---
_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.
article_processing_charge: No
arxiv: 1
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
orcid: 0000-0002-0659-3201
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: 2025-09-22T09:32:23Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00454-015-9742-6
external_id:
arxiv:
- '1212.0649'
isi:
- '000367625500001'
intvolume: ' 55'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 55
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
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: 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: 2025-09-22T07:44:59Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/13062
ec_funded: 1
external_id:
arxiv:
- '1401.0442'
isi:
- '000383054200034'
intvolume: ' 144'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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
orcid: 0000-0001-8878-8397
- 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.
corr_author: '1'
date_created: 2018-12-11T11:51:51Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2025-09-18T14:30:52Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/s00454-016-9794-2
ec_funded: 1
external_id:
isi:
- '000377722100005'
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'
isi: 1
issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
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
article_processing_charge: No
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: 2025-09-22T09:19:17Z
day: '02'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-319-39441-1_13
ec_funded: 1
external_id:
isi:
- '000389805800013'
intvolume: ' 9667'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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
arxiv: 1
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.
corr_author: '1'
date_created: 2018-12-11T11:50:57Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2025-09-22T09:09:31Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/12812
ec_funded: 1
external_id:
arxiv:
- '1411.7563'
isi:
- '000369298400038'
intvolume: ' 144'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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."
article_processing_charge: No
arxiv: 1
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.
corr_author: '1'
date_created: 2018-12-11T11:50:58Z
date_published: 2016-04-02T00:00:00Z
date_updated: 2025-09-22T09:07:52Z
day: '02'
department:
- _id: HeEd
doi: 10.1080/10586458.2015.1048011
ec_funded: 1
external_id:
arxiv:
- '1504.00116'
isi:
- '000372490500002'
intvolume: ' 25'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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: '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: 2025-09-23T13:44:16Z
day: '01'
ddc:
- '004'
- '514'
department:
- _id: HeEd
doi: 10.1016/j.patrec.2015.12.012
external_id:
isi:
- '000386874700003'
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'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 83
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."
article_processing_charge: No
arxiv: 1
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.
corr_author: '1'
date_created: 2018-12-11T11:51:11Z
date_published: 2016-12-01T00:00:00Z
date_updated: 2025-09-22T08:29:12Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s10474-016-0648-4
external_id:
arxiv:
- '1605.00794'
isi:
- '000387471100014'
intvolume: ' 150'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 150
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.
corr_author: '1'
date_created: 2018-12-11T11:51:12Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2024-10-09T20:57:05Z
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: '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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: 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.
corr_author: '1'
date_created: 2018-12-11T11:51:24Z
date_published: 2016-10-15T00:00:00Z
date_updated: 2025-09-22T08:23:27Z
day: '15'
department:
- _id: HeEd
doi: 10.1007/s11856-016-1429-z
ec_funded: 1
external_id:
arxiv:
- '1506.06014'
isi:
- '000386356400012'
intvolume: ' 216'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 216
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.
article_processing_charge: No
arxiv: 1
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: 2025-09-18T10:57:52Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.11.003
external_id:
arxiv:
- '1510.00251'
isi:
- '000370090400011'
intvolume: ' 33'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 33
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: '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: '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."
article_processing_charge: No
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Edelsbrunner H, Pausinger F. 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.
corr_author: '1'
date_created: 2018-12-11T11:53:20Z
date_published: 2016-01-10T00:00:00Z
date_updated: 2026-04-09T14:26:05Z
day: '10'
ddc:
- '004'
department:
- _id: HeEd
doi: 10.1016/j.aim.2015.10.004
ec_funded: 1
external_id:
isi:
- '000375634100016'
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'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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
article_processing_charge: No
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
Foundation; 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 Foundation.'
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 Foundation, 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 Foundation, 2015, pp. 3070–78.
short: R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information
Processing Systems Foundation, 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: 2025-06-03T11:41:36Z
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 Foundation
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: '1793'
abstract:
- lang: eng
text: We present a software platform for reconstructing and analyzing the growth
of a plant root system from a time-series of 3D voxelized shapes. It aligns the
shapes with each other, constructs a geometric graph representation together with
the function that records the time of growth, and organizes the branches into
a hierarchy that reflects the order of creation. The software includes the automatic
computation of structural and dynamic traits for each root in the system enabling
the quantification of growth on fine-scale. These are important advances in plant
phenotyping with applications to the study of genetic and environmental influences
on growth.
article_number: e0127657
article_processing_charge: No
author:
- first_name: Olga
full_name: Symonova, Olga
id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87
last_name: Symonova
orcid: 0000-0003-2012-9947
- first_name: Christopher
full_name: Topp, Christopher
last_name: Topp
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for
the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6).
doi:10.1371/journal.pone.0127657'
apa: 'Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software
platform for the reconstruction and analysis of growing plant roots. PLoS One.
Public Library of Science. https://doi.org/10.1371/journal.pone.0127657'
chicago: 'Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots:
A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.”
PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.'
ieee: 'O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots,” PLoS One,
vol. 10, no. 6. Public Library of Science, 2015.'
ista: 'Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform
for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.'
mla: 'Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction
and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657,
Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.'
short: O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).
corr_author: '1'
date_created: 2018-12-11T11:54:02Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2025-09-23T08:30:43Z
day: '01'
ddc:
- '000'
department:
- _id: MaJö
- _id: HeEd
doi: 10.1371/journal.pone.0127657
external_id:
isi:
- '000356630900069'
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'
isi: 1
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:
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relation: research_data
status: public
scopus_import: '1'
status: public
title: 'DynamicRoots: A software platform for the reconstruction and analysis of growing
plant roots'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 10
year: '2015'
...
---
OA_place: publisher
OA_type: free access
_id: '1805'
abstract:
- lang: eng
text: 'We consider the problem of deciding whether the persistent homology group
of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex
X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded
in double-struck R3. As a consequence, we show that it is NP-hard to simplify
level and sublevel sets of scalar functions on double-struck S3 within a given
tolerance constraint. This problem has relevance to the visualization of medical
images by isosurfaces. We also show an implication to the theory of well groups
of scalar functions: not every well group can be realized by some level set, and
deciding whether a well group can be realized is NP-hard.'
article_processing_charge: No
article_type: original
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Olivier
full_name: Devillers, Olivier
last_name: Devillers
- first_name: Marc
full_name: Glisse, Marc
last_name: Glisse
- first_name: André
full_name: Lieutier, André
last_name: Lieutier
citation:
ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications.
2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010'
apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015).
Homological reconstruction and simplification in R3. Computational Geometry:
Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010'
chicago: 'Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André
Lieutier. “Homological Reconstruction and Simplification in R3.” Computational
Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.'
ieee: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological
reconstruction and simplification in R3,” Computational Geometry: Theory and
Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.'
ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction
and simplification in R3. Computational Geometry: Theory and Applications. 48(8),
606–621.'
mla: 'Attali, Dominique, et al. “Homological Reconstruction and Simplification in
R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier,
2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.'
short: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational
Geometry: Theory and Applications 48 (2015) 606–621.'
corr_author: '1'
date_created: 2018-12-11T11:54:06Z
date_published: 2015-06-03T00:00:00Z
date_updated: 2025-09-23T09:18:30Z
day: '03'
department:
- _id: HeEd
doi: 10.1016/j.comgeo.2014.08.010
ec_funded: 1
external_id:
isi:
- '000357353200006'
intvolume: ' 48'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.1016/j.comgeo.2014.08.010
month: '06'
oa: 1
oa_version: Published Version
page: 606 - 621
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: 'Computational Geometry: Theory and Applications'
publication_status: published
publisher: Elsevier
publist_id: '5305'
quality_controlled: '1'
related_material:
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relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Homological reconstruction and simplification in R3
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 48
year: '2015'
...