---
_id: '5986'
abstract:
- lang: eng
text: "Given a triangulation of a point set in the plane, a flip deletes an edge
e whose removal leaves a convex quadrilateral, and replaces e by the opposite
diagonal of the quadrilateral. It is well known that any triangulation of a point
set can be reconfigured to any other triangulation by some sequence of flips.
We explore this question in the setting where each edge of a triangulation has
a label, and a flip transfers the label of the removed edge to the new edge. It
is not true that every labelled triangulation of a point set can be reconfigured
to every other labelled triangulation via a sequence of flips, but we characterize
when this is possible. There is an obvious necessary condition: for each label
l, if edge e has label l in the first triangulation and edge f has label l in
the second triangulation, then there must be some sequence of flips that moves
label l from e to f, ignoring all other labels. Bose, Lubiw, Pathak and Verdonschot
formulated the Orbit Conjecture, which states that this necessary condition is
also sufficient, i.e. that all labels can be simultaneously mapped to their destination
if and only if each label individually can be mapped to its destination. We prove
this conjecture. Furthermore, we give a polynomial-time algorithm (with \U0001D442(\U0001D45B8)
being a crude bound on the run-time) to find a sequence of flips to reconfigure
one labelled triangulation to another, if such a sequence exists, and we prove
an upper bound of \U0001D442(\U0001D45B7) on the length of the flip sequence.
Our proof uses the topological result that the sets of pairwise non-crossing edges
on a planar point set form a simplicial complex that is homeomorphic to a high-dimensional
ball (this follows from a result of Orden and Santos; we give a different proof
based on a shelling argument). The dual cell complex of this simplicial ball,
called the flip complex, has the usual flip graph as its 1-skeleton. We use properties
of the 2-skeleton of the flip complex to prove the Orbit Conjecture."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Anna
full_name: Lubiw, Anna
last_name: Lubiw
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Lubiw A, Masárová Z, Wagner U. A proof of the orbit conjecture for flipping
edge-labelled triangulations. Discrete & Computational Geometry. 2019;61(4):880-898.
doi:10.1007/s00454-018-0035-8
apa: Lubiw, A., Masárová, Z., & Wagner, U. (2019). A proof of the orbit conjecture
for flipping edge-labelled triangulations. Discrete & Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-018-0035-8
chicago: Lubiw, Anna, Zuzana Masárová, and Uli Wagner. “A Proof of the Orbit Conjecture
for Flipping Edge-Labelled Triangulations.” Discrete & Computational Geometry.
Springer Nature, 2019. https://doi.org/10.1007/s00454-018-0035-8.
ieee: A. Lubiw, Z. Masárová, and U. Wagner, “A proof of the orbit conjecture for
flipping edge-labelled triangulations,” Discrete & Computational Geometry,
vol. 61, no. 4. Springer Nature, pp. 880–898, 2019.
ista: Lubiw A, Masárová Z, Wagner U. 2019. A proof of the orbit conjecture for flipping
edge-labelled triangulations. Discrete & Computational Geometry. 61(4), 880–898.
mla: Lubiw, Anna, et al. “A Proof of the Orbit Conjecture for Flipping Edge-Labelled
Triangulations.” Discrete & Computational Geometry, vol. 61, no. 4,
Springer Nature, 2019, pp. 880–98, doi:10.1007/s00454-018-0035-8.
short: A. Lubiw, Z. Masárová, U. Wagner, Discrete & Computational Geometry 61
(2019) 880–898.
date_created: 2019-02-14T11:54:08Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-09-07T13:17:36Z
day: '01'
ddc:
- '000'
department:
- _id: UlWa
doi: 10.1007/s00454-018-0035-8
external_id:
arxiv:
- '1710.02741'
isi:
- '000466130000009'
file:
- access_level: open_access
checksum: e1bff88f1d77001b53b78c485ce048d7
content_type: application/pdf
creator: dernst
date_created: 2019-02-14T11:57:22Z
date_updated: 2020-07-14T12:47:14Z
file_id: '5988'
file_name: 2018_DiscreteGeometry_Lubiw.pdf
file_size: 556276
relation: main_file
file_date_updated: 2020-07-14T12:47:14Z
has_accepted_license: '1'
intvolume: ' 61'
isi: 1
issue: '4'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 880-898
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '683'
relation: earlier_version
status: public
- id: '7944'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: A proof of the orbit conjecture for flipping edge-labelled triangulations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 61
year: '2019'
...
---
_id: '5886'
abstract:
- lang: eng
text: Problems involving quantum impurities, in which one or a few particles are
interacting with a macroscopic environment, represent a pervasive paradigm, spanning
across atomic, molecular, and condensed-matter physics. In this paper we introduce
new variational approaches to quantum impurities and apply them to the Fröhlich
polaron–a quasiparticle formed out of an electron (or other point-like impurity)
in a polar medium, and to the angulon–a quasiparticle formed out of a rotating
molecule in a bosonic bath. We benchmark these approaches against established
theories, evaluating their accuracy as a function of the impurity-bath coupling.
article_processing_charge: No
author:
- first_name: Xiang
full_name: Li, Xiang
id: 4B7E523C-F248-11E8-B48F-1D18A9856A87
last_name: Li
- first_name: Giacomo
full_name: Bighin, Giacomo
id: 4CA96FD4-F248-11E8-B48F-1D18A9856A87
last_name: Bighin
orcid: 0000-0001-8823-9777
- first_name: Enderalp
full_name: Yakaboylu, Enderalp
id: 38CB71F6-F248-11E8-B48F-1D18A9856A87
last_name: Yakaboylu
orcid: 0000-0001-5973-0874
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
citation:
ama: 'Li X, Bighin G, Yakaboylu E, Lemeshko M. Variational approaches to quantum
impurities: from the Fröhlich polaron to the angulon. Molecular Physics.
2019. doi:10.1080/00268976.2019.1567852'
apa: 'Li, X., Bighin, G., Yakaboylu, E., & Lemeshko, M. (2019). Variational
approaches to quantum impurities: from the Fröhlich polaron to the angulon. Molecular
Physics. Taylor and Francis. https://doi.org/10.1080/00268976.2019.1567852'
chicago: 'Li, Xiang, Giacomo Bighin, Enderalp Yakaboylu, and Mikhail Lemeshko. “Variational
Approaches to Quantum Impurities: From the Fröhlich Polaron to the Angulon.” Molecular
Physics. Taylor and Francis, 2019. https://doi.org/10.1080/00268976.2019.1567852.'
ieee: 'X. Li, G. Bighin, E. Yakaboylu, and M. Lemeshko, “Variational approaches
to quantum impurities: from the Fröhlich polaron to the angulon,” Molecular
Physics. Taylor and Francis, 2019.'
ista: 'Li X, Bighin G, Yakaboylu E, Lemeshko M. 2019. Variational approaches to
quantum impurities: from the Fröhlich polaron to the angulon. Molecular Physics.'
mla: 'Li, Xiang, et al. “Variational Approaches to Quantum Impurities: From the
Fröhlich Polaron to the Angulon.” Molecular Physics, Taylor and Francis,
2019, doi:10.1080/00268976.2019.1567852.'
short: X. Li, G. Bighin, E. Yakaboylu, M. Lemeshko, Molecular Physics (2019).
date_created: 2019-01-27T22:59:10Z
date_published: 2019-01-18T00:00:00Z
date_updated: 2023-09-07T13:16:42Z
day: '18'
ddc:
- '530'
department:
- _id: MiLe
doi: 10.1080/00268976.2019.1567852
ec_funded: 1
external_id:
isi:
- '000474641400008'
file:
- access_level: open_access
checksum: 178964744b636a6f036372f4f090a657
content_type: application/pdf
creator: dernst
date_created: 2019-01-29T08:32:57Z
date_updated: 2020-07-14T12:47:13Z
file_id: '5896'
file_name: 2019_MolecularPhysics_Li.pdf
file_size: 1309966
relation: main_file
file_date_updated: 2020-07-14T12:47:13Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 26031614-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P29902
name: Quantum rotations in the presence of a many-body environment
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Molecular Physics
publication_identifier:
issn:
- '00268976'
publication_status: published
publisher: Taylor and Francis
quality_controlled: '1'
related_material:
record:
- id: '8958'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Variational approaches to quantum impurities: from the Fröhlich polaron to
the angulon'
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2019'
...
---
_id: '6556'
abstract:
- lang: eng
text: 'Motivated by fixed-parameter tractable (FPT) problems in computational topology,
we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined
to be the minimum treewidth of the face pairing graph of any triangulation T of
M. In this setting the relationship between the topology of a 3-manifold and its
treewidth is of particular interest. First, as a corollary of work of Jaco and
Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth
tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination
with our earlier work with Wagner, this yields that for non-Haken manifolds the
Heegaard genus and the treewidth are within a constant factor. Second, we characterize
all 3-manifolds of treewidth one: These are precisely the lens spaces and a single
other Seifert fibered space. Furthermore, we show that all remaining orientable
Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth
two. In particular, for every spherical 3-manifold we exhibit a triangulation
of treewidth at most two. Our results further validate the parameter of treewidth
(and other related parameters such as cutwidth or congestion) to be useful for
topological computing, and also shed more light on the scope of existing FPT-algorithms
in the field.'
alternative_title:
- LIPIcs
article_processing_charge: No
author:
- first_name: Kristóf
full_name: Huszár, Kristóf
id: 33C26278-F248-11E8-B48F-1D18A9856A87
last_name: Huszár
orcid: 0000-0002-5445-5057
- first_name: Jonathan
full_name: Spreer, Jonathan
last_name: Spreer
citation:
ama: 'Huszár K, Spreer J. 3-manifold triangulations with small treewidth. In: 35th
International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl
- Leibniz-Zentrum für Informatik; 2019:44:1-44:20. doi:10.4230/LIPIcs.SoCG.2019.44'
apa: 'Huszár, K., & Spreer, J. (2019). 3-manifold triangulations with small
treewidth. In 35th International Symposium on Computational Geometry (Vol.
129, p. 44:1-44:20). Portland, Oregon, United States: Schloss Dagstuhl - Leibniz-Zentrum
für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2019.44'
chicago: Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small
Treewidth.” In 35th International Symposium on Computational Geometry,
129:44:1-44:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPIcs.SoCG.2019.44.
ieee: K. Huszár and J. Spreer, “3-manifold triangulations with small treewidth,”
in 35th International Symposium on Computational Geometry, Portland, Oregon,
United States, 2019, vol. 129, p. 44:1-44:20.
ista: 'Huszár K, Spreer J. 2019. 3-manifold triangulations with small treewidth.
35th International Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, LIPIcs, vol. 129, 44:1-44:20.'
mla: Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small
Treewidth.” 35th International Symposium on Computational Geometry, vol.
129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20, doi:10.4230/LIPIcs.SoCG.2019.44.
short: K. Huszár, J. Spreer, in:, 35th International Symposium on Computational
Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20.
conference:
end_date: 2019-06-21
location: Portland, Oregon, United States
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2019-06-18
date_created: 2019-06-11T20:09:57Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-09-07T13:18:26Z
day: '01'
ddc:
- '516'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2019.44
external_id:
arxiv:
- '1812.05528'
file:
- access_level: open_access
checksum: 29d18c435368468aa85823dabb157e43
content_type: application/pdf
creator: kschuh
date_created: 2019-06-12T06:45:33Z
date_updated: 2020-07-14T12:47:33Z
file_id: '6557'
file_name: 2019_LIPIcs-Huszar.pdf
file_size: 905885
relation: main_file
file_date_updated: 2020-07-14T12:47:33Z
has_accepted_license: '1'
intvolume: ' 129'
keyword:
- computational 3-manifold topology
- fixed-parameter tractability
- layered triangulations
- structural graph theory
- treewidth
- cutwidth
- Heegaard genus
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 44:1-44:20
publication: 35th International Symposium on Computational Geometry
publication_identifier:
isbn:
- 978-3-95977-104-7
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
record:
- id: '8032'
relation: part_of_dissertation
status: public
scopus_import: '1'
status: public
title: 3-manifold triangulations with small treewidth
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: 129
year: '2019'
...
---
_id: '7093'
abstract:
- lang: eng
text: "In graph theory, as well as in 3-manifold topology, there exist several width-type
parameters to describe how \"simple\" or \"thin\" a given graph or 3-manifold
is. These parameters, such as pathwidth or treewidth for graphs, or the concept
of thin position for 3-manifolds, play an important role when studying algorithmic
problems; in particular, there is a variety of problems in computational 3-manifold
topology - some of them known to be computationally hard in general - that become
solvable in polynomial time as soon as the dual graph of the input triangulation
has bounded treewidth.\r\nIn view of these algorithmic results, it is natural
to ask whether every 3-manifold admits a triangulation of bounded treewidth. We
show that this is not the case, i.e., that there exists an infinite family of
closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth
(the latter implies the former, but we present two separate proofs).\r\nWe derive
these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann,
Schultens and Saito by exhibiting explicit connections between the topology of
a 3-manifold M on the one hand and width-type parameters of the dual graphs of
triangulations of M on the other hand, answering a question that had been raised
repeatedly by researchers in computational 3-manifold topology. In particular,
we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has
a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M
is at most 18(k+1) (resp. 4(3k+1))."
article_processing_charge: No
article_type: original
author:
- first_name: Kristóf
full_name: Huszár, Kristóf
id: 33C26278-F248-11E8-B48F-1D18A9856A87
last_name: Huszár
orcid: 0000-0002-5445-5057
- first_name: Jonathan
full_name: Spreer, Jonathan
last_name: Spreer
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Huszár K, Spreer J, Wagner U. On the treewidth of triangulated 3-manifolds.
Journal of Computational Geometry. 2019;10(2):70–98. doi:10.20382/JOGC.V10I2A5
apa: Huszár, K., Spreer, J., & Wagner, U. (2019). On the treewidth of triangulated
3-manifolds. Journal of Computational Geometry. Computational Geometry
Laborartoy. https://doi.org/10.20382/JOGC.V10I2A5
chicago: Huszár, Kristóf, Jonathan Spreer, and Uli Wagner. “On the Treewidth of
Triangulated 3-Manifolds.” Journal of Computational Geometry. Computational
Geometry Laborartoy, 2019. https://doi.org/10.20382/JOGC.V10I2A5.
ieee: K. Huszár, J. Spreer, and U. Wagner, “On the treewidth of triangulated 3-manifolds,”
Journal of Computational Geometry, vol. 10, no. 2. Computational Geometry
Laborartoy, pp. 70–98, 2019.
ista: Huszár K, Spreer J, Wagner U. 2019. On the treewidth of triangulated 3-manifolds.
Journal of Computational Geometry. 10(2), 70–98.
mla: Huszár, Kristóf, et al. “On the Treewidth of Triangulated 3-Manifolds.” Journal
of Computational Geometry, vol. 10, no. 2, Computational Geometry Laborartoy,
2019, pp. 70–98, doi:10.20382/JOGC.V10I2A5.
short: K. Huszár, J. Spreer, U. Wagner, Journal of Computational Geometry 10 (2019)
70–98.
date_created: 2019-11-23T12:14:09Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-09-07T13:18:26Z
day: '01'
ddc:
- '514'
department:
- _id: UlWa
doi: 10.20382/JOGC.V10I2A5
external_id:
arxiv:
- '1712.00434'
file:
- access_level: open_access
checksum: c872d590d38d538404782bca20c4c3f5
content_type: application/pdf
creator: khuszar
date_created: 2019-11-23T12:35:16Z
date_updated: 2020-07-14T12:47:49Z
file_id: '7094'
file_name: 479-1917-1-PB.pdf
file_size: 857590
relation: main_file
file_date_updated: 2020-07-14T12:47:49Z
has_accepted_license: '1'
intvolume: ' 10'
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 70–98
publication: Journal of Computational Geometry
publication_identifier:
issn:
- 1920-180X
publication_status: published
publisher: Computational Geometry Laborartoy
quality_controlled: '1'
related_material:
record:
- id: '285'
relation: earlier_version
status: public
- id: '8032'
relation: part_of_dissertation
status: public
status: public
title: On the treewidth of triangulated 3-manifolds
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 10
year: '2019'
...
---
_id: '7197'
abstract:
- lang: eng
text: During bacterial cell division, the tubulin-homolog FtsZ forms a ring-like
structure at the center of the cell. This Z-ring not only organizes the division
machinery, but treadmilling of FtsZ filaments was also found to play a key role
in distributing proteins at the division site. What regulates the architecture,
dynamics and stability of the Z-ring is currently unknown, but FtsZ-associated
proteins are known to play an important role. Here, using an in vitro reconstitution
approach, we studied how the well-conserved protein ZapA affects FtsZ treadmilling
and filament organization into large-scale patterns. Using high-resolution fluorescence
microscopy and quantitative image analysis, we found that ZapA cooperatively increases
the spatial order of the filament network, but binds only transiently to FtsZ
filaments and has no effect on filament length and treadmilling velocity. Together,
our data provides a model for how FtsZ-associated proteins can increase the precision
and stability of the bacterial cell division machinery in a switch-like manner.
acknowledged_ssus:
- _id: LifeSc
- _id: Bio
article_number: '5744'
article_processing_charge: No
article_type: original
author:
- first_name: Paulo R
full_name: Dos Santos Caldas, Paulo R
id: 38FCDB4C-F248-11E8-B48F-1D18A9856A87
last_name: Dos Santos Caldas
orcid: 0000-0001-6730-4461
- first_name: Maria D
full_name: Lopez Pelegrin, Maria D
id: 319AA9CE-F248-11E8-B48F-1D18A9856A87
last_name: Lopez Pelegrin
- first_name: Daniel J. G.
full_name: Pearce, Daniel J. G.
last_name: Pearce
- first_name: Nazmi B
full_name: Budanur, Nazmi B
id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
last_name: Budanur
orcid: 0000-0003-0423-5010
- first_name: Jan
full_name: Brugués, Jan
last_name: Brugués
- first_name: Martin
full_name: Loose, Martin
id: 462D4284-F248-11E8-B48F-1D18A9856A87
last_name: Loose
orcid: 0000-0001-7309-9724
citation:
ama: Dos Santos Caldas PR, Lopez Pelegrin MD, Pearce DJG, Budanur NB, Brugués J,
Loose M. Cooperative ordering of treadmilling filaments in cytoskeletal networks
of FtsZ and its crosslinker ZapA. Nature Communications. 2019;10. doi:10.1038/s41467-019-13702-4
apa: Dos Santos Caldas, P. R., Lopez Pelegrin, M. D., Pearce, D. J. G., Budanur,
N. B., Brugués, J., & Loose, M. (2019). Cooperative ordering of treadmilling
filaments in cytoskeletal networks of FtsZ and its crosslinker ZapA. Nature
Communications. Springer Nature. https://doi.org/10.1038/s41467-019-13702-4
chicago: Dos Santos Caldas, Paulo R, Maria D Lopez Pelegrin, Daniel J. G. Pearce,
Nazmi B Budanur, Jan Brugués, and Martin Loose. “Cooperative Ordering of Treadmilling
Filaments in Cytoskeletal Networks of FtsZ and Its Crosslinker ZapA.” Nature
Communications. Springer Nature, 2019. https://doi.org/10.1038/s41467-019-13702-4.
ieee: P. R. Dos Santos Caldas, M. D. Lopez Pelegrin, D. J. G. Pearce, N. B. Budanur,
J. Brugués, and M. Loose, “Cooperative ordering of treadmilling filaments in cytoskeletal
networks of FtsZ and its crosslinker ZapA,” Nature Communications, vol.
10. Springer Nature, 2019.
ista: Dos Santos Caldas PR, Lopez Pelegrin MD, Pearce DJG, Budanur NB, Brugués J,
Loose M. 2019. Cooperative ordering of treadmilling filaments in cytoskeletal
networks of FtsZ and its crosslinker ZapA. Nature Communications. 10, 5744.
mla: Dos Santos Caldas, Paulo R., et al. “Cooperative Ordering of Treadmilling Filaments
in Cytoskeletal Networks of FtsZ and Its Crosslinker ZapA.” Nature Communications,
vol. 10, 5744, Springer Nature, 2019, doi:10.1038/s41467-019-13702-4.
short: P.R. Dos Santos Caldas, M.D. Lopez Pelegrin, D.J.G. Pearce, N.B. Budanur,
J. Brugués, M. Loose, Nature Communications 10 (2019).
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