American Mathematical
Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96,
doi:10.4169/amer.math.monthly.124.7.588.
short: A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.
date_created: 2018-12-11T11:49:09Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2023-10-17T11:24:57Z
day: '01'
department:
- _id: HeEd
doi: 10.4169/amer.math.monthly.124.7.588
ec_funded: 1
external_id:
arxiv:
- '1605.07997'
isi:
- '000413947300002'
intvolume: ' 124'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.07997
month: '01'
oa: 1
oa_version: Submitted Version
page: 588 - 596
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: The American Mathematical Monthly
publication_identifier:
issn:
- '00029890'
publication_status: published
publisher: Mathematical Association of America
publist_id: '6534'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the lengths of curves passing through boundary points of a planar convex
shape
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 124
year: '2017'
...
---
_id: '1149'
abstract:
- lang: eng
text: 'We study the usefulness of two most prominent publicly available rigorous
ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other
based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable
of handling entire sets of initial conditions and provide tight rigorous outer
enclosures of the images under a time-T map. We conduct extensive benchmark computations
using the well-known Lorenz system, and compare the computation time against the
final accuracy achieved. We also discuss the effect of a few technical parameters,
such as the order of the numerical integration method, the value of T, and the
phase space resolution. We conclude that COSY may provide more precise results
due to its ability of avoiding the variable dependency problem. However, the overall
cost of computations conducted using CAPD is typically lower, especially when
intervals of parameters are involved. Moreover, access to COSY is limited (registration
required) and the rigorous ODE integrators are not publicly available, while CAPD
is an open source free software project. Therefore, we recommend the latter integrator
for this kind of computations. Nevertheless, proper choice of the various integration
parameters turns out to be of even greater importance than the choice of the integrator
itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved.'
acknowledgement: "MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9,
and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially
supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry
of Education, Science, Technology, Culture and Sports, Japan. KM was supported by
NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR
and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part
of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch conducted
by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER)
through COMPETE – Programa Operacional Factores de Competitividade (POFC) and from
the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT)
in the framework of the research project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008);
from the People Programme (Marie Curie Actions) of the European Union's Seventh
Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from
the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department
of Mathematics of Kyoto University for making their server available for conducting
the computations described in the paper, and to the reviewers for helpful comments
that contributed towards increasing the quality of the paper."
author:
- first_name: Tomoyuki
full_name: Miyaji, Tomoyuki
last_name: Miyaji
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Marcio
full_name: Gameiro, Marcio
last_name: Gameiro
- first_name: Hiroshi
full_name: Kokubu, Hiroshi
last_name: Kokubu
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
citation:
ama: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous
ODE integrators for multi scale set oriented computations. Applied Numerical
Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005
apa: Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016).
A study of rigorous ODE integrators for multi scale set oriented computations.
Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005
chicago: Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and
Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set
Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016.
https://doi.org/10.1016/j.apnum.2016.04.005.
ieee: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study
of rigorous ODE integrators for multi scale set oriented computations,” Applied
Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.
ista: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of
rigorous ODE integrators for multi scale set oriented computations. Applied Numerical
Mathematics. 107, 34–47.
mla: Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale
Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier,
2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.
short: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical
Mathematics 107 (2016) 34–47.
date_created: 2018-12-11T11:50:25Z
date_published: 2016-09-01T00:00:00Z
date_updated: 2021-01-12T06:48:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.apnum.2016.04.005
ec_funded: 1
intvolume: ' 107'
language:
- iso: eng
month: '09'
oa_version: None
page: 34 - 47
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Applied Numerical Mathematics
publication_status: published
publisher: Elsevier
publist_id: '6209'
quality_controlled: '1'
scopus_import: 1
status: public
title: A study of rigorous ODE integrators for multi scale set oriented computations
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 107
year: '2016'
...
---
_id: '1216'
abstract:
- lang: eng
text: 'A framework fo r extracting features in 2D transient flows, based on the
acceleration field to ensure Galilean invariance is proposed in this paper. The
minima of the acceleration magnitude (a superset of acceleration zeros) are extracted
and discriminated into vortices and saddle points, based on the spectral properties
of the velocity Jacobian. The extraction of topological features is performed
with purely combinatorial algorithms from discrete computational topology. The
feature points are prioritized with persistence, as a physically meaningful importance
measure. These feature points are tracked in time with a robust algorithm for
tracking features. Thus, a space-time hierarchy of the minima is built and vortex
merging events are detected. We apply the acceleration feature extraction strategy
to three two-dimensional shear flows: (1) an incompressible periodic cylinder
wake, (2) an incompressible planar mixing layer and (3) a weakly compressible
planar jet. The vortex-like acceleration feature points are shown to be well aligned
with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure
field and minima of λ2.'
acknowledgement: "The authors acknowledge funding of the German Re-\r\nsearch Foundation
\ (DFG) via the Collaborative Re-\r\nsearch Center (SFB 557) \\Control of
\ Complex Turbu-\r\nlent Shear Flows\" and the Emmy Noether Program.\r\nFurther
\ funding was provided by the Zuse Institute\r\nBerlin (ZIB), the DFG-CNRS
\ research group \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence
'Closed-loop control of turbulent shear ows\r\nusing reduced-order models' (TUCOROM)
of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean Social
\ Fund (ESF App. No. 100098251). We\r\nthank the Ambrosys Ltd. Society
\ for Complex Sys-\r\ntems Management and the Bernd R. Noack Cybernet-\r\nics
\ Foundation for additional support. A part of this\r\nwork was performed
using HPC resources from GENCI-[CCRT/CINES/IDRIS] supported by the Grant 2011-\r\n[x2011020912"
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: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Hans
full_name: Hege, Hans
last_name: Hege
- first_name: Bernd
full_name: Noack, Bernd
last_name: Noack
- first_name: Guillaume
full_name: Daviller, Guillaume
last_name: Daviller
- first_name: Marek
full_name: Morzyński, Marek
last_name: Morzyński
citation:
ama: Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady
shear flows. Archives of Mechanics. 2016;68(1):55-80.
apa: Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., &
Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. Archives
of Mechanics. Polish Academy of Sciences Publishing House.
chicago: Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume
Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear
Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House,
2016.
ieee: J. Kasten et al., “Acceleration feature points of unsteady shear flows,”
Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing
House, pp. 55–80, 2016.
ista: Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M.
2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics.
68(1), 55–80.
mla: Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.”
Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing
House, 2016, pp. 55–80.
short: J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński,
Archives of Mechanics 68 (2016) 55–80.
date_created: 2018-12-11T11:50:46Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:09Z
day: '01'
department:
- _id: HeEd
intvolume: ' 68'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf
month: '01'
oa: 1
oa_version: Published Version
page: 55 - 80
publication: Archives of Mechanics
publication_status: published
publisher: Polish Academy of Sciences Publishing House
publist_id: '6118'
quality_controlled: '1'
scopus_import: 1
status: public
title: Acceleration feature points of unsteady shear flows
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2016'
...
---
_id: '1222'
abstract:
- lang: eng
text: We consider packings of congruent circles on a square flat torus, i.e., periodic
(w.r.t. a square lattice) planar circle packings, with the maximal circle radius.
This problem is interesting due to a practical reason—the problem of “super resolution
of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly,
for the case N=7 there are three different optimal arrangements. Our proof is
based on a computer enumeration of toroidal irreducible contact graphs.
acknowledgement: We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy
for some useful comments and remarks, and especially Thom Sulanke for modifying
surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant
DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported
by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg
State University) under RF Government Grant 11.G34.31.0026.
author:
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
- first_name: Anton
full_name: Nikitenko, Anton
id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
last_name: Nikitenko
citation:
ama: Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat
torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6
apa: Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles
on a square flat torus. Discrete & Computational Geometry. Springer.
https://doi.org/10.1007/s00454-015-9742-6
chicago: Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles
on a Square Flat Torus.” Discrete & Computational Geometry. Springer,
2016. https://doi.org/10.1007/s00454-015-9742-6.
ieee: O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square
flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer,
pp. 1–20, 2016.
ista: Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square
flat torus. Discrete & Computational Geometry. 55(1), 1–20.
mla: Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on
a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no.
1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.
short: O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.
date_created: 2018-12-11T11:50:48Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:11Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-015-9742-6
intvolume: ' 55'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1212.0649
month: '01'
oa: 1
oa_version: Preprint
page: 1 - 20
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '6111'
quality_controlled: '1'
scopus_import: 1
status: public
title: Optimal packings of congruent circles on a square flat torus
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2016'
...
---
_id: '1237'
abstract:
- lang: eng
text: 'Bitmap images of arbitrary dimension may be formally perceived as unions
of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology
and homology groups are well known topological invariants of such sets. Cohomological
operations, such as the cup product, provide higher-order algebraic topological
invariants, especially important for digital images of dimension higher than 3.
If such an operation is determined at the level of simplicial chains [see e.g.
González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively
computable. However, decomposing a cubical complex into a simplicial one deleteriously
affects the efficiency of such an approach. In order to avoid this overhead, a
direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015,
253-275] for the cup product in cohomology, and implemented in the ChainCon software
package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for
the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series,
1947, 290-320] directly at the level of cubical chains, and we prove the correctness
of this formula. An implementation of this formula is programmed in C++ within
the ChainCon software framework. We provide a few examples and discuss the effectiveness
of this approach. One specific application follows from the fact that Steenrod
squares yield tests for the topological extension problem: Can a given map A →
Sd to a sphere Sd be extended to a given super-complex X of A? In particular,
the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value
r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the
extension problem.'
acknowledgement: The research conducted by both authors has received funding from
the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework
Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and
no. 622033 (for P. P.).
alternative_title:
- LNCS
author:
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: 'Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667.
Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13'
apa: 'Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares
(Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image
Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13'
chicago: Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,”
9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13.
ieee: 'M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented
at the CTIC: Computational Topology in Image Context, Marseille, France, 2016,
vol. 9667, pp. 140–151.'
ista: 'Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC:
Computational Topology in Image Context, LNCS, vol. 9667, 140–151.'
mla: Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares.
Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.
short: M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2018-12-11T11:50:52Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2021-01-12T06:49:18Z
day: '02'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_13
ec_funded: 1
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 140 - 151
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication_status: published
publisher: Springer
publist_id: '6096'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computation of cubical Steenrod squares
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 9667
year: '2016'
...
---
_id: '1252'
abstract:
- lang: eng
text: We study the homomorphism induced in homology by a closed correspondence between
topological spaces, using projections from the graph of the correspondence to
its domain and codomain. We provide assumptions under which the homomorphism induced
by an outer approximation of a continuous map coincides with the homomorphism
induced in homology by the map. In contrast to more classical results we do not
require that the projection to the domain have acyclic preimages. Moreover, we
show that it is possible to retrieve correct homological information from a correspondence
even if some data is missing or perturbed. Finally, we describe an application
to combinatorial maps that are either outer approximations of continuous maps
or reconstructions of such maps from a finite set of data points.
acknowledgement: "The authors gratefully acknowledge the support of the Lorenz Center
which\r\nprovided an opportunity for us to discuss in depth the work of this paper.
Research leading to these results has received funding from Fundo Europeu de Desenvolvimento
Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade
(POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia
e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie
Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013)
under REA grant agreement no. 622033 (supporting PP). The work of the first and
third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019,
1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second
author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029),
Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan."
article_processing_charge: No
article_type: original
author:
- first_name: Shaun
full_name: Harker, Shaun
last_name: Harker
- first_name: Hiroshi
full_name: Kokubu, Hiroshi
last_name: Kokubu
- first_name: Konstantin
full_name: Mischaikow, Konstantin
last_name: Mischaikow
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from
a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801.
doi:10.1090/proc/12812
apa: Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing
a map on homology from a correspondence. Proceedings of the American Mathematical
Society. American Mathematical Society. https://doi.org/10.1090/proc/12812
chicago: Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk.
“Inducing a Map on Homology from a Correspondence.” Proceedings of the American
Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812.
ieee: S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on
homology from a correspondence,” Proceedings of the American Mathematical Society,
vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.
ista: Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology
from a correspondence. Proceedings of the American Mathematical Society. 144(4),
1787–1801.
mla: Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings
of the American Mathematical Society, vol. 144, no. 4, American Mathematical
Society, 2016, pp. 1787–801, doi:10.1090/proc/12812.
short: S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American
Mathematical Society 144 (2016) 1787–1801.
date_created: 2018-12-11T11:50:57Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2022-05-24T09:35:58Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/12812
ec_funded: 1
external_id:
arxiv:
- '1411.7563'
intvolume: ' 144'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1411.7563
month: '04'
oa: 1
oa_version: Preprint
page: 1787 - 1801
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Proceedings of the American Mathematical Society
publication_identifier:
issn:
- 1088-6826
publication_status: published
publisher: American Mathematical Society
publist_id: '6075'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inducing a map on homology from a correspondence
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...
---
_id: '1254'
abstract:
- lang: eng
text: We use rigorous numerical techniques to compute a lower bound for the exponent
of expansivity outside a neighborhood of the critical point for thousands of intervals
of parameter values in the quadratic family. We first compute a radius of the
critical neighborhood outside which the map is uniformly expanding. This radius
is taken as small as possible, yet large enough for our numerical procedure to
succeed in proving that the expansivity exponent outside this neighborhood is
positive. Then, for each of the intervals, we compute a lower bound for this expansivity
exponent, valid for all the parameters in that interval. We illustrate and study
the distribution of the radii and the expansivity exponents. The results of our
computations are mathematically rigorous. The source code of the software and
the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/.
acknowledgement: "AG and PP were partially supported by Abdus Salam International
Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS,
and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento
Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade
(POFC) and from the Portuguese national funds through Fundação para a Ciência e
a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions)
of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant
agreement no. 622033. The authors gratefully acknowledge the Department of\r\nMathematics
\ of Kyoto University for providing access\r\nto their server for conducting
\ computations for this\r\nproject."
author:
- first_name: Ali
full_name: Golmakani, Ali
last_name: Golmakani
- first_name: Stefano
full_name: Luzzatto, Stefano
last_name: Luzzatto
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical
neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124.
doi:10.1080/10586458.2015.1048011
apa: Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity
outside a critical neighborhood in the quadratic family. Experimental Mathematics.
Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011
chicago: Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity
Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics.
Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011.
ieee: A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside
a critical neighborhood in the quadratic family,” Experimental Mathematics,
vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.
ista: Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a
critical neighborhood in the quadratic family. Experimental Mathematics. 25(2),
116–124.
mla: Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood
in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor
and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011.
short: A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016)
116–124.
date_created: 2018-12-11T11:50:58Z
date_published: 2016-04-02T00:00:00Z
date_updated: 2021-01-12T06:49:25Z
day: '02'
department:
- _id: HeEd
doi: 10.1080/10586458.2015.1048011
ec_funded: 1
intvolume: ' 25'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1504.00116
month: '04'
oa: 1
oa_version: Preprint
page: 116 - 124
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: Experimental Mathematics
publication_status: published
publisher: Taylor and Francis
publist_id: '6071'
quality_controlled: '1'
scopus_import: 1
status: public
title: Uniform expansivity outside a critical neighborhood in the quadratic family
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2016'
...
---
_id: '1272'
abstract:
- lang: eng
text: We study different means to extend offsetting based on skeletal structures
beyond the well-known constant-radius and mitered offsets supported by Voronoi
diagrams and straight skeletons, for which the orthogonal distance of offset elements
to their respective input elements is constant and uniform over all input elements.
Our main contribution is a new geometric structure, called variable-radius Voronoi
diagram, which supports the computation of variable-radius offsets, i.e., offsets
whose distance to the input is allowed to vary along the input. We discuss properties
of this structure and sketch a prototype implementation that supports the computation
of variable-radius offsets based on this new variant of Voronoi diagrams.
acknowledgement: 'This work was supported by Austrian Science Fund (FWF): P25816-N15.'
author:
- 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
citation:
ama: Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using
skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721.
doi:10.1080/16864360.2016.1150718
apa: Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of
planar structures using skeletons. Computer-Aided Design and Applications.
Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718
chicago: Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting
of Planar Structures Using Skeletons.” Computer-Aided Design and Applications.
Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718.
ieee: M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures
using skeletons,” Computer-Aided Design and Applications, vol. 13, no.
5. Taylor and Francis, pp. 712–721, 2016.
ista: Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures
using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.
mla: Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.”
Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis,
2016, pp. 712–21, doi:10.1080/16864360.2016.1150718.
short: M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13
(2016) 712–721.
date_created: 2018-12-11T11:51:04Z
date_published: 2016-09-02T00:00:00Z
date_updated: 2021-01-12T06:49:32Z
day: '02'
ddc:
- '004'
- '516'
department:
- _id: HeEd
doi: 10.1080/16864360.2016.1150718
file:
- access_level: open_access
checksum: c746f3a48edb62b588d92ea5d0fd2c0e
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:20Z
date_updated: 2020-07-14T12:44:42Z
file_id: '5206'
file_name: IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf
file_size: 1678369
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
has_accepted_license: '1'
intvolume: ' 13'
issue: '5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '09'
oa: 1
oa_version: Published Version
page: 712 - 721
publication: Computer-Aided Design and Applications
publication_status: published
publisher: Taylor and Francis
publist_id: '6048'
pubrep_id: '694'
quality_controlled: '1'
scopus_import: 1
status: public
title: Generalized offsetting of planar structures using skeletons
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 13
year: '2016'
...
---
_id: '1295'
abstract:
- lang: eng
text: Voronoi diagrams and Delaunay triangulations have been extensively used to
represent and compute geometric features of point configurations. We introduce
a generalization to poset diagrams and poset complexes, which contain order-k
and degree-k Voronoi diagrams and their duals as special cases. Extending a result
of Aurenhammer from 1990, we show how to construct poset diagrams as weighted
Voronoi diagrams of average balls.
acknowledgement: This work is partially supported by the Toposys project FP7-ICT-318493-STREP,
and by ESF under the ACAT Research Network Programme.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
citation:
ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages.
Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030'
apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls
II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier.
https://doi.org/10.1016/j.endm.2016.09.030'
chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier,
2016. https://doi.org/10.1016/j.endm.2016.09.030.'
ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted
averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier,
pp. 169–174, 2016.'
ista: 'Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted
averages. Electronic Notes in Discrete Mathematics. 54, 169–174.'
mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls
II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol.
54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030.'
short: H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics
54 (2016) 169–174.
date_created: 2018-12-11T11:51:12Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:49:41Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.endm.2016.09.030
ec_funded: 1
intvolume: ' 54'
language:
- iso: eng
month: '10'
oa_version: None
page: 169 - 174
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Electronic Notes in Discrete Mathematics
publication_status: published
publisher: Elsevier
publist_id: '5976'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Multiple covers with balls II: Weighted averages'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 54
year: '2016'
...
---
_id: '1292'
abstract:
- lang: eng
text: We give explicit formulas and algorithms for the computation of the Thurston–Bennequin
invariant of a nullhomologous Legendrian knot on a page of a contact open book
and on Heegaard surfaces in convex position. Furthermore, we extend the results
to rationally nullhomologous knots in arbitrary 3-manifolds.
acknowledgement: "The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful
discussions and advice and Christian Evers for helpful remarks on a draft version."
author:
- first_name: Sebastian
full_name: Durst, Sebastian
last_name: Durst
- first_name: Marc
full_name: Kegel, Marc
last_name: Kegel
- first_name: Mirko D
full_name: Klukas, Mirko D
id: 34927512-F248-11E8-B48F-1D18A9856A87
last_name: Klukas
citation:
ama: Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in
open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4
apa: Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin
invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4
chicago: Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin
Invariant in Open Books.” Acta Mathematica Hungarica. Springer, 2016. https://doi.org/10.1007/s10474-016-0648-4.
ieee: S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant
in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer,
pp. 441–455, 2016.
ista: Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant
in open books. Acta Mathematica Hungarica. 150(2), 441–455.
mla: Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open
Books.” Acta Mathematica Hungarica, vol. 150, no. 2, Springer, 2016, pp.
441–55, doi:10.1007/s10474-016-0648-4.
short: S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455.
date_created: 2018-12-11T11:51:11Z
date_published: 2016-12-01T00:00:00Z
date_updated: 2021-01-12T06:49:40Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10474-016-0648-4
intvolume: ' 150'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.00794
month: '12'
oa: 1
oa_version: Preprint
page: 441 - 455
publication: Acta Mathematica Hungarica
publication_status: published
publisher: Springer
publist_id: '6023'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computing the Thurston–Bennequin invariant in open books
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 150
year: '2016'
...
---
_id: '1330'
abstract:
- lang: eng
text: In this paper we investigate the existence of closed billiard trajectories
in not necessarily smooth convex bodies. In particular, we show that if a body
K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K
is acute (in a certain sense), then there is a closed billiard trajectory in K.
acknowledgement: Supported by People Programme (Marie Curie Actions) of the European
Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734].
Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a
ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part
by the Moebius Contest Foundation for Young Scientists, and in part by the Simons
Foundation.
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
citation:
ama: Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel
Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z
apa: Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute
angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z
chicago: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with
Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z.
ieee: A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,”
Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845,
2016.
ista: Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles.
Israel Journal of Mathematics. 216(2), 833–845.
mla: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute
Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016,
pp. 833–45, doi:10.1007/s11856-016-1429-z.
short: A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.
date_created: 2018-12-11T11:51:24Z
date_published: 2016-10-15T00:00:00Z
date_updated: 2021-01-12T06:49:56Z
day: '15'
department:
- _id: HeEd
doi: 10.1007/s11856-016-1429-z
ec_funded: 1
intvolume: ' 216'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1506.06014
month: '10'
oa: 1
oa_version: Preprint
page: 833 - 845
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Israel Journal of Mathematics
publication_status: published
publisher: Springer
publist_id: '5938'
quality_controlled: '1'
scopus_import: 1
status: public
title: Billiards in convex bodies with acute angles
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 216
year: '2016'
...
---
_id: '1360'
abstract:
- lang: eng
text: 'We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard
trajectories in convex bodies, when the length is measured with a (possibly asymmetric)
norm. We prove a lower bound for the length of the shortest closed billiard trajectory,
related to the non-symmetric Mahler problem. With this technique we are able to
give short and elementary proofs to some known results. '
acknowledgement: The first and third authors were supported by the Dynasty Foundation.
The first, second and third authors were supported by the Russian Foundation for
Basic Re- search grant 15-31-20403 (mol a ved).
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
- first_name: Anastasia
full_name: Sharipova, Anastasia
last_name: Sharipova
citation:
ama: Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed
billiard trajectories in asymmetric normed spaces. Proceedings of the American
Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062
apa: Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary
approach to closed billiard trajectories in asymmetric normed spaces. Proceedings
of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062
chicago: Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova.
“Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2016. https://doi.org/10.1090/proc/13062.
ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach
to closed billiard trajectories in asymmetric normed spaces,” Proceedings of
the American Mathematical Society, vol. 144, no. 10. American Mathematical
Society, pp. 4501–4513, 2016.
ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach
to closed billiard trajectories in asymmetric normed spaces. Proceedings of the
American Mathematical Society. 144(10), 4501–4513.
mla: Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories
in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society,
vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.
short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American
Mathematical Society 144 (2016) 4501–4513.
date_created: 2018-12-11T11:51:34Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:50:09Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/13062
ec_funded: 1
intvolume: ' 144'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1401.0442
month: '10'
oa: 1
oa_version: Preprint
page: 4501 - 4513
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5885'
quality_controlled: '1'
scopus_import: 1
status: public
title: Elementary approach to closed billiard trajectories in asymmetric normed spaces
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...
---
_id: '1408'
abstract:
- lang: eng
text: 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map (Formula presented.) on a compact
space K that are invariant with respect to perturbations of f. The perturbations
are arbitrary continuous maps within (Formula presented.) distance r from f for
a given (Formula presented.). The main drawback of the approach is that the computability
of well groups was shown only when (Formula presented.) or (Formula presented.).
Our contribution to the theory of well groups is twofold: on the one hand we improve
on the computability issue, but on the other hand we present a range of examples
where the well groups are incomplete invariants, that is, fail to capture certain
important robust properties of the zero set. For the first part, we identify a
computable subgroup of the well group that is obtained by cap product with the
pullback of the orientation of (Formula presented.) by f. In other words, well
groups can be algorithmically approximated from below. When f is smooth and (Formula
presented.), our approximation of the (Formula presented.)th well group is exact.
For the second part, we find examples of maps (Formula presented.) with all well
groups isomorphic but whose perturbations have different zero sets. We discuss
on a possible replacement of the well groups of vector valued maps by an invariant
of a better descriptive power and computability status.'
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
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. On computability and triviality of well groups. Discrete
& Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2
apa: Franek, P., & Krcál, M. (2016). On computability and triviality of well
groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2
chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well
Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.
ieee: P. Franek and M. Krcál, “On computability and triviality of well groups,”
Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164,
2016.
ista: Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete
& Computational Geometry. 56(1), 126–164.
mla: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.”
Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016,
pp. 126–64, doi:10.1007/s00454-016-9794-2.
short: P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.
date_created: 2018-12-11T11:51:51Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2023-02-23T10:02:11Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-016-9794-2
ec_funded: 1
file:
- access_level: open_access
checksum: e0da023abf6b72abd8c6a8c76740d53c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:55Z
date_updated: 2020-07-14T12:44:53Z
file_id: '4846'
file_name: IST-2016-614-v1+1_s00454-016-9794-2.pdf
file_size: 905303
relation: main_file
file_date_updated: 2020-07-14T12:44:53Z
has_accepted_license: '1'
intvolume: ' 56'
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 126 - 164
project:
- _id: 25F8B9BC-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M01980
name: Robust invariants of Nonlinear Systems
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5799'
pubrep_id: '614'
quality_controlled: '1'
related_material:
record:
- id: '1510'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: On computability and triviality of well groups
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 56
year: '2016'
...
---
_id: '1289'
abstract:
- lang: eng
text: 'Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI)
magnifying endoscopic (ME) images of the stomach, we combine methods from image
processing, topology, geometry, and machine learning to classify patterns into
three classes: oval, tubular and irregular. Training the algorithm on a small
number of images of each type, we achieve a high rate of correct classifications.
The analysis of the learning algorithm reveals that a handful of geometric and
topological features are responsible for the overwhelming majority of decisions.'
article_processing_charge: No
author:
- first_name: Olga
full_name: Dunaeva, Olga
last_name: Dunaeva
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Lukyanov, Anton
last_name: Lukyanov
- first_name: Michael
full_name: Machin, Michael
last_name: Machin
- first_name: Daria
full_name: Malkova, Daria
last_name: Malkova
- first_name: Roman
full_name: Kuvaev, Roman
last_name: Kuvaev
- first_name: Sergey
full_name: Kashin, Sergey
last_name: Kashin
citation:
ama: Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy
images with persistent homology. Pattern Recognition Letters. 2016;83(1):13-22.
doi:10.1016/j.patrec.2015.12.012
apa: Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev,
R., & Kashin, S. (2016). The classification of endoscopy images with persistent
homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2015.12.012
chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria
Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images
with Persistent Homology.” Pattern Recognition Letters. Elsevier, 2016.
https://doi.org/10.1016/j.patrec.2015.12.012.
ieee: O. Dunaeva et al., “The classification of endoscopy images with persistent
homology,” Pattern Recognition Letters, vol. 83, no. 1. Elsevier, pp. 13–22,
2016.
ista: Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin
S. 2016. The classification of endoscopy images with persistent homology. Pattern
Recognition Letters. 83(1), 13–22.
mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent
Homology.” Pattern Recognition Letters, vol. 83, no. 1, Elsevier, 2016,
pp. 13–22, doi:10.1016/j.patrec.2015.12.012.
short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev,
S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.
date_created: 2018-12-11T11:51:10Z
date_published: 2016-11-01T00:00:00Z
date_updated: 2023-02-23T10:04:40Z
day: '01'
ddc:
- '004'
- '514'
department:
- _id: HeEd
doi: 10.1016/j.patrec.2015.12.012
file:
- access_level: open_access
checksum: 33458bbb8c32a339e1adeca6d5a1112d
content_type: application/pdf
creator: dernst
date_created: 2019-04-17T07:55:51Z
date_updated: 2020-07-14T12:44:42Z
file_id: '6334'
file_name: 2016-Edelsbrunner_The_classification.pdf
file_size: 1921113
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
has_accepted_license: '1'
intvolume: ' 83'
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
page: 13 - 22
publication: Pattern Recognition Letters
publication_status: published
publisher: Elsevier
publist_id: '6027'
pubrep_id: '975'
quality_controlled: '1'
related_material:
record:
- id: '1568'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: The classification of endoscopy images with persistent homology
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: 83
year: '2016'
...
---
_id: '1617'
abstract:
- lang: eng
text: 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d
is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of
equal measure and placing a random point inside each of the N=md cubes. We prove
that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d,
where the upper bound with an unspecified constant Cd was proven earlier by Beck.
Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality
and a suitably taylored Bernstein inequality; we have reasons to believe that
the upper bound has the sharp scaling in N. Additional heuristics suggest that
jittered sampling should be able to improve known bounds on the inverse of the
star-discrepancy in the regime N≳dd. We also prove a partition principle showing
that every partition of [0,1]d combined with a jittered sampling construction
gives rise to a set whose expected squared L2-discrepancy is smaller than that
of purely random points.'
acknowledgement: We are grateful to the referee whose suggestions greatly improved
the quality and clarity of the exposition.
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 discrepancy of jittered sampling. Journal
of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003
apa: Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered
sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003
chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003.
ieee: F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,”
Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.
ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling.
Journal of Complexity. 33, 199–216.
mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216,
doi:10.1016/j.jco.2015.11.003.
short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.
date_created: 2018-12-11T11:53:03Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2021-01-12T06:52:02Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.11.003
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1510.00251
month: '04'
oa: 1
oa_version: Submitted Version
page: 199 - 216
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5549'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the discrepancy of jittered sampling
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2016'
...
---
_id: '5806'
abstract:
- lang: eng
text: Although the concept of functional plane for naive plane is studied and reported
in the literature in great detail, no similar study is yet found for naive sphere.
This article exposes the first study in this line, opening up further prospects
of analyzing the topological properties of sphere in the discrete space. We show
that each quadraginta octant Q of a naive sphere forms a bijection with its projected
pixel set on a unique coordinate plane, which thereby serves as the functional
plane of Q, and hence gives rise to merely mono-jumps during back projection.
The other two coordinate planes serve as para-functional and dia-functional planes
for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds
neither of the two. Owing to this, the quadraginta octants form symmetry groups
and subgroups with equivalent jump conditions. We also show a potential application
in generating a special class of discrete 3D circles based on back projection
and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry,
uniqueness, and bounded distance from the underlying real sphere and real plane.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere
with application to circle drawing. In: Discrete Geometry for Computer Imagery.
Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20'
apa: 'Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants
of naive sphere with application to circle drawing. In Discrete Geometry for
Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20'
chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta
Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry
for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.'
ieee: R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive
sphere with application to circle drawing,” in Discrete Geometry for Computer
Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267.
ista: 'Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive
sphere with application to circle drawing. Discrete Geometry for Computer Imagery.
DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS,
vol. 9647, 256–267.'
mla: Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants
of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for
Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.
short: R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer
Nature, Cham, 2016, pp. 256–267.
conference:
end_date: 2016-04-20
location: Nantes, France
name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery'
start_date: 2016-04-18
date_created: 2019-01-08T20:44:37Z
date_published: 2016-04-09T00:00:00Z
date_updated: 2022-01-28T08:10:11Z
day: '09'
department:
- _id: HeEd
doi: 10.1007/978-3-319-32360-2_20
extern: '1'
intvolume: ' 9647'
language:
- iso: eng
month: '04'
oa_version: None
page: 256-267
place: Cham
publication: Discrete Geometry for Computer Imagery
publication_identifier:
eisbn:
- 978-3-319-32360-2
isbn:
- 978-3-319-32359-6
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On functionality of quadraginta octants of naive sphere with application to
circle drawing
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9647
year: '2016'
...
---
_id: '5805'
abstract:
- lang: eng
text: Discretization of sphere in the integer space follows a particular discretization
scheme, which, in principle, conforms to some topological model. This eventually
gives rise to interesting topological properties of a discrete spherical surface,
which need to be investigated for its analytical characterization. This paper
presents some novel results on the local topological properties of the naive model
of discrete sphere. They follow from the bijection of each quadraginta octant
of naive sphere with its projection map called f -map on the corresponding functional
plane and from the characterization of certain jumps in the f-map. As an application,
we have shown how these properties can be used in designing an efficient reconstruction
algorithm for a naive spherical surface from an input voxel set when it is sparse
or noisy.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Nabhasmita
full_name: Sen, Nabhasmita
last_name: Sen
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: 'Sen N, Biswas R, Bhowmick P. On some local topological properties of naive
discrete sphere. In: Computational Topology in Image Context. Vol 9667.
Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23'
apa: 'Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological
properties of naive discrete sphere. In Computational Topology in Image Context
(Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23'
chicago: 'Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological
Properties of Naive Discrete Sphere.” In Computational Topology in Image Context,
9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.'
ieee: 'N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties
of naive discrete sphere,” in Computational Topology in Image Context,
vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.'
ista: 'Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of
naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol.
9667, 253–264.'
mla: Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete
Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature,
2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23.
short: N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context,
Springer Nature, Cham, 2016, pp. 253–264.
conference:
end_date: 2016-06-17
location: Marseille, France
name: 'CTIC: Computational Topology in Image Context'
start_date: 2016-06-15
date_created: 2019-01-08T20:44:24Z
date_published: 2016-06-02T00:00:00Z
date_updated: 2022-01-28T08:01:22Z
day: '02'
department:
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_23
extern: '1'
intvolume: ' 9667'
language:
- iso: eng
month: '06'
oa_version: None
page: 253-264
place: Cham
publication: Computational Topology in Image Context
publication_identifier:
eisbn:
- 978-3-319-39441-1
eissn:
- 1611-3349
isbn:
- 978-3-319-39440-4
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On some local topological properties of naive discrete sphere
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9667
year: '2016'
...
---
_id: '5809'
abstract:
- lang: eng
text: A discrete spherical circle is a topologically well-connected 3D circle in
the integer space, which belongs to a discrete sphere as well as a discrete plane.
It is one of the most important 3D geometric primitives, but has not possibly
yet been studied up to its merit. This paper is a maiden exposition of some of
its elementary properties, which indicates a sense of its profound theoretical
prospects in the framework of digital geometry. We have shown how different types
of discretization can lead to forbidden and admissible classes, when one attempts
to define the discretization of a spherical circle in terms of intersection between
a discrete sphere and a discrete plane. Several fundamental theoretical results
have been presented, the algorithm for construction of discrete spherical circles
has been discussed, and some test results have been furnished to demonstrate its
practicality and usefulness.
article_processing_charge: No
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
- first_name: Valentin E.
full_name: Brimkov, Valentin E.
last_name: Brimkov
citation:
ama: 'Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete
spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer
Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7'
apa: 'Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity
and smoothness of discrete spherical circles. In Combinatorial image analysis
(Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7'
chicago: 'Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity
and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis,
9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.'
ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness
of discrete spherical circles,” in Combinatorial image analysis, vol. 9448,
Cham: Springer Nature, 2016, pp. 86–100.'
ista: 'Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness
of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.'
mla: Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical
Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016,
pp. 86–100, doi:10.1007/978-3-319-26145-4_7.
short: R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis,
Springer Nature, Cham, 2016, pp. 86–100.
conference:
end_date: 2015-11-27
location: Kolkata, India
name: 'IWCIA: International Workshop on Combinatorial Image Analysis'
start_date: 2015-11-24
date_created: 2019-01-08T20:45:19Z
date_published: 2016-01-06T00:00:00Z
date_updated: 2022-01-28T08:13:03Z
day: '06'
department:
- _id: HeEd
doi: 10.1007/978-3-319-26145-4_7
extern: '1'
intvolume: ' 9448'
language:
- iso: eng
month: '01'
oa_version: None
page: 86-100
place: Cham
publication: Combinatorial image analysis
publication_identifier:
eisbn:
- 978-3-319-26145-4
eissn:
- 1611-3349
isbn:
- 978-3-319-26144-7
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On the connectivity and smoothness of discrete spherical circles
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9448
year: '2016'
...
---
_id: '1662'
abstract:
- lang: eng
text: We introduce a modification of the classic notion of intrinsic volume using
persistence moments of height functions. Evaluating the modified first intrinsic
volume on digital approximations of a compact body with smoothly embedded boundary
in Rn, we prove convergence to the first intrinsic volume of the body as the resolution
of the approximation improves. We have weaker results for the other modified intrinsic
volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional
unit ball.
acknowledgement: "This research is partially supported by the Toposys project FP7-ICT-318493-STREP,
and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne
Marie Svane for her comments on an early version of this paper. The second author
wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for
enlightening discussions and their kind hospitality during a visit of their department
in 2014."
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. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004
apa: Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence
of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016.
https://doi.org/10.1016/j.aim.2015.10.004.
ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic
volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703,
2016.
ista: Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic
volume. Advances in Mathematics. 287, 674–703.
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press,
2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.
short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.
date_created: 2018-12-11T11:53:20Z
date_published: 2016-01-10T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '10'
ddc:
- '004'
department:
- _id: HeEd
doi: 10.1016/j.aim.2015.10.004
ec_funded: 1
file:
- access_level: open_access
checksum: f8869ec110c35c852ef6a37425374af7
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:12:10Z
date_updated: 2020-07-14T12:45:10Z
file_id: '4928'
file_name: IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf
file_size: 248985
relation: main_file
file_date_updated: 2020-07-14T12:45:10Z
has_accepted_license: '1'
intvolume: ' 287'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 674 - 703
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '5488'
pubrep_id: '774'
quality_controlled: '1'
related_material:
record:
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Approximation and convergence of the intrinsic volume
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 287
year: '2016'
...
---
_id: '1424'
abstract:
- lang: eng
text: We consider the problem of statistical computations with persistence diagrams,
a summary representation of topological features in data. These diagrams encode
persistent homology, a widely used invariant in topological data analysis. While
several avenues towards a statistical treatment of the diagrams have been explored
recently, we follow an alternative route that is motivated by the success of methods
based on the embedding of probability measures into reproducing kernel Hilbert
spaces. In fact, a positive definite kernel on persistence diagrams has recently
been proposed, connecting persistent homology to popular kernel-based learning
techniques such as support vector machines. However, important properties of that
kernel enabling a principled use in the context of probability measure embeddings
remain to be explored. Our contribution is to close this gap by proving universality
of a variant of the original kernel, and to demonstrate its effective use in twosample
hypothesis testing on synthetic as well as real-world data.
acknowledgement: This work was partially supported by the Austrian Science FUnd, project
no. KLI 00012.
alternative_title:
- Advances in Neural Information Processing Systems
author:
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Marc
full_name: Niethammer, Marc
last_name: Niethammer
- first_name: Weili
full_name: Lin, Weili
last_name: Lin
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
citation:
ama: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data
analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems;
2015:3070-3078.'
apa: 'Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical
topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented
at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information
Processing Systems.'
chicago: Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer.
“Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural
Information Processing Systems, 2015.
ieee: 'R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological
data analysis-A kernel perspective,” presented at the NIPS: Neural Information
Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.'
ista: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological
data analysis-A kernel perspective. NIPS: Neural Information Processing Systems,
Advances in Neural Information Processing Systems, vol. 28, 3070–3078.'
mla: Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective.
Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78.
short: R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information
Processing Systems, 2015, pp. 3070–3078.
conference:
end_date: 2015-12-12
location: Montreal, Canada
name: 'NIPS: Neural Information Processing Systems'
start_date: 2015-12-07
date_created: 2018-12-11T11:51:56Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2021-01-12T06:50:38Z
day: '01'
department:
- _id: HeEd
intvolume: ' 28'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective
month: '12'
oa: 1
oa_version: Submitted Version
page: 3070 - 3078
publication_status: published
publisher: Neural Information Processing Systems
publist_id: '5782'
quality_controlled: '1'
status: public
title: Statistical topological data analysis-A kernel perspective
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2015'
...
---
_id: '1483'
abstract:
- lang: eng
text: Topological data analysis offers a rich source of valuable information to
study vision problems. Yet, so far we lack a theoretically sound connection to
popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In
this work, we establish such a connection by designing a multi-scale kernel for
persistence diagrams, a stable summary representation of topological features
in data. We show that this kernel is positive definite and prove its stability
with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets
for 3D shape classification/retrieval and texture recognition show considerable
performance gains of the proposed method compared to an alternative approach that
is based on the recently introduced persistence landscapes.
author:
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
citation:
ama: 'Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for
topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106'
apa: 'Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale
kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR:
Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106'
chicago: Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable
Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106.
ieee: 'J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel
for topological machine learning,” presented at the CVPR: Computer Vision and
Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.'
ista: 'Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel
for topological machine learning. CVPR: Computer Vision and Pattern Recognition,
4741–4748.'
mla: Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine
Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106.
short: J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.
conference:
end_date: 2015-06-12
location: Boston, MA, USA
name: 'CVPR: Computer Vision and Pattern Recognition'
start_date: 2015-06-07
date_created: 2018-12-11T11:52:17Z
date_published: 2015-10-14T00:00:00Z
date_updated: 2021-01-12T06:51:03Z
day: '14'
department:
- _id: HeEd
doi: 10.1109/CVPR.2015.7299106
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1412.6821
month: '10'
oa: 1
oa_version: Preprint
page: 4741 - 4748
publication_identifier:
eisbn:
- '978-1-4673-6964-0 '
publication_status: published
publisher: IEEE
publist_id: '5709'
scopus_import: 1
status: public
title: A stable multi-scale kernel for topological machine learning
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '1495'
abstract:
- lang: eng
text: 'Motivated by biological questions, we study configurations of equal-sized
disks in the Euclidean plane that neither pack nor cover. Measuring the quality
by the probability that a random point lies in exactly one disk, we show that
the regular hexagonal grid gives the maximum among lattice configurations. '
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
- first_name: Vitaliy
full_name: Kurlin, Vitaliy
last_name: Kurlin
citation:
ama: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings
of the 27th Canadian Conference on Computational Geometry. Vol 2015-August.
Queen’s University; 2015:128-135.'
apa: 'Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk
packing. In Proceedings of the 27th Canadian Conference on Computational Geometry
(Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.'
chicago: Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed
Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational
Geometry, 2015–August:128–35. Queen’s University, 2015.
ieee: H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in
Proceedings of the 27th Canadian Conference on Computational Geometry,
Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.
ista: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings
of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference
on Computational Geometry vol. 2015–August, 128–135.'
mla: Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the
27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s
University, 2015, pp. 128–35.
short: H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th
Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.
conference:
end_date: 2015-08-12
location: Ontario, Canada
name: 'CCCG: Canadian Conference on Computational Geometry'
start_date: 2015-08-10
date_created: 2018-12-11T11:52:21Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2021-01-12T06:51:09Z
day: '01'
department:
- _id: HeEd
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1505.03402
month: '08'
oa: 1
oa_version: Submitted Version
page: 128-135
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the 27th Canadian Conference on Computational Geometry
publication_status: published
publisher: Queen's University
publist_id: '5684'
quality_controlled: '1'
scopus_import: 1
status: public
title: Relaxed disk packing
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 2015-August
year: '2015'
...
---
_id: '1510'
abstract:
- lang: eng
text: 'The concept of well group in a special but important case captures homological
properties of the zero set of a continuous map f from K to R^n on a compact space
K that are invariant with respect to perturbations of f. The perturbations are
arbitrary continuous maps within L_infty distance r from f for a given r >
0. The main drawback of the approach is that the computability of well groups
was shown only when dim K = n or n = 1. Our contribution to the theory of well
groups is twofold: on the one hand we improve on the computability issue, but
on the other hand we present a range of examples where the well groups are incomplete
invariants, that is, fail to capture certain important robust properties of the
zero set. For the first part, we identify a computable subgroup of the well group
that is obtained by cap product with the pullback of the orientation of R^n by
f. In other words, well groups can be algorithmically approximated from below.
When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well
group is exact. For the second part, we find examples of maps f, f'' from K to
R^n with all well groups isomorphic but whose perturbations have different zero
sets. We discuss on a possible replacement of the well groups of vector valued
maps by an invariant of a better descriptive power and computability status. '
alternative_title:
- LIPIcs
author:
- first_name: Peter
full_name: Franek, Peter
id: 473294AE-F248-11E8-B48F-1D18A9856A87
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. On computability and triviality of well groups. In: Vol
34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842'
apa: 'Franek, P., & Krcál, M. (2015). On computability and triviality of well
groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational
Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SOCG.2015.842'
chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well
Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842.
ieee: 'P. Franek and M. Krcál, “On computability and triviality of well groups,”
presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands,
2015, vol. 34, pp. 842–856.'
ista: 'Franek P, Krcál M. 2015. On computability and triviality of well groups.
SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.'
mla: Franek, Peter, and Marek Krcál. On Computability and Triviality of Well
Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015,
pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842.
short: P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2015, pp. 842–856.
conference:
end_date: 2015-06-25
location: Eindhoven, Netherlands
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2015-06-22
date_created: 2018-12-11T11:52:26Z
date_published: 2015-06-11T00:00:00Z
date_updated: 2023-02-21T17:02:57Z
day: '11'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.4230/LIPIcs.SOCG.2015.842
ec_funded: 1
file:
- access_level: open_access
checksum: 49eb5021caafaabe5356c65b9c5f8c9c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:19Z
date_updated: 2020-07-14T12:44:59Z
file_id: '5001'
file_name: IST-2016-503-v1+1_32.pdf
file_size: 623563
relation: main_file
file_date_updated: 2020-07-14T12:44:59Z
has_accepted_license: '1'
intvolume: ' 34'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 842 - 856
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '5667'
pubrep_id: '503'
quality_controlled: '1'
related_material:
record:
- id: '1408'
relation: later_version
status: public
scopus_import: 1
status: public
title: On computability and triviality of well groups
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: 34
year: '2015'
...
---
_id: '1531'
abstract:
- lang: eng
text: The Heat Kernel Signature (HKS) is a scalar quantity which is derived from
the heat kernel of a given shape. Due to its robustness, isometry invariance,
and multiscale nature, it has been successfully applied in many geometric applications.
From a more general point of view, the HKS can be considered as a descriptor of
the metric of a Riemannian manifold. Given a symmetric positive definite tensor
field we may interpret it as the metric of some Riemannian manifold and thereby
apply the HKS to visualize and analyze the given tensor data. In this paper, we
propose a generalization of this approach that enables the treatment of indefinite
tensor fields, like the stress tensor, by interpreting them as a generator of
a positive definite tensor field. To investigate the usefulness of this approach
we consider the stress tensor from the two-point-load model example and from a
mechanical work piece.
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. Visualizing symmetric indefinite 2D tensor
fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40.
1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13'
apa: Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite
2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz
(Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued
Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13
chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric
Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data, edited by
Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13.
ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D
tensor fields using The Heat Kernel Signature,” in Visualization and Processing
of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz
and T. Schultz, Eds. Springer, 2015, pp. 257–267.
ista: 'Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D
tensor fields using The Heat Kernel Signature. In: Visualization and Processing
of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization,
vol. 40, 257–267.'
mla: Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields
Using The Heat Kernel Signature.” Visualization and Processing of Higher Order
Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz,
1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13.
short: V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization
and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer,
2015, pp. 257–267.
date_created: 2018-12-11T11:52:33Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2022-06-10T09:50:14Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-319-15090-1_13
edition: '1'
editor:
- first_name: Ingrid
full_name: Hotz, Ingrid
last_name: Hotz
- first_name: Thomas
full_name: Schultz, Thomas
last_name: Schultz
intvolume: ' 40'
language:
- iso: eng
month: '01'
oa_version: None
page: 257 - 267
publication: Visualization and Processing of Higher Order Descriptors for Multi-Valued
Data
publication_identifier:
isbn:
- 978-3-319-15089-5
publication_status: published
publisher: Springer
publist_id: '5640'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 40
year: '2015'
...
---
_id: '1555'
abstract:
- lang: eng
text: We show that incorporating spatial dispersal of individuals into a simple
vaccination epidemic model may give rise to a model that exhibits rich dynamical
behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as
a basis, we describe the spread of an infectious disease in a population split
into two regions. In each subpopulation, both forward and backward bifurcations
can occur. This implies that for disconnected regions the two-patch system may
admit several steady states. We consider traveling between the regions and investigate
the impact of spatial dispersal of individuals on the model dynamics. We establish
conditions for the existence of multiple nontrivial steady states in the system,
and we study the structure of the equilibria. The mathematical analysis reveals
an unusually rich dynamical behavior, not normally found in the simple epidemic
models. In addition to the disease-free equilibrium, eight endemic equilibria
emerge from backward transcritical and saddle-node bifurcation points, forming
an interesting bifurcation diagram. Stability of steady states, their bifurcations,
and the global dynamics are investigated with analytical tools, numerical simulations,
and rigorous set-oriented numerical computations.
acknowledgement: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg,
Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported
by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework
Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de
Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de
Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia
e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645
(ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559
in the framework of the EPIDELAY project.
article_processing_charge: No
article_type: original
author:
- first_name: Diána
full_name: Knipl, Diána
last_name: Knipl
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
- first_name: Gergely
full_name: Röst, Gergely
last_name: Röst
citation:
ama: Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination
model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017.
doi:10.1137/140993934
apa: Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure
in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems.
Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934
chicago: Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure
in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems.
Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934.
ieee: D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two
patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol.
14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.
ista: Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch
vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.
mla: Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination
Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society
for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934.
short: D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems
14 (2015) 980–1017.
date_created: 2018-12-11T11:52:42Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T06:51:34Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1137/140993934
ec_funded: 1
intvolume: ' 14'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://discovery.ucl.ac.uk/1473750/1/99393.pdf
month: '01'
oa: 1
oa_version: Published Version
page: 980 - 1017
project:
- _id: 255F06BE-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '622033'
name: Persistent Homology - Images, Data and Maps
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
eissn:
- 1536-0040
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '5616'
quality_controlled: '1'
scopus_import: 1
status: public
title: Rich bifurcation structure in a two patch vaccination model
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2015'
...
---
_id: '1568'
abstract:
- lang: eng
text: Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI)
magnifying endoscopy (ME) images of the stomach, we combine methods from image
processing, computational topology, and machine learning to classify patterns
into normal, tubular, vessel. Training the algorithm on a small number of images
of each type, we achieve a high rate of correct classifications. The analysis
of the learning algorithm reveals that a handful of geometric and topological
features are responsible for the overwhelming majority of decisions.
acknowledgement: This research is supported by the project No. 477 of P.G. Demidov
Yaroslavl State University within State Assignment for Research.
author:
- first_name: Olga
full_name: Dunaeva, Olga
last_name: Dunaeva
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Anton
full_name: Lukyanov, Anton
last_name: Lukyanov
- first_name: Michael
full_name: Machin, Michael
last_name: Machin
- first_name: Daria
full_name: Malkova, Daria
last_name: Malkova
citation:
ama: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification
of endoscopy images with persistent homology. In: Proceedings - 16th International
Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE;
2015:7034731. doi:10.1109/SYNASC.2014.81'
apa: 'Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D.
(2015). The classification of endoscopy images with persistent homology. In Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81'
chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and
Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.”
In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms
for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.
ieee: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The
classification of endoscopy images with persistent homology,” in Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing, Timisoara, Romania, 2015, p. 7034731.
ista: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification
of endoscopy images with persistent homology. Proceedings - 16th International
Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC:
Symbolic and Numeric Algorithms for Scientific Computing, 7034731.'
mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent
Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric
Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81.
short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings
- 16th International Symposium on Symbolic and Numeric Algorithms for Scientific
Computing, IEEE, 2015, p. 7034731.
conference:
end_date: 2014-09-25
location: Timisoara, Romania
name: 'SYNASC: Symbolic and Numeric Algorithms for Scientific Computing'
start_date: 2014-09-22
date_created: 2018-12-11T11:52:46Z
date_published: 2015-02-05T00:00:00Z
date_updated: 2023-02-21T16:57:29Z
day: '05'
department:
- _id: HeEd
doi: 10.1109/SYNASC.2014.81
language:
- iso: eng
month: '02'
oa_version: None
page: '7034731'
publication: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms
for Scientific Computing
publication_status: published
publisher: IEEE
publist_id: '5603'
quality_controlled: '1'
related_material:
record:
- id: '1289'
relation: later_version
status: public
scopus_import: 1
status: public
title: The classification of endoscopy images with persistent homology
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2015'
...
---
_id: '1567'
abstract:
- lang: eng
text: My personal journey to the fascinating world of geometric forms started more
than 30 years ago with the invention of alpha shapes in the plane. It took about
10 years before we generalized the concept to higher dimensions, we produced working
software with a graphics interface for the three-dimensional case. At the same
time, we added homology to the computations. Needless to say that this foreshadowed
the inception of persistent homology, because it suggested the study of filtrations
to capture the scale of a shape or data set. Importantly, this method has fast
algorithms. The arguably most useful result on persistent homology is the stability
of its diagrams under perturbations.
alternative_title:
- LNCS
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
citation:
ama: 'Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International
Symposium. Vol 9411. Springer Nature; 2015.'
apa: 'Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd
International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer
Nature.'
chicago: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In
23rd International Symposium, Vol. 9411. Springer Nature, 2015.
ieee: H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd
International Symposium, Los Angeles, CA, United States, 2015, vol. 9411.
ista: 'Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International
Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.'
mla: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd
International Symposium, vol. 9411, Springer Nature, 2015.
short: H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.
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: 2018-12-11T11:52:46Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2022-01-28T08:25:00Z
day: '01'
department:
- _id: HeEd
intvolume: ' 9411'
language:
- iso: eng
month: '01'
oa_version: None
publication: 23rd International Symposium
publication_status: published
publisher: Springer Nature
publist_id: '5604'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Shape, homology, persistence, and stability
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9411
year: '2015'
...
---
_id: '1563'
abstract:
- lang: eng
text: For a given self-map $f$ of $M$, a closed smooth connected and simply-connected
manifold of dimension $m\geq 4$, we provide an algorithm for estimating the values
of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic
points in the smooth homotopy class of $f$. Our results are based on the combinatorial
scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed
Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm
programmed in C++ is publicly available at {\tt http://www.pawelpilarczyk.com/combtop/}.
author:
- first_name: Grzegorz
full_name: Graff, Grzegorz
last_name: Graff
- first_name: Pawel
full_name: Pilarczyk, Pawel
id: 3768D56A-F248-11E8-B48F-1D18A9856A87
last_name: Pilarczyk
citation:
ama: Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number
of periodic points for smooth self-maps of simply-connected manifolds. Topological
Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014
apa: Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating
the minimal number of periodic points for smooth self-maps of simply-connected
manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder
Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014
chicago: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder
Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.
ieee: G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal
number of periodic points for smooth self-maps of simply-connected manifolds,”
Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder
Center for Nonlinear Studies, pp. 273–286, 2015.
ista: Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal
number of periodic points for smooth self-maps of simply-connected manifolds.
Topological Methods in Nonlinear Analysis. 45(1), 273–286.
mla: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating
the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected
Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1,
Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014.
short: G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015)
273–286.
date_created: 2018-12-11T11:52:44Z
date_published: 2015-03-01T00:00:00Z
date_updated: 2021-01-12T06:51:37Z
day: '01'
department:
- _id: HeEd
doi: 10.12775/TMNA.2015.014
intvolume: ' 45'
issue: '1'
language:
- iso: eng
month: '03'
oa_version: None
page: 273 - 286
publication: Topological Methods in Nonlinear Analysis
publication_status: published
publisher: Juliusz Schauder Center for Nonlinear Studies
publist_id: '5608'
quality_controlled: '1'
scopus_import: 1
status: public
title: An algorithmic approach to estimating the minimal number of periodic points
for smooth self-maps of simply-connected manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2015'
...
---
_id: '1578'
abstract:
- lang: eng
text: We prove that the dual of the digital Voronoi diagram constructed by flooding
the plane from the data points gives a geometrically and topologically correct
dual triangulation. This provides the proof of correctness for recently developed
GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional
Delaunay triangulations.
acknowledgement: "The research of the second author is partially supported by NSF
under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n"
author:
- first_name: Thanhtung
full_name: Cao, Thanhtung
last_name: Cao
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Tiowseng
full_name: Tan, Tiowseng
last_name: Tan
citation:
ama: Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital
Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001
apa: Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically
correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001
chicago: Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations
from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry.
Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001.
ieee: T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct
digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier,
pp. 507–519, 2015.
ista: Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct
digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.
mla: Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi
Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp.
507–19, doi:10.1016/j.comgeo.2015.04.001.
short: T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.
date_created: 2018-12-11T11:52:49Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2021-01-12T06:51:43Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.04.001
intvolume: ' 48'
issue: '7'
language:
- iso: eng
month: '08'
oa_version: None
page: 507 - 519
publication: Computational Geometry
publication_status: published
publisher: Elsevier
publist_id: '5593'
quality_controlled: '1'
scopus_import: 1
status: public
title: Triangulations from topologically correct digital Voronoi diagrams
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2015'
...
---
_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.
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: 2023-02-23T10:05:22Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2015.01.004
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'
issue: '5'
language:
- iso: eng
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2015'
...
---
_id: '1582'
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.
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. Weighted straight skeletons
in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133.
doi:10.1016/j.comgeo.2014.08.006'
apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted
straight skeletons in the plane. Computational Geometry: Theory and Applications.
Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006'
chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory
and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.'
ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight
skeletons in the plane,” Computational Geometry: Theory and Applications,
vol. 48, no. 2. Elsevier, pp. 120–133, 2015.'
ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight
skeletons in the plane. Computational Geometry: Theory and Applications. 48(2),
120–133.'
mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational
Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33,
doi:10.1016/j.comgeo.2014.08.006.'
short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry:
Theory and Applications 48 (2015) 120–133.'
date_created: 2018-12-11T11:52:51Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2023-02-23T10:05:27Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.006
file:
- access_level: open_access
checksum: c1ef67f6ec925e12f73a96b8fe285ab4
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:28Z
date_updated: 2020-07-14T12:45:02Z
file_id: '5215'
file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf
file_size: 505987
relation: main_file
file_date_updated: 2020-07-14T12:45:02Z
has_accepted_license: '1'
intvolume: ' 48'
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 120 - 133
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5589'
pubrep_id: '474'
quality_controlled: '1'
related_material:
record:
- id: '1584'
relation: other
status: public
scopus_import: 1
status: public
title: 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2015'
...
---
_id: '1583'
abstract:
- lang: eng
text: We study the characteristics of straight skeletons of monotone polygonal chains
and use them to devise an algorithm for computing positively weighted straight
skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space,
where n denotes the number of vertices of the polygon.
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. A simple algorithm for computing
positively weighted straight skeletons of monotone polygons. Information Processing
Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021
apa: Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple
algorithm for computing positively weighted straight skeletons of monotone polygons.
Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021
chicago: Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader.
“A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone
Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021.
ieee: T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm
for computing positively weighted straight skeletons of monotone polygons,” Information
Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.
ista: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm
for computing positively weighted straight skeletons of monotone polygons. Information
Processing Letters. 115(2), 243–247.
mla: Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted
Straight Skeletons of Monotone Polygons.” Information Processing Letters,
vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021.
short: T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing
Letters 115 (2015) 243–247.
date_created: 2018-12-11T11:52:51Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2021-01-12T06:51:45Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1016/j.ipl.2014.09.021
file:
- access_level: open_access
checksum: 2779a648610c9b5c86d0b51a62816d23
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:18:45Z
date_updated: 2020-07-14T12:45:03Z
file_id: '5367'
file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf
file_size: 270137
relation: main_file
file_date_updated: 2020-07-14T12:45:03Z
has_accepted_license: '1'
intvolume: ' 115'
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 243 - 247
publication: Information Processing Letters
publication_status: published
publisher: Elsevier
publist_id: '5588'
pubrep_id: '473'
quality_controlled: '1'
scopus_import: 1
status: public
title: A simple algorithm for computing positively weighted straight skeletons of
monotone polygons
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: 115
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
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: International Symposium on Graph Drawing'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:54Z
date_published: 2015-11-27T00:00:00Z
date_updated: 2022-01-28T09:10:37Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-27261-0_28
intvolume: ' 9411'
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
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'
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).
date_created: 2018-12-11T11:53:27Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2021-01-12T06:52:30Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2751524
intvolume: ' 62'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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 → ∞.'
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: 2021-01-12T06:52:41Z
day: '14'
department:
- _id: HeEd
doi: 10.1137/140993843
ec_funded: 1
intvolume: ' 47'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 47
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
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.
date_created: 2018-12-11T11:54:14Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2021-01-12T06:53:28Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10955-015-1238-5
ec_funded: 1
intvolume: ' 160'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: arxiv.org/abs/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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 160
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. "
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.
date_created: 2018-12-11T11:54:49Z
date_published: 2015-03-06T00:00:00Z
date_updated: 2021-01-12T06:54:12Z
day: '06'
department:
- _id: HeEd
doi: 10.1016/j.physleta.2014.12.010
intvolume: ' 379'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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.
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: 2021-01-12T06:54:53Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10208-014-9223-y
ec_funded: 1
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'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2015'
...
---
_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.'
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.'
date_created: 2018-12-11T11:54:06Z
date_published: 2015-06-03T00:00:00Z
date_updated: 2023-02-23T10:59:19Z
day: '03'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.010
ec_funded: 1
intvolume: ' 48'
issue: '8'
language:
- iso: eng
month: '06'
oa_version: None
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: '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
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
- 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).
date_created: 2018-12-11T11:54:02Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-02-23T14:06:33Z
day: '01'
ddc:
- '000'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657
file:
- access_level: open_access
checksum: d20f26461ca575276ad3ed9ce4bfc787
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:30Z
date_updated: 2020-07-14T12:45:16Z
file_id: '5150'
file_name: IST-2016-454-v1+1_journal.pone.0127657.pdf
file_size: 1850825
relation: main_file
file_date_updated: 2020-07-14T12:45:16Z
has_accepted_license: '1'
intvolume: ' 10'
issue: '6'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: PLoS One
publication_status: published
publisher: Public Library of Science
publist_id: '5318'
pubrep_id: '454'
quality_controlled: '1'
related_material:
record:
- id: '9737'
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
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
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
- 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: 2023-02-23T10:14:42Z
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: '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.
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.
date_created: 2018-12-11T11:54:02Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.06.002
intvolume: ' 31'
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:
record:
- id: '1399'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: A Koksma-Hlawka inequality for general discrepancy systems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2015'
...
---
_id: '1399'
abstract:
- lang: eng
text: This thesis is concerned with the computation and approximation of intrinsic
volumes. Given a smooth body M and a certain digital approximation of it, we develop
algorithms to approximate various intrinsic volumes of M using only measurements
taken from its digital approximations. The crucial idea behind our novel algorithms
is to link the recent theory of persistent homology to the theory of intrinsic
volumes via the Crofton formula from integral geometry and, in particular, via
Euler characteristic computations. Our main contributions are a multigrid convergent
digital algorithm to compute the first intrinsic volume of a solid body in R^n
as well as an appropriate integration pipeline to approximate integral-geometric
integrals defined over the Grassmannian manifold.
alternative_title:
- ISTA Thesis
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
citation:
ama: Pausinger F. On the approximation of intrinsic volumes. 2015.
apa: Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute
of Science and Technology Austria.
chicago: Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute
of Science and Technology Austria, 2015.
ieee: F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science
and Technology Austria, 2015.
ista: Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of
Science and Technology Austria.
mla: Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute
of Science and Technology Austria, 2015.
short: F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science
and Technology Austria, 2015.
date_created: 2018-12-11T11:51:48Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
degree_awarded: PhD
department:
- _id: HeEd
language:
- iso: eng
month: '06'
oa_version: None
page: '144'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '5808'
related_material:
record:
- id: '1662'
relation: part_of_dissertation
status: public
- id: '1792'
relation: part_of_dissertation
status: public
- id: '2255'
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
title: On the approximation of intrinsic volumes
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2015'
...
---
_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: 2022-06-21T12:01:47Z
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: '1816'
abstract:
- lang: eng
text: Watermarking techniques for vector graphics dislocate vertices in order to
embed imperceptible, yet detectable, statistical features into the input data.
The embedding process may result in a change of the topology of the input data,
e.g., by introducing self-intersections, which is undesirable or even disastrous
for many applications. In this paper we present a watermarking framework for two-dimensional
vector graphics that employs conventional watermarking techniques but still provides
the guarantee that the topology of the input data is preserved. The geometric
part of this framework computes so-called maximum perturbation regions (MPR) of
vertices. We propose two efficient algorithms to compute MPRs based on Voronoi
diagrams and constrained triangulations. Furthermore, we present two algorithms
to conditionally correct the watermarked data in order to increase the watermark
embedding capacity and still guarantee topological correctness. While we focus
on the watermarking of input formed by straight-line segments, one of our approaches
can also be extended to circular arcs. We conclude the paper by demonstrating
and analyzing the applicability of our framework in conjunction with two well-known
watermarking techniques.
acknowledgement: 'Work by Martin Held and Stefan Huber was supported by Austrian Science
Fund (FWF): L367-N15 and P25816-N15.'
author:
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Peter
full_name: Meerwald, Peter
last_name: Meerwald
- first_name: Roland
full_name: Kwitt, Roland
last_name: Kwitt
citation:
ama: Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector
graphics. International Journal of Computational Geometry and Applications.
2014;24(1):61-86. doi:10.1142/S0218195914500034
apa: Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving
watermarking of vector graphics. International Journal of Computational Geometry
and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034
chicago: Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving
Watermarking of Vector Graphics.” International Journal of Computational Geometry
and Applications. World Scientific Publishing, 2014. https://doi.org/10.1142/S0218195914500034.
ieee: S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking
of vector graphics,” International Journal of Computational Geometry and Applications,
vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.
ista: Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking
of vector graphics. International Journal of Computational Geometry and Applications.
24(1), 61–86.
mla: Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.”
International Journal of Computational Geometry and Applications, vol.
24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034.
short: S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational
Geometry and Applications 24 (2014) 61–86.
date_created: 2018-12-11T11:54:10Z
date_published: 2014-03-16T00:00:00Z
date_updated: 2021-01-12T06:53:23Z
day: '16'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1142/S0218195914500034
file:
- access_level: open_access
checksum: be45c133ab4d43351260e21beaa8f4b1
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:43Z
date_updated: 2020-07-14T12:45:17Z
file_id: '4704'
file_name: IST-2016-443-v1+1_S0218195914500034.pdf
file_size: 991734
relation: main_file
file_date_updated: 2020-07-14T12:45:17Z
has_accepted_license: '1'
intvolume: ' 24'
issue: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 61 - 86
publication: International Journal of Computational Geometry and Applications
publication_status: published
publisher: World Scientific Publishing
publist_id: '5290'
pubrep_id: '443'
quality_controlled: '1'
scopus_import: 1
status: public
title: Topology-preserving watermarking of vector graphics
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2014'
...
---
_id: '1842'
abstract:
- lang: eng
text: We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2
outerplanar triangulations in both convex and general cases. We also prove that
the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by
O(n3) and O(n10), in the convex and general case, respectively. We then apply
similar methods to prove an (Formula presented.) upper bound on the Ramsey number
of a path with n ordered vertices.
acknowledgement: Marek Krčál was supported by the ERC Advanced Grant No. 267165.
author:
- first_name: Josef
full_name: Cibulka, Josef
last_name: Cibulka
- first_name: Pu
full_name: Gao, Pu
last_name: Gao
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Tomáš
full_name: Valla, Tomáš
last_name: Valla
- first_name: Pavel
full_name: Valtr, Pavel
last_name: Valtr
citation:
ama: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number
of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79.
doi:10.1007/s00454-014-9646-x
apa: Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the
geometric ramsey number of outerplanar graphs. Discrete & Computational
Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x
chicago: Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On
the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational
Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x.
ieee: J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey
number of outerplanar graphs,” Discrete & Computational Geometry, vol.
53, no. 1. Springer, pp. 64–79, 2014.
ista: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey
number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79.
mla: Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.”
Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014,
pp. 64–79, doi:10.1007/s00454-014-9646-x.
short: J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational
Geometry 53 (2014) 64–79.
date_created: 2018-12-11T11:54:18Z
date_published: 2014-11-14T00:00:00Z
date_updated: 2021-01-12T06:53:33Z
day: '14'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-014-9646-x
intvolume: ' 53'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.7004
month: '11'
oa: 1
oa_version: Submitted Version
page: 64 - 79
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5260'
scopus_import: 1
status: public
title: On the geometric ramsey number of outerplanar graphs
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2014'
...
---
_id: '1876'
abstract:
- lang: eng
text: We study densities of functionals over uniformly bounded triangulations of
a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay
triangulation if this is the case for finite sets.
article_processing_charge: No
article_type: original
author:
- first_name: Nikolai
full_name: Dolbilin, Nikolai
last_name: Dolbilin
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Alexey
full_name: Glazyrin, Alexey
last_name: Glazyrin
- first_name: Oleg
full_name: Musin, Oleg
last_name: Musin
citation:
ama: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 2014;14(3):491-504. doi:10.17323/1609-4514-2014-14-3-491-504
apa: Dolbilin, N., Edelsbrunner, H., Glazyrin, A., & Musin, O. (2014). Functionals
on triangulations of delaunay sets. Moscow Mathematical Journal. Independent
University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-3-491-504
chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin.
“Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal.
Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504.
ieee: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations
of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent
University of Moscow, pp. 491–504, 2014.
ista: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations
of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.
mla: Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.”
Moscow Mathematical Journal, vol. 14, no. 3, Independent University of
Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504.
short: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical
Journal 14 (2014) 491–504.
date_created: 2018-12-11T11:54:29Z
date_published: 2014-07-01T00:00:00Z
date_updated: 2022-03-03T11:47:09Z
day: '01'
department:
- _id: HeEd
doi: 10.17323/1609-4514-2014-14-3-491-504
external_id:
arxiv:
- '1211.7053'
intvolume: ' 14'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1211.7053
month: '07'
oa: 1
oa_version: Submitted Version
page: 491 - 504
publication: Moscow Mathematical Journal
publication_identifier:
issn:
- '16093321'
publication_status: published
publisher: Independent University of Moscow
publist_id: '5220'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functionals on triangulations of delaunay sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...
---
_id: '1929'
abstract:
- lang: eng
text: We propose an algorithm for the generalization of cartographic objects that
can be used to represent maps on different scales.
acknowledgement: We would like to offer our special thanks to students of the Department
of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev
for participation in developing the program and assistance in preparation of test
data. This work was supported by grant 11.G34.31.0053 from the government of the
Russian Federation.
article_processing_charge: No
article_type: original
author:
- first_name: V V
full_name: Alexeev, V V
last_name: Alexeev
- first_name: V G
full_name: Bogaevskaya, V G
last_name: Bogaevskaya
- first_name: M M
full_name: Preobrazhenskaya, M M
last_name: Preobrazhenskaya
- first_name: A Y
full_name: Ukhalov, A Y
last_name: Ukhalov
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Olga
full_name: Yakimova, Olga
last_name: Yakimova
citation:
ama: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H,
Yakimova O. An algorithm for cartographic generalization that preserves global
topology. Journal of Mathematical Sciences. 2014;203(6):754-760. doi:10.1007/s10958-014-2165-8
apa: Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y.,
Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization
that preserves global topology. Journal of Mathematical Sciences. Springer.
https://doi.org/10.1007/s10958-014-2165-8
chicago: Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert
Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization
That Preserves Global Topology.” Journal of Mathematical Sciences. Springer,
2014. https://doi.org/10.1007/s10958-014-2165-8.
ieee: V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H.
Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that
preserves global topology,” Journal of Mathematical Sciences, vol. 203,
no. 6. Springer, pp. 754–760, 2014.
ista: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner
H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves
global topology. Journal of Mathematical Sciences. 203(6), 754–760.
mla: Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves
Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer,
2014, pp. 754–60, doi:10.1007/s10958-014-2165-8.
short: V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner,
O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-11-16T00:00:00Z
date_updated: 2022-05-24T10:39:06Z
day: '16'
department:
- _id: HeEd
doi: 10.1007/s10958-014-2165-8
intvolume: ' 203'
issue: '6'
language:
- iso: eng
month: '11'
oa_version: None
page: 754 - 760
publication: Journal of Mathematical Sciences
publication_identifier:
eissn:
- 1573-8795
issn:
- 1072-3374
publication_status: published
publisher: Springer
publist_id: '5165'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An algorithm for cartographic generalization that preserves global topology
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 203
year: '2014'
...
---
_id: '1930'
abstract:
- lang: eng
text: (Figure Presented) Data acquisition, numerical inaccuracies, and sampling
often introduce noise in measurements and simulations. Removing this noise is
often necessary for efficient analysis and visualization of this data, yet many
denoising techniques change the minima and maxima of a scalar field. For example,
the extrema can appear or disappear, spatially move, and change their value. This
can lead to wrong interpretations of the data, e.g., when the maximum temperature
over an area is falsely reported being a few degrees cooler because the denoising
method is unaware of these features. Recently, a topological denoising technique
based on a global energy optimization was proposed, which allows the topology-controlled
denoising of 2D scalar fields. While this method preserves the minima and maxima,
it is constrained by the size of the data. We extend this work to large 2D data
and medium-sized 3D data by introducing a novel domain decomposition approach.
It allows processing small patches of the domain independently while still avoiding
the introduction of new critical points. Furthermore, we propose an iterative
refinement of the solution, which decreases the optimization energy compared to
the previous approach and therefore gives smoother results that are closer to
the input. We illustrate our technique on synthetic and real-world 2D and 3D data
sets that highlight potential applications.
acknowledgement: RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship;
MPC-VCC
author:
- first_name: David
full_name: Günther, David
last_name: Günther
- first_name: Alec
full_name: Jacobson, Alec
last_name: Jacobson
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
- first_name: Hans
full_name: Seidel, Hans
last_name: Seidel
- first_name: Olga
full_name: Sorkine Hornung, Olga
last_name: Sorkine Hornung
- first_name: Tino
full_name: Weinkauf, Tino
last_name: Weinkauf
citation:
ama: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594.
doi:10.1109/TVCG.2014.2346432
apa: Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O.,
& Weinkauf, T. (2014). Fast and memory-efficient topological denoising of
2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics.
IEEE. https://doi.org/10.1109/TVCG.2014.2346432
chicago: Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine
Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics.
IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432.
ieee: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and
T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar
fields,” IEEE Transactions on Visualization and Computer Graphics, vol.
20, no. 12. IEEE, pp. 2585–2594, 2014.
ista: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf
T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields.
IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.
mla: Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of
2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics,
vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432.
short: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T.
Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.
date_created: 2018-12-11T11:54:46Z
date_published: 2014-12-31T00:00:00Z
date_updated: 2021-01-12T06:54:09Z
day: '31'
department:
- _id: HeEd
doi: 10.1109/TVCG.2014.2346432
intvolume: ' 20'
issue: '12'
language:
- iso: eng
month: '12'
oa_version: None
page: 2585 - 2594
publication: IEEE Transactions on Visualization and Computer Graphics
publication_status: published
publisher: IEEE
publist_id: '5164'
quality_controlled: '1'
scopus_import: 1
status: public
title: Fast and memory-efficient topological denoising of 2D and 3D scalar fields
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2014'
...
---
_id: '2043'
abstract:
- lang: eng
text: Persistent homology is a popular and powerful tool for capturing topological
features of data. Advances in algorithms for computing persistent homology have
reduced the computation time drastically – as long as the algorithm does not exhaust
the available memory. Following up on a recently presented parallel method for
persistence computation on shared memory systems [1], we demonstrate that a simple
adaption of the standard reduction algorithm leads to a variant for distributed
systems. Our algorithmic design ensures that the data is distributed over the
nodes without redundancy; this permits the computation of much larger instances
than on a single machine. Moreover, we observe that the parallelism at least compensates
for the overhead caused by communication between nodes, and often even speeds
up the computation compared to sequential and even parallel shared memory algorithms.
In our experiments, we were able to compute the persistent homology of filtrations
with more than a billion (109) elements within seconds on a cluster with 32 nodes
using less than 6GB of memory per node.
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
orcid: 0000-0002-8030-9299
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
citation:
ama: 'Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology.
In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering
and Experiments. Society of Industrial and Applied Mathematics; 2014:31-38.
doi:10.1137/1.9781611973198.4'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation
of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of
the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland,
USA: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4'
chicago: Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation
of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering
and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society
of Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4.
ieee: U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent
homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments,
Portland, USA, 2014, pp. 31–38.
ista: 'Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent
homology. Proceedings of the Workshop on Algorithm Engineering and Experiments.
ALENEX: Algorithm Engineering and Experiments, 31–38.'
mla: Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings
of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch
and Ulrich Meyer, Society of Industrial and Applied Mathematics, 2014, pp. 31–38,
doi:10.1137/1.9781611973198.4.
short: U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings
of the Workshop on Algorithm Engineering and Experiments, Society of Industrial
and Applied Mathematics, 2014, pp. 31–38.
conference:
end_date: 2014-01-05
location: Portland, USA
name: 'ALENEX: Algorithm Engineering and Experiments'
start_date: 2014-01-05
date_created: 2018-12-11T11:55:23Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:54:56Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973198.4
ec_funded: 1
editor:
- first_name: Catherine
full_name: ' McGeoch, Catherine'
last_name: ' McGeoch'
- first_name: Ulrich
full_name: Meyer, Ulrich
last_name: Meyer
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.0710
month: '01'
oa: 1
oa_version: Submitted Version
page: 31 - 38
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Workshop on Algorithm Engineering and Experiments
publication_status: published
publisher: Society of Industrial and Applied Mathematics
publist_id: '5008'
quality_controlled: '1'
scopus_import: 1
status: public
title: Distributed computation of persistent homology
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2044'
abstract:
- lang: eng
text: We present a parallel algorithm for computing the persistent homology of a
filtered chain complex. Our approach differs from the commonly used reduction
algorithm by first computing persistence pairs within local chunks, then simplifying
the unpaired columns, and finally applying standard reduction on the simplified
matrix. The approach generalizes a technique by Günther et al., which uses discrete
Morse Theory to compute persistence; we derive the same worst-case complexity
bound in a more general context. The algorithm employs several practical optimization
techniques, which are of independent interest. Our sequential implementation of
the algorithm is competitive with state-of-the-art methods, and we further improve
the performance through parallel computation.
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
orcid: 0000-0002-8030-9299
- first_name: Jan
full_name: Reininghaus, Jan
id: 4505473A-F248-11E8-B48F-1D18A9856A87
last_name: Reininghaus
citation:
ama: 'Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent
Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological
Methods in Data Analysis and Visualization III. Mathematics and Visualization.
Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7'
apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing
Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R.
Peikert (Eds.), Topological Methods in Data Analysis and Visualization III
(pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7'
chicago: 'Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress:
Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis
and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci,
and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7.'
ieee: 'U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent
Homology in Chunks,” in Topological Methods in Data Analysis and Visualization
III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014,
pp. 103–117.'
ista: 'Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent
Homology in Chunks. In: Topological Methods in Data Analysis and Visualization
III. , 103–117.'
mla: 'Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in
Chunks.” Topological Methods in Data Analysis and Visualization III, edited
by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.'
short: U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci,
R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III,
Springer, 2014, pp. 103–117.
date_created: 2018-12-11T11:55:23Z
date_published: 2014-03-19T00:00:00Z
date_updated: 2021-01-12T06:54:56Z
day: '19'
department:
- _id: HeEd
doi: 10.1007/978-3-319-04099-8_7
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
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1303.0477
month: '03'
oa: 1
oa_version: Submitted Version
page: 103 - 117
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_status: published
publisher: Springer
publist_id: '5007'
quality_controlled: '1'
scopus_import: 1
series_title: Mathematics and Visualization
status: public
title: 'Clear and Compress: Computing Persistent Homology in Chunks'
type: book_chapter
user_id: 4435EBFC-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).'
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: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582168
ec_funded: 1
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: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2156'
abstract:
- lang: eng
text: We propose a metric for Reeb graphs, called the functional distortion distance.
Under this distance, the Reeb graph is stable against small changes of input functions.
At the same time, it remains discriminative at differentiating input functions.
In particular, the main result is that the functional distortion distance between
two Reeb graphs is bounded from below by the bottleneck distance between both
the ordinary and extended persistence diagrams for appropriate dimensions. As
an application of our results, we analyze a natural simplification scheme for
Reeb graphs, and show that persistent features in Reeb graph remains persistent
under simplification. Understanding the stability of important features of the
Reeb graph under simplification is an interesting problem on its own right, and
critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).
acknowledgement: National Science Foundation under grants CCF-1319406, CCF-1116258.
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Xiaoyin
full_name: Ge, Xiaoyin
last_name: Ge
- first_name: Yusu
full_name: Wang, Yusu
last_name: Wang
citation:
ama: 'Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings
of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169'
apa: 'Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb
graphs. In Proceedings of the Annual Symposium on Computational Geometry
(pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169'
chicago: Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb
Graphs.” In Proceedings of the Annual Symposium on Computational Geometry,
464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.
ieee: U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in
Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan,
2014, pp. 464–473.
ista: 'Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings
of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, 464–473.'
mla: Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings
of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73,
doi:10.1145/2582112.2582169.
short: U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 464–473.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:02Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:39Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582169
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1307.2839
month: '06'
oa: 1
oa_version: Submitted Version
page: 464 - 473
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: '4850'
quality_controlled: '1'
scopus_import: 1
status: public
title: Measuring distance between Reeb graphs
type: conference
user_id: 4435EBFC-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
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
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582167
ec_funded: 1
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: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2177'
abstract:
- lang: eng
text: We give evidence for the difficulty of computing Betti numbers of simplicial
complexes over a finite field. We do this by reducing the rank computation for
sparse matrices with to non-zero entries to computing Betti numbers of simplicial
complexes consisting of at most a constant times to simplices. Together with the
known reduction in the other direction, this implies that the two problems have
the same computational complexity.
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Salman
full_name: Parsa, Salman
id: 4BDBD4F2-F248-11E8-B48F-1D18A9856A87
last_name: Parsa
citation:
ama: 'Edelsbrunner H, Parsa S. On the computational complexity of betti numbers
reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11'
apa: 'Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity
of betti numbers reductions from matrix rank. In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM.
https://doi.org/10.1137/1.9781611973402.11'
chicago: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity
of Betti Numbers Reductions from Matrix Rank.” In Proceedings of the Annual
ACM-SIAM Symposium on Discrete Algorithms, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11.
ieee: H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers
reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, Portland, USA, 2014, pp. 152–160.
ista: 'Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers
reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete
Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.'
mla: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of
Betti Numbers Reductions from Matrix Rank.” Proceedings of the Annual ACM-SIAM
Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11.
short: H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium
on Discrete Algorithms, SIAM, 2014, pp. 152–160.
conference:
end_date: 2014-01-07
location: Portland, USA
name: 'SODA: Symposium on Discrete Algorithms'
start_date: 2014-01-05
date_created: 2018-12-11T11:56:09Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:55:48Z
day: '01'
department:
- _id: HeEd
doi: 10.1137/1.9781611973402.11
language:
- iso: eng
month: '01'
oa_version: None
page: 152 - 160
publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
publication_status: published
publisher: SIAM
publist_id: '4805'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the computational complexity of betti numbers reductions from matrix rank
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2184'
abstract:
- lang: eng
text: 'Given topological spaces X,Y, a fundamental problem of algebraic topology
is understanding the structure of all continuous maps X→ Y. We consider a computational
version, where X,Y are given as finite simplicial complexes, and the goal is to
compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem
in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected;
in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical
tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and
simplicial sets) with algorithmic tools from effective algebraic topology (locally
effective simplicial sets and objects with effective homology). In contrast, [X,Y]
is known to be uncomputable for general X,Y, since for X = S1 it includes a well
known undecidable problem: testing triviality of the fundamental group of Y. In
follow-up papers, the algorithm is shown to run in polynomial time for d fixed,
and extended to other problems, such as the extension problem, where we are given
a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or
computing the Z2-index-everything in the stable range. Outside the stable range,
the extension problem is undecidable.'
acknowledgement: The research by M. K. was supported by project GAUK 49209. The research
by M. K. was also supported by project 1M0545 by the Ministry of Education of the
Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague
(project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss
National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).
article_number: '17 '
author:
- first_name: Martin
full_name: Čadek, Martin
last_name: Čadek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Francis
full_name: Sergeraert, Francis
last_name: Sergeraert
- first_name: Lukáš
full_name: Vokřínek, Lukáš
last_name: Vokřínek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing
all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629
apa: Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner,
U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629
chicago: Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek,
and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM.
ACM, 2014. https://doi.org/10.1145/2597629.
ieee: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner,
“Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3.
ACM, 2014.
ista: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing
all maps into a sphere. Journal of the ACM. 61(3), 17.
mla: Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the
ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629.
short: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal
of the ACM 61 (2014).
date_created: 2018-12-11T11:56:12Z
date_published: 2014-05-01T00:00:00Z
date_updated: 2021-01-12T06:55:50Z
day: '01'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2597629
intvolume: ' 61'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1105.6257
month: '05'
oa: 1
oa_version: Preprint
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '4797'
quality_controlled: '1'
scopus_import: 1
status: public
title: Computing all maps into a sphere
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 61
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 Publishing House; 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 Publishing House. https://doi.org/10.4171/120-1/3'
chicago: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory
and Practice,” 31–50. European Mathematical Society Publishing House, 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 Publishing House, 2014, pp. 31–50,
doi:10.4171/120-1/3.'
short: H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing
House, 2014, pp. 31–50.
conference:
end_date: 2012-07-07
location: Kraków, Poland
name: 'ECM: European Congress of Mathematics'
start_date: 2012-07-02
date_created: 2018-12-11T12:00:16Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T07:00:36Z
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 Publishing House
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: '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
date_created: 2022-03-21T07:09:03Z
date_published: 2014-11-08T00:00:00Z
date_updated: 2023-02-23T12:20:55Z
day: '08'
department:
- _id: HeEd
doi: 10.1007/978-3-319-13075-0_10
intvolume: ' 8889'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8889
year: '2014'
...
---
_id: '6853'
abstract:
- lang: eng
text: This monograph presents a short course in computational geometry and topology.
In the first part the book covers Voronoi diagrams and Delaunay triangulations,
then it presents the theory of alpha complexes which play a crucial role in biology.
The central part of the book is the homology theory and their computation, including
the theory of persistence which is indispensable for applications, e.g. shape
reconstruction. The target audience comprises researchers and practitioners in
mathematics, biology, neuroscience and computer science, but the book may also
be beneficial to graduate students of these fields.
alternative_title:
- SpringerBriefs in Applied Sciences and Technology
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
citation:
ama: 'Edelsbrunner H. A Short Course in Computational Geometry and Topology.
1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0'
apa: 'Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology
(1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0'
chicago: 'Edelsbrunner, Herbert. A Short Course in Computational Geometry and
Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham:
Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.'
ieee: 'H. Edelsbrunner, A Short Course in Computational Geometry and Topology,
1st ed. Cham: Springer Nature, 2014.'
ista: 'Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology
1st ed., Cham: Springer Nature, IX, 110p.'
mla: Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology.
1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0.
short: H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st
ed., Springer Nature, Cham, 2014.
date_created: 2019-09-06T09:22:33Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2022-03-04T07:47:54Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/978-3-319-05957-0
edition: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: IX, 110
place: Cham
publication_identifier:
eisbn:
- 9-783-3190-5957-0
eissn:
- 2191-5318
isbn:
- 9-783-3190-5956-3
issn:
- 2191-530X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- description: available as eBook via catalog IST BookList
relation: other
url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106
- description: available via catalog IST BookList
relation: other
url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842
scopus_import: '1'
series_title: SpringerBriefs in Applied Sciences and Technology
status: public
title: A Short Course in Computational Geometry and Topology
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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: '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: 2023-09-05T15:33:45Z
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: '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.
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.
date_created: 2018-12-11T11:56:36Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10851-013-0468-x
ec_funded: 1
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'
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:
- '09249907'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
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: 2023-09-20T09:42:40Z
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: '2012'
abstract:
- lang: eng
text: The classical sphere packing problem asks for the best (infinite) arrangement
of non-overlapping unit balls which cover as much space as possible. We define
a generalized version of the problem, where we allow each ball a limited amount
of overlap with other balls. We study two natural choices of overlap measures
and obtain the optimal lattice packings in a parameterized family of lattices
which contains the FCC, BCC, and integer lattice.
acknowledgement: We thank Herbert Edelsbrunner for his valuable discussions and ideas
on the topic of this paper. The second author has been supported by the Max Planck
Center for Visual Computing and Communication
article_number: '1401.0468'
article_processing_charge: No
author:
- first_name: Mabel
full_name: Iglesias Ham, Mabel
id: 41B58C0C-F248-11E8-B48F-1D18A9856A87
last_name: Iglesias Ham
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
orcid: 0000-0002-8030-9299
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
citation:
ama: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv.
doi:10.48550/arXiv.1401.0468
apa: Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited
overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468
chicago: Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing
with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.
ieee: M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,”
arXiv. .
ista: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv,
1401.0468.
mla: Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv,
1401.0468, doi:10.48550/arXiv.1401.0468.
short: M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.).
date_created: 2018-12-11T11:55:12Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2023-10-18T08:06:45Z
day: '01'
department:
- _id: HeEd
- _id: CaUh
doi: 10.48550/arXiv.1401.0468
external_id:
arxiv:
- '1401.0468'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://cccg.ca/proceedings/2014/papers/paper23.pdf
month: '01'
oa: 1
oa_version: Submitted Version
publication: arXiv
publication_status: submitted
publist_id: '5064'
status: public
title: Sphere packing with limited overlap
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2209'
abstract:
- lang: eng
text: "A straight skeleton is a well-known geometric structure, and several algorithms
exist to construct the straight skeleton for a given polygon or planar straight-line
graph. In this paper, we ask the reverse question: Given the straight skeleton
(in form of a planar straight-line graph, with some rays to infinity), can we
reconstruct a planar straight-line graph for which this was the straight skeleton?
We show how to reduce this problem to the problem of finding a line that intersects
a set of convex polygons. We can find these convex polygons and all such lines
in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number
of edges of the input graph. We also explain how our approach can be used for
recognizing Voronoi diagrams of points, thereby completing a partial solution
provided by Ash and Bolker in 1985.\r\n"
alternative_title:
- '2013 10th International Symposium on Voronoi Diagrams in Science and Engineering
(ISVD 2013) '
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
citation:
ama: 'Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams
and reconstructing their input. In: IEEE; 2013:37-46. doi:10.1109/ISVD.2013.11'
apa: 'Biedl, T., Held, M., & Huber, S. (2013). Recognizing straight skeletons
and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at
the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia:
IEEE. https://doi.org/10.1109/ISVD.2013.11'
chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons
and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. https://doi.org/10.1109/ISVD.2013.11.
ieee: 'T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi
diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams
in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.'
ista: 'Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi
diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and
Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science
and Engineering (ISVD 2013) , , 37–46.'
mla: Biedl, Therese, et al. Recognizing Straight Skeletons and Voronoi Diagrams
and Reconstructing Their Input. IEEE, 2013, pp. 37–46, doi:10.1109/ISVD.2013.11.
short: T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.
conference:
end_date: 2013-07-10
location: St. Petersburg, Russia
name: 'ISVD: Voronoi Diagrams in Science and Engineering'
start_date: 2013-07-08
date_created: 2018-12-11T11:56:20Z
date_published: 2013-12-01T00:00:00Z
date_updated: 2021-01-12T06:56:00Z
day: '01'
department:
- _id: HeEd
doi: 10.1109/ISVD.2013.11
language:
- iso: eng
month: '12'
oa_version: None
page: 37 - 46
publication_identifier:
eisbn:
- '978-0-7695-5037-4 '
publication_status: published
publisher: IEEE
publist_id: '4763'
quality_controlled: '1'
scopus_import: 1
status: public
title: Recognizing straight skeletons and Voronoi diagrams and reconstructing their
input
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2210'
abstract:
- lang: eng
text: 'A straight skeleton is a well-known geometric structure, and several algorithms
exist to construct the straight skeleton for a given polygon. In this paper, we
ask the reverse question: Given the straight skeleton (in form of a tree with
a drawing in the plane, but with the exact position of the leaves unspecified),
can we reconstruct the polygon? We show that in most cases there exists at most
one polygon; in the remaining case there is an infinite number of polygons determined
by one angle that can range in an interval. We can find this (set of) polygon(s)
in linear time in the Real RAM computer model.'
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
citation:
ama: 'Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons.
In: 29th European Workshop on Computational Geometry. TU Braunschweig;
2013:95-98.'
apa: 'Biedl, T., Held, M., & Huber, S. (2013). Reconstructing polygons from
embedded straight skeletons. In 29th European Workshop on Computational Geometry
(pp. 95–98). Braunschweig, Germany: TU Braunschweig.'
chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons
from Embedded Straight Skeletons.” In 29th European Workshop on Computational
Geometry, 95–98. TU Braunschweig, 2013.
ieee: T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight
skeletons,” in 29th European Workshop on Computational Geometry, Braunschweig,
Germany, 2013, pp. 95–98.
ista: 'Biedl T, Held M, Huber S. 2013. Reconstructing polygons from embedded straight
skeletons. 29th European Workshop on Computational Geometry. EuroCG: European
Workshop on Computational Geometry, 95–98.'
mla: Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.”
29th European Workshop on Computational Geometry, TU Braunschweig, 2013,
pp. 95–98.
short: T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational
Geometry, TU Braunschweig, 2013, pp. 95–98.
conference:
end_date: 2013-03-20
location: Braunschweig, Germany
name: 'EuroCG: European Workshop on Computational Geometry'
start_date: 2013-03-17
date_created: 2018-12-11T11:56:21Z
date_published: 2013-03-01T00:00:00Z
date_updated: 2021-01-12T06:56:00Z
day: '01'
department:
- _id: HeEd
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf
month: '03'
oa: 1
oa_version: Submitted Version
page: 95 - 98
publication: 29th European Workshop on Computational Geometry
publication_status: published
publisher: TU Braunschweig
publist_id: '4762'
status: public
title: Reconstructing polygons from embedded straight skeletons
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2304'
abstract:
- lang: eng
text: This extended abstract is concerned with the irregularities of distribution
of one-dimensional permuted van der Corput sequences that are generated from linear
permutations. We show how to obtain upper bounds for the discrepancy and diaphony
of these sequences, by relating them to Kronecker sequences and applying earlier
results of Faure and Niederreiter.
acknowledgement: This research is supported by the Graduate school of IST Austria
(Institute of Science and Technology Austria).
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Pausinger F. Van der Corput sequences and linear permutations. Electronic
Notes in Discrete Mathematics. 2013;43:43-50. doi:10.1016/j.endm.2013.07.008
apa: Pausinger, F. (2013). Van der Corput sequences and linear permutations. Electronic
Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2013.07.008
chicago: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.”
Electronic Notes in Discrete Mathematics. Elsevier, 2013. https://doi.org/10.1016/j.endm.2013.07.008.
ieee: F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic
Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013.
ista: Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic
Notes in Discrete Mathematics. 43, 43–50.
mla: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic
Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008.
short: F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.
date_created: 2018-12-11T11:56:53Z
date_published: 2013-09-05T00:00:00Z
date_updated: 2021-01-12T06:56:39Z
day: '05'
department:
- _id: HeEd
doi: 10.1016/j.endm.2013.07.008
intvolume: ' 43'
language:
- iso: eng
month: '09'
oa_version: None
page: 43 - 50
publication: Electronic Notes in Discrete Mathematics
publication_status: published
publisher: Elsevier
publist_id: '4623'
quality_controlled: '1'
scopus_import: 1
status: public
title: Van der Corput sequences and linear permutations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 43
year: '2013'
...
---
_id: '2807'
abstract:
- lang: eng
text: 'We consider several basic problems of algebraic topology, with connections
to combinatorial and geometric questions, from the point of view of computational
complexity. The extension problem asks, given topological spaces X; Y , a subspace
A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X
→ Y . For computational purposes, we assume that X and Y are represented as finite
simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map.
In this generality the problem is undecidable, as follows from Novikov''s result
from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study
the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected;
informally, this means that Y has \no holes up to dimension k-1" (a basic
example of such a Y is the sphere Sk). We prove that, on the one hand, this problem
is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2,
we obtain an algorithm that solves the extension problem in polynomial time assuming
Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides
a classification of all extensions up to homotopy (continuous deformation). This
relies on results of our SODA 2012 paper, and the main new ingredient is a machinery
of objects with polynomial-time homology, which is a polynomial-time analog of
objects with effective homology developed earlier by Sergeraert et al. We also
consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected
Y . Their computability was established by Brown in 1957; we show that πk(Y )
can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick
proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where
Y is a cell complex with certain rather compact encoding. We strengthen his result
to #P-hardness for Y given as a simplicial complex. '
author:
- first_name: Martin
full_name: Čadek, Martin
last_name: Čadek
- first_name: Marek
full_name: Krcál, Marek
id: 33E21118-F248-11E8-B48F-1D18A9856A87
last_name: Krcál
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Lukáš
full_name: Vokřínek, Lukáš
last_name: Vokřínek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps:
Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of
Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683'
apa: 'Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013).
Extending continuous maps: Polynomiality and undecidability. In 45th Annual
ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United
States: ACM. https://doi.org/10.1145/2488608.2488683'
chicago: 'Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner.
“Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual
ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.'
ieee: 'M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous
maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory
of computing, Palo Alto, CA, United States, 2013, pp. 595–604.'
ista: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous
maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of
computing. STOC: Symposium on the Theory of Computing, 595–604.'
mla: 'Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.”
45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604,
doi:10.1145/2488608.2488683.'
short: M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual
ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604.
conference:
end_date: 2013-06-04
location: Palo Alto, CA, United States
name: 'STOC: Symposium on the Theory of Computing'
start_date: 2013-06-01
date_created: 2018-12-11T11:59:42Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2021-01-12T06:59:51Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1145/2488608.2488683
file:
- access_level: open_access
checksum: 06c2ce5c1135fbc1f71ca15eeb242dcf
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:29Z
date_updated: 2020-07-14T12:45:48Z
file_id: '5081'
file_name: IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf
file_size: 447945
relation: main_file
file_date_updated: 2020-07-14T12:45:48Z
has_accepted_license: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Submitted Version
page: 595 - 604
publication: 45th Annual ACM Symposium on theory of computing
publication_status: published
publisher: ACM
publist_id: '4078'
pubrep_id: '533'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'Extending continuous maps: Polynomiality and undecidability'
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2812'
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 ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel
sets of scalar functions on 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.'
acknowledgement: Some of the authors were partially supported by the GIGA ANR grant
(contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827).
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. In: Proceedings of the 29th Annual Symposium on Computational
Geometry. ACM; 2013:117-125. doi:10.1145/2462356.2462373'
apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2013).
Homological reconstruction and simplification in R3. In Proceedings of the
29th annual symposium on Computational Geometry (pp. 117–125). Rio de Janeiro,
Brazil: ACM. https://doi.org/10.1145/2462356.2462373'
chicago: Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André
Lieutier. “Homological Reconstruction and Simplification in R3.” In Proceedings
of the 29th Annual Symposium on Computational Geometry, 117–25. ACM, 2013.
https://doi.org/10.1145/2462356.2462373.
ieee: D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological
reconstruction and simplification in R3,” in Proceedings of the 29th annual
symposium on Computational Geometry, Rio de Janeiro, Brazil, 2013, pp. 117–125.
ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction
and simplification in R3. Proceedings of the 29th annual symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 117–125.'
mla: Attali, Dominique, et al. “Homological Reconstruction and Simplification in
R3.” Proceedings of the 29th Annual Symposium on Computational Geometry,
ACM, 2013, pp. 117–25, doi:10.1145/2462356.2462373.
short: D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings
of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125.
conference:
end_date: 2013-06-20
location: Rio de Janeiro, Brazil
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2013-06-17
date_created: 2018-12-11T11:59:44Z
date_published: 2013-06-01T00:00:00Z
date_updated: 2023-02-23T10:15:15Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2462356.2462373
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://hal.archives-ouvertes.fr/hal-00833791/
month: '06'
oa: 1
oa_version: Submitted Version
page: 117 - 125
publication: Proceedings of the 29th annual symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4072'
quality_controlled: '1'
related_material:
record:
- id: '1805'
relation: later_version
status: public
scopus_import: 1
status: public
title: Homological reconstruction and simplification in R3
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2013'
...
---
_id: '2822'
abstract:
- lang: eng
text: Identification of genes that control root system architecture in crop plants
requires innovations that enable high-throughput and accurate measurements of
root system architecture through time. We demonstrate the ability of a semiautomated
3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative
genetic basis of root system growth in a rice biparental mapping population, Bala
x Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for
a suite of 25 traits that quantified the distribution, shape, extent of exploration,
and the intrinsic size of root networks at days 12, 14, and 16 of growth in a
gellan gum medium. From these data we identified 89 quantitative trait loci, some
of which correspond to those found previously in soil-grown plants, and provide
evidence for genetic tradeoffs in root growth allocations, such as between the
extent and thoroughness of exploration. We also developed a multivariate method
for generating and mapping central root architecture phenotypes and used it to
identify five major quantitative trait loci (r2 = 24-37%), two of which were not
identified by our univariate analysis. Our imaging and analytical platform provides
a means to identify genes with high potential for improving root traits and agronomic
qualities of crops.
author:
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Anjali
full_name: Iyer Pascuzzi, Anjali
last_name: Iyer Pascuzzi
- first_name: Jill
full_name: Anderson, Jill
last_name: Anderson
- first_name: Cheng
full_name: Lee, Cheng
last_name: Lee
- first_name: Paul
full_name: Zurek, Paul
last_name: Zurek
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
- first_name: Ying
full_name: Zheng, Ying
last_name: Zheng
- first_name: Alexander
full_name: Bucksch, Alexander
last_name: Bucksch
- first_name: Yuriy
full_name: Mileyko, Yuriy
last_name: Mileyko
- first_name: Taras
full_name: Galkovskyi, Taras
last_name: Galkovskyi
- first_name: Brad
full_name: Moore, Brad
last_name: Moore
- first_name: John
full_name: Harer, John
last_name: Harer
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Thomas
full_name: Mitchell Olds, Thomas
last_name: Mitchell Olds
- first_name: Joshua
full_name: Weitz, Joshua
last_name: Weitz
- first_name: Philip
full_name: Benfey, Philip
last_name: Benfey
citation:
ama: Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative
trait locus mapping identify core regions of the rice genome controlling root
architecture. PNAS. 2013;110(18):E1695-E1704. doi:10.1073/pnas.1304354110
apa: Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O.,
… Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify
core regions of the rice genome controlling root architecture. PNAS. National
Academy of Sciences. https://doi.org/10.1073/pnas.1304354110
chicago: Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul
Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait
Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.”
PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1304354110.
ieee: C. Topp et al., “3D phenotyping and quantitative trait locus mapping
identify core regions of the rice genome controlling root architecture,” PNAS,
vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013.
ista: Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y,
Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell
Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping
identify core regions of the rice genome controlling root architecture. PNAS.
110(18), E1695–E1704.
mla: Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping
Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS,
vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:10.1073/pnas.1304354110.
short: C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y.
Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner,
T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704.
date_created: 2018-12-11T11:59:47Z
date_published: 2013-04-30T00:00:00Z
date_updated: 2021-01-12T06:59:58Z
day: '30'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1073/pnas.1304354110
external_id:
pmid:
- '25673779'
intvolume: ' 110'
issue: '18'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/
month: '04'
oa: 1
oa_version: Submitted Version
page: E1695 - E1704
pmid: 1
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
publist_id: '3979'
quality_controlled: '1'
scopus_import: 1
status: public
title: 3D phenotyping and quantitative trait locus mapping identify core regions of
the rice genome controlling root architecture
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 110
year: '2013'
...
---
_id: '2843'
abstract:
- lang: eng
text: 'Mathematical objects can be measured unambiguously, but not so objects from
our physical world. Even the total length of tubelike shapes has its difficulties.
We introduce a combination of geometric, probabilistic, and topological methods
to design a stable length estimate for tube-like shapes; that is: one that is
insensitive to small shape changes.'
alternative_title:
- LNCS
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.
In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery.
Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0'
apa: 'Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like
shapes. In 17th IAPR International Conference on Discrete Geometry for Computer
Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0'
chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry
for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0.
ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
in 17th IAPR International Conference on Discrete Geometry for Computer Imagery,
Seville, Spain, 2013, vol. 7749, pp. XV–XIX.
ista: 'Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes.
17th IAPR International Conference on Discrete Geometry for Computer Imagery.
DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.'
mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer
Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0.
short: H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on
Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.
conference:
end_date: 2013-03-22
location: Seville, Spain
name: 'DGCI: Discrete Geometry for Computer Imagery'
start_date: 2013-03-20
date_created: 2018-12-11T11:59:53Z
date_published: 2013-02-21T00:00:00Z
date_updated: 2023-02-23T10:35:00Z
day: '21'
department:
- _id: HeEd
doi: 10.1007/978-3-642-37067-0
intvolume: ' 7749'
language:
- iso: eng
month: '02'
oa_version: None
page: XV - XIX
publication: 17th IAPR International Conference on Discrete Geometry for Computer
Imagery
publication_status: published
publisher: Springer
publist_id: '3952'
quality_controlled: '1'
related_material:
record:
- id: '2255'
relation: later_version
status: public
scopus_import: 1
status: public
title: Stable length estimates of tube-like shapes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7749
year: '2013'
...
---
_id: '2859'
abstract:
- lang: eng
text: Given a continuous function f:X-R on a topological space, we consider the
preimages of intervals and their homology groups and show how to read the ranks
of these groups from the extended persistence diagram of f. In addition, we quantify
the robustness of the homology classes under perturbations of f using well groups,
and we show how to read the ranks of these groups from the same extended persistence
diagram. The special case X=R3 has ramifications in the fields of medical imaging
and scientific visualization.
author:
- first_name: Paul
full_name: Bendich, Paul
id: 43F6EC54-F248-11E8-B48F-1D18A9856A87
last_name: Bendich
- 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: Morozov, Dmitriy
last_name: Morozov
- first_name: Amit
full_name: Patel, Amit
id: 34A254A0-F248-11E8-B48F-1D18A9856A87
last_name: Patel
citation:
ama: Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level
and interlevel sets. Homology, Homotopy and Applications. 2013;15(1):51-72.
doi:10.4310/HHA.2013.v15.n1.a3
apa: Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2013). Homology
and robustness of level and interlevel sets. Homology, Homotopy and Applications.
International Press. https://doi.org/10.4310/HHA.2013.v15.n1.a3
chicago: Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology
and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications.
International Press, 2013. https://doi.org/10.4310/HHA.2013.v15.n1.a3.
ieee: P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness
of level and interlevel sets,” Homology, Homotopy and Applications, vol.
15, no. 1. International Press, pp. 51–72, 2013.
ista: Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness
of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72.
mla: Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.”
Homology, Homotopy and Applications, vol. 15, no. 1, International Press,
2013, pp. 51–72, doi:10.4310/HHA.2013.v15.n1.a3.
short: P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and
Applications 15 (2013) 51–72.
date_created: 2018-12-11T11:59:58Z
date_published: 2013-05-01T00:00:00Z
date_updated: 2021-01-12T07:00:18Z
day: '01'
department:
- _id: HeEd
doi: 10.4310/HHA.2013.v15.n1.a3
external_id:
arxiv:
- '1102.3389'
intvolume: ' 15'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1102.3389v1
month: '05'
oa: 1
oa_version: Preprint
page: 51 - 72
publication: Homology, Homotopy and Applications
publication_status: published
publisher: International Press
publist_id: '3930'
quality_controlled: '1'
scopus_import: 1
status: public
title: Homology and robustness of level and interlevel sets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2013'
...
---
_id: '2887'
abstract:
- lang: eng
text: 'Root system growth and development is highly plastic and is influenced by
the surrounding environment. Roots frequently grow in heterogeneous environments
that include interactions from neighboring plants and physical impediments in
the rhizosphere. To investigate how planting density and physical objects affect
root system growth, we grew rice in a transparent gel system in close proximity
with another plant or a physical object. Root systems were imaged and reconstructed
in three dimensions. Root-root interaction strength was calculated using quantitative
metrics that characterize the extent towhich the reconstructed root systems overlap
each other. Surprisingly, we found the overlap of root systems of the same genotype
was significantly higher than that of root systems of different genotypes. Root
systems of the same genotype tended to grow toward each other but those of different
genotypes appeared to avoid each other. Shoot separation experiments excluded
the possibility of aerial interactions, suggesting root communication. Staggered
plantings indicated that interactions likely occur at root tips in close proximity.
Recognition of obstacles also occurred through root tips, but through physical
contact in a size-dependent manner. These results indicate that root systems use
two different forms of communication to recognize objects and alter root architecture:
root-root recognition, possibly mediated through root exudates, and root-object
recognition mediated by physical contact at the root tips. This finding suggests
that root tips act as local sensors that integrate rhizosphere information into
global root architectural changes.'
article_processing_charge: No
article_type: original
author:
- first_name: Suqin
full_name: Fang, Suqin
last_name: Fang
- first_name: Randy
full_name: Clark, Randy
last_name: Clark
- first_name: Ying
full_name: Zheng, Ying
last_name: Zheng
- first_name: Anjali
full_name: Iyer Pascuzzi, Anjali
last_name: Iyer Pascuzzi
- first_name: Joshua
full_name: Weitz, Joshua
last_name: Weitz
- first_name: Leon
full_name: Kochian, Leon
last_name: Kochian
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Hong
full_name: Liao, Hong
last_name: Liao
- first_name: Philip
full_name: Benfey, Philip
last_name: Benfey
citation:
ama: Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses
by rice roots. PNAS. 2013;110(7):2670-2675. doi:10.1073/pnas.1222821110
apa: Fang, S., Clark, R., Zheng, Y., Iyer Pascuzzi, A., Weitz, J., Kochian, L.,
… Benfey, P. (2013). Genotypic recognition and spatial responses by rice roots.
PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1222821110
chicago: Fang, Suqin, Randy Clark, Ying Zheng, Anjali Iyer Pascuzzi, Joshua Weitz,
Leon Kochian, Herbert Edelsbrunner, Hong Liao, and Philip Benfey. “Genotypic Recognition
and Spatial Responses by Rice Roots.” PNAS. National Academy of Sciences,
2013. https://doi.org/10.1073/pnas.1222821110.
ieee: S. Fang et al., “Genotypic recognition and spatial responses by rice
roots,” PNAS, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675,
2013.
ista: Fang S, Clark R, Zheng Y, Iyer Pascuzzi A, Weitz J, Kochian L, Edelsbrunner
H, Liao H, Benfey P. 2013. Genotypic recognition and spatial responses by rice
roots. PNAS. 110(7), 2670–2675.
mla: Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.”
PNAS, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75,
doi:10.1073/pnas.1222821110.
short: S. Fang, R. Clark, Y. Zheng, A. Iyer Pascuzzi, J. Weitz, L. Kochian, H. Edelsbrunner,
H. Liao, P. Benfey, PNAS 110 (2013) 2670–2675.
date_created: 2018-12-11T12:00:09Z
date_published: 2013-02-12T00:00:00Z
date_updated: 2021-01-12T07:00:29Z
day: '12'
department:
- _id: HeEd
doi: 10.1073/pnas.1222821110
external_id:
pmid:
- '23362379'
intvolume: ' 110'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/
month: '02'
oa: 1
oa_version: Published Version
page: 2670 - 2675
pmid: 1
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
publist_id: '3872'
quality_controlled: '1'
scopus_import: 1
status: public
title: Genotypic recognition and spatial responses by rice roots
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 110
year: '2013'
...