---
_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
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.
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
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: 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: '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: '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: '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: '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: '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: '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: '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: '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'
...