---
_id: '2132'
abstract:
- lang: eng
text: We consider discrete porous medium equations of the form ∂tρt=Δϕ(ρt), where
Δ is the generator of a reversible continuous time Markov chain on a finite set
χ, and ϕ is an increasing function. We show that these equations arise as gradient
flows of certain entropy functionals with respect to suitable non-local transportation
metrics. This may be seen as a discrete analogue of the Wasserstein gradient flow
structure for porous medium equations in ℝn discovered by Otto. We present a one-dimensional
counterexample to geodesic convexity and discuss Gromov-Hausdorff convergence
to the Wasserstein metric.
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Jan
full_name: Jan Maas
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: Erbar M, Maas J. Gradient flow structures for discrete porous medium equations.
*Discrete and Continuous Dynamical Systems- Series A*. 2014;34(4):1355-1374.
doi:10.3934/dcds.2014.34.1355
apa: Erbar, M., & Maas, J. (2014). Gradient flow structures for discrete porous
medium equations. *Discrete and Continuous Dynamical Systems- Series A*.
Southwest Missouri State University. https://doi.org/10.3934/dcds.2014.34.1355
chicago: Erbar, Matthias, and Jan Maas. “Gradient Flow Structures for Discrete Porous
Medium Equations.” *Discrete and Continuous Dynamical Systems- Series A*.
Southwest Missouri State University, 2014. https://doi.org/10.3934/dcds.2014.34.1355 .
ieee: M. Erbar and J. Maas, “Gradient flow structures for discrete porous medium
equations,” *Discrete and Continuous Dynamical Systems- Series A*, vol. 34,
no. 4. Southwest Missouri State University, pp. 1355–1374, 2014.
ista: Erbar M, Maas J. 2014. Gradient flow structures for discrete porous medium
equations. Discrete and Continuous Dynamical Systems- Series A. 34(4), 1355–1374.
mla: Erbar, Matthias, and Jan Maas. “Gradient Flow Structures for Discrete Porous
Medium Equations.” *Discrete and Continuous Dynamical Systems- Series A*,
vol. 34, no. 4, Southwest Missouri State University, 2014, pp. 1355–74, doi:10.3934/dcds.2014.34.1355
.
short: M. Erbar, J. Maas, Discrete and Continuous Dynamical Systems- Series A 34
(2014) 1355–1374.
date_created: 2018-12-11T11:55:54Z
date_published: 2014-04-01T00:00:00Z
date_updated: 2021-01-12T06:55:30Z
day: '01'
doi: '10.3934/dcds.2014.34.1355 '
extern: 1
intvolume: ' 34'
issue: '4'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1212.1129
month: '04'
oa: 1
page: 1355 - 1374
publication: Discrete and Continuous Dynamical Systems- Series A
publication_status: published
publisher: Southwest Missouri State University
publist_id: '4903'
quality_controlled: 0
status: public
title: Gradient flow structures for discrete porous medium equations
type: journal_article
volume: 34
year: '2014'
...
---
_id: '2133'
abstract:
- lang: eng
text: "Let ℭ denote the Clifford algebra over ℝ\U0001D45B, which is the von Neumann
algebra generated by n self-adjoint operators Q j , j = 1,…,n satisfying the canonical
anticommutation relations, Q i Q j + Q j Q i = 2δ ij I, and let τ denote the
normalized trace on ℭ. This algebra arises in quantum mechanics as the algebra
of observables generated by n fermionic degrees of freedom. Let \U0001D513 denote
the set of all positive operators \U0001D70C∈ℭ such that τ(ρ) = 1; these are the
non-commutative analogs of probability densities in the non-commutative probability
space (ℭ,\U0001D70F). The fermionic Fokker–Planck equation is a quantum-mechanical
analog of the classical Fokker–Planck equation with which it has much in common,
such as the same optimal hypercontractivity properties. In this paper we construct
a Riemannian metric on \U0001D513 that we show to be a natural analog of the classical
2-Wasserstein metric, and we show that, in analogy with the classical case, the
fermionic Fokker–Planck equation is gradient flow in this metric for the relative
entropy with respect to the ground state. We derive a number of consequences of
this, such as a sharp Talagrand inequality for this metric, and we prove a number
of results pertaining to this metric. Several open problems are raised."
author:
- first_name: Eric
full_name: Carlen, Eric
last_name: Carlen
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: Carlen E, Maas J. An analog of the 2-Wasserstein metric in non-commutative
probability under which the fermionic Fokker-Planck equation is gradient flow
for the entropy. *Communications in Mathematical Physics*. 2014;331(3):887-926.
doi:10.1007/s00220-014-2124-8
apa: Carlen, E., & Maas, J. (2014). An analog of the 2-Wasserstein metric in
non-commutative probability under which the fermionic Fokker-Planck equation is
gradient flow for the entropy. *Communications in Mathematical Physics*.
Springer. https://doi.org/10.1007/s00220-014-2124-8
chicago: Carlen, Eric, and Jan Maas. “An Analog of the 2-Wasserstein Metric in Non-Commutative
Probability under Which the Fermionic Fokker-Planck Equation Is Gradient Flow
for the Entropy.” *Communications in Mathematical Physics*. Springer, 2014.
https://doi.org/10.1007/s00220-014-2124-8.
ieee: E. Carlen and J. Maas, “An analog of the 2-Wasserstein metric in non-commutative
probability under which the fermionic Fokker-Planck equation is gradient flow
for the entropy,” *Communications in Mathematical Physics*, vol. 331, no.
3. Springer, pp. 887–926, 2014.
ista: Carlen E, Maas J. 2014. An analog of the 2-Wasserstein metric in non-commutative
probability under which the fermionic Fokker-Planck equation is gradient flow
for the entropy. Communications in Mathematical Physics. 331(3), 887–926.
mla: Carlen, Eric, and Jan Maas. “An Analog of the 2-Wasserstein Metric in Non-Commutative
Probability under Which the Fermionic Fokker-Planck Equation Is Gradient Flow
for the Entropy.” *Communications in Mathematical Physics*, vol. 331, no.
3, Springer, 2014, pp. 887–926, doi:10.1007/s00220-014-2124-8.
short: E. Carlen, J. Maas, Communications in Mathematical Physics 331 (2014) 887–926.
date_created: 2018-12-11T11:55:54Z
date_published: 2014-11-01T00:00:00Z
date_updated: 2021-01-12T06:55:30Z
day: '01'
doi: 10.1007/s00220-014-2124-8
extern: '1'
intvolume: ' 331'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'http://arxiv.org/abs/1203.5377 '
month: '11'
oa: 1
oa_version: Submitted Version
page: 887 - 926
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4901'
quality_controlled: '1'
status: public
title: An analog of the 2-Wasserstein metric in non-commutative probability under
which the fermionic Fokker-Planck equation is gradient flow for the entropy
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 331
year: '2014'
...
---
_id: '2140'
abstract:
- lang: eng
text: We propose a technique for engineering momentum-dependent dissipation in Bose-Einstein
condensates with non-local interactions. The scheme relies on the use of momentum-dependent
dark-states in close analogy to velocity-selective coherent population trapping.
During the short-time dissipative dynamics, the system is driven into a particular
finite-momentum phonon mode, which in real space corresponds to an ordered structure
with non-local density-density correlations. Dissipation-induced ordering can
be observed and studied in present-day experiments using cold atoms with dipole-dipole
or off-resonant Rydberg interactions. Due to its dissipative nature, the ordering
does not require artificial breaking of translational symmetry by an opticallattice
or harmonic trap. This opens up a perspective of direct cooling of quantum gases
into strongly-interacting phases.
acknowledgement: This work was supported by NSF through a grant for the Institute
for Theoretical Atomic, Molecular, and Optical Physics at Harvard University and
Smithsonian Astrophysical Observatory as well as the Harvard Quantum Optics Center.
article_number: '070401'
author:
- first_name: Johannes
full_name: Otterbach, Johannes
last_name: Otterbach
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
citation:
ama: Otterbach J, Lemeshko M. Dissipative preparation of spatial order in Rydberg-dressed
Bose-Einstein condensates. *Physical Review Letters*. 2014;113(7). doi:10.1103/PhysRevLett.113.070401
apa: Otterbach, J., & Lemeshko, M. (2014). Dissipative preparation of spatial
order in Rydberg-dressed Bose-Einstein condensates. *Physical Review Letters*.
American Physical Society. https://doi.org/10.1103/PhysRevLett.113.070401
chicago: Otterbach, Johannes, and Mikhail Lemeshko. “Dissipative Preparation of
Spatial Order in Rydberg-Dressed Bose-Einstein Condensates.” *Physical Review
Letters*. American Physical Society, 2014. https://doi.org/10.1103/PhysRevLett.113.070401.
ieee: J. Otterbach and M. Lemeshko, “Dissipative preparation of spatial order in
Rydberg-dressed Bose-Einstein condensates,” *Physical Review Letters*, vol.
113, no. 7. American Physical Society, 2014.
ista: Otterbach J, Lemeshko M. 2014. Dissipative preparation of spatial order in
Rydberg-dressed Bose-Einstein condensates. Physical Review Letters. 113(7), 070401.
mla: Otterbach, Johannes, and Mikhail Lemeshko. “Dissipative Preparation of Spatial
Order in Rydberg-Dressed Bose-Einstein Condensates.” *Physical Review Letters*,
vol. 113, no. 7, 070401, American Physical Society, 2014, doi:10.1103/PhysRevLett.113.070401.
short: J. Otterbach, M. Lemeshko, Physical Review Letters 113 (2014).
date_created: 2018-12-11T11:55:56Z
date_published: 2014-08-11T00:00:00Z
date_updated: 2021-01-12T06:55:33Z
day: '11'
doi: 10.1103/PhysRevLett.113.070401
extern: '1'
intvolume: ' 113'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1308.5905
month: '08'
oa: 1
oa_version: Submitted Version
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '4884'
status: public
title: Dissipative preparation of spatial order in Rydberg-dressed Bose-Einstein condensates
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 113
year: '2014'
...
---
_id: '2141'
abstract:
- lang: eng
text: The computation of the winning set for Büchi objectives in alternating games
on graphs is a central problem in computer-aided verification with a large number
of applications. The long-standing best known upper bound for solving the problem
is Õ(n ⋅ m), where n is the number of vertices and m is the number of edges in
the graph. We are the first to break the Õ(n ⋅ m) boundary by presenting a new
technique that reduces the running time to O(n2). This bound also leads to O(n2)-time
algorithms for computing the set of almost-sure winning vertices for Büchi objectives
(1) in alternating games with probabilistic transitions (improving an earlier
bound of Õ(n ⋅ m)), (2) in concurrent graph games with constant actions (improving
an earlier bound of O(n3)), and (3) in Markov decision processes (improving for
m>n4/3 an earlier bound of O(m ⋅ √m)). We then show how to maintain the winning
set for Büchi objectives in alternating games under a sequence of edge insertions
or a sequence of edge deletions in O(n) amortized time per operation. Our algorithms
are the first dynamic algorithms for this problem. We then consider another core
graph theoretic problem in verification of probabilistic systems, namely computing
the maximal end-component decomposition of a graph. We present two improved static
algorithms for the maximal end-component decomposition problem. Our first algorithm
is an O(m ⋅ √m)-time algorithm, and our second algorithm is an O(n2)-time algorithm
which is obtained using the same technique as for alternating Büchi games. Thus,
we obtain an O(min &lcu;m ⋅ √m,n2})-time algorithm improving the long-standing
O(n ⋅ m) time bound. Finally, we show how to maintain the maximal end-component
decomposition of a graph under a sequence of edge insertions or a sequence of
edge deletions in O(n) amortized time per edge deletion, and O(m) worst-case time
per edge insertion. Again, our algorithms are the first dynamic algorithms for
this problem.
article_number: a15
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Monika
full_name: Henzinger, Monika
last_name: Henzinger
citation:
ama: Chatterjee K, Henzinger M. Efficient and dynamic algorithms for alternating
Büchi games and maximal end-component decomposition. *Journal of the ACM*.
2014;61(3). doi:10.1145/2597631
apa: Chatterjee, K., & Henzinger, M. (2014). Efficient and dynamic algorithms
for alternating Büchi games and maximal end-component decomposition. *Journal
of the ACM*. ACM. https://doi.org/10.1145/2597631
chicago: Chatterjee, Krishnendu, and Monika Henzinger. “Efficient and Dynamic Algorithms
for Alternating Büchi Games and Maximal End-Component Decomposition.” *Journal
of the ACM*. ACM, 2014. https://doi.org/10.1145/2597631.
ieee: K. Chatterjee and M. Henzinger, “Efficient and dynamic algorithms for alternating
Büchi games and maximal end-component decomposition,” *Journal of the ACM*,
vol. 61, no. 3. ACM, 2014.
ista: Chatterjee K, Henzinger M. 2014. Efficient and dynamic algorithms for alternating
Büchi games and maximal end-component decomposition. Journal of the ACM. 61(3),
a15.
mla: Chatterjee, Krishnendu, and Monika Henzinger. “Efficient and Dynamic Algorithms
for Alternating Büchi Games and Maximal End-Component Decomposition.” *Journal
of the ACM*, vol. 61, no. 3, a15, ACM, 2014, doi:10.1145/2597631.
short: K. Chatterjee, M. Henzinger, Journal of the ACM 61 (2014).
date_created: 2018-12-11T11:55:57Z
date_published: 2014-05-01T00:00:00Z
date_updated: 2021-01-12T07:41:31Z
day: '01'
department:
- _id: KrCh
doi: 10.1145/2597631
ec_funded: 1
intvolume: ' 61'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://eprints.cs.univie.ac.at/3933/
month: '05'
oa: 1
oa_version: Submitted Version
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25892FC0-B435-11E9-9278-68D0E5697425
grant_number: ICT15-003
name: Efficient Algorithms for Computer Aided Verification
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication: Journal of the ACM
publication_status: published
publisher: ACM
publist_id: '4883'
quality_controlled: '1'
related_material:
record:
- id: '3165'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Efficient and dynamic algorithms for alternating Büchi games and maximal end-component
decomposition
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 61
year: '2014'
...
---
_id: '2153'
abstract:
- lang: eng
text: 'We define a simple, explicit map sending a morphism f : M → N of pointwise
finite dimensional persistence modules to a matching between the barcodes of M
and N. Our main result is that, in a precise sense, the quality of this matching
is tightly controlled by the lengths of the longest intervals in the barcodes
of ker f and coker f . As an immediate corollary, we obtain a new proof of the
algebraic stability theorem for persistence barcodes [5, 9], a fundamental result
in the theory of persistent homology. In contrast to previous proofs, ours shows
explicitly how a δ-interleaving morphism between two persistence modules induces
a δ-matching between the barcodes of the two modules. Our main result also specializes
to a structure theorem for submodules and quotients of persistence modules. Copyright
is held by the owner/author(s).'
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Michael
full_name: Lesnick, Michael
last_name: Lesnick
citation:
ama: 'Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability
of persistence. In: *Proceedings of the Annual Symposium on Computational Geometry*.
ACM; 2014:355-364. doi:10.1145/2582112.2582168'
apa: 'Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the
algebraic stability of persistence. In *Proceedings of the Annual Symposium
on Computational Geometry* (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168'
chicago: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and
the Algebraic Stability of Persistence.” In *Proceedings of the Annual Symposium
on Computational Geometry*, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168.
ieee: U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic
stability of persistence,” in *Proceedings of the Annual Symposium on Computational
Geometry*, Kyoto, Japan, 2014, pp. 355–364.
ista: 'Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic
stability of persistence. Proceedings of the Annual Symposium on Computational
Geometry. SoCG: Symposium on Computational Geometry, 355–364.'
mla: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the
Algebraic Stability of Persistence.” *Proceedings of the Annual Symposium on
Computational Geometry*, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.
short: U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 355–364.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582168
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1311.3681
month: '06'
oa: 1
oa_version: Submitted Version
page: 355 - 364
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4853'
quality_controlled: '1'
scopus_import: 1
status: public
title: Induced matchings of barcodes and the algebraic stability of persistence
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2154'
abstract:
- lang: eng
text: A result of Boros and Füredi (d = 2) and of Bárány (arbitrary d) asserts that
for every d there exists cd > 0 such that for every n-point set P ⊂ ℝd, some
point of ℝd is covered by at least (Formula presented.) of the d-simplices spanned
by the points of P. The largest possible value of cd has been the subject of ongoing
research. Recently Gromov improved the existing lower bounds considerably by introducing
a new, topological proof method. We provide an exposition of the combinatorial
component of Gromov's approach, in terms accessible to combinatorialists and discrete
geometers, and we investigate the limits of his method. In particular, we give
tighter bounds on the cofilling profiles for the (n - 1)-simplex. These bounds
yield a minor improvement over Gromov's lower bounds on cd for large d, but they
also show that the room for further improvement through the cofilling profiles
alone is quite small. We also prove a slightly better lower bound for c3 by an
approach using an additional structure besides the cofilling profiles. We formulate
a combinatorial extremal problem whose solution might perhaps lead to a tight
lower bound for cd.
acknowledgement: Swiss National Science Foundation (SNF 200021-125309, 200020-138230,
200020-12507)
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Matoušek J, Wagner U. On Gromov’s method of selecting heavily covered points.
*Discrete & Computational Geometry*. 2014;52(1):1-33. doi:10.1007/s00454-014-9584-7
apa: Matoušek, J., & Wagner, U. (2014). On Gromov’s method of selecting heavily
covered points. *Discrete & Computational Geometry*. Springer. https://doi.org/10.1007/s00454-014-9584-7
chicago: Matoušek, Jiří, and Uli Wagner. “On Gromov’s Method of Selecting Heavily
Covered Points.” *Discrete & Computational Geometry*. Springer, 2014.
https://doi.org/10.1007/s00454-014-9584-7.
ieee: J. Matoušek and U. Wagner, “On Gromov’s method of selecting heavily covered
points,” *Discrete & Computational Geometry*, vol. 52, no. 1. Springer,
pp. 1–33, 2014.
ista: Matoušek J, Wagner U. 2014. On Gromov’s method of selecting heavily covered
points. Discrete & Computational Geometry. 52(1), 1–33.
mla: Matoušek, Jiří, and Uli Wagner. “On Gromov’s Method of Selecting Heavily Covered
Points.” *Discrete & Computational Geometry*, vol. 52, no. 1, Springer,
2014, pp. 1–33, doi:10.1007/s00454-014-9584-7.
short: J. Matoušek, U. Wagner, Discrete & Computational Geometry 52 (2014) 1–33.
date_created: 2018-12-11T11:56:01Z
date_published: 2014-07-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/s00454-014-9584-7
intvolume: ' 52'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1102.3515
month: '07'
oa: 1
oa_version: Submitted Version
page: 1 - 33
project:
- _id: 25FA3206-B435-11E9-9278-68D0E5697425
grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '4852'
quality_controlled: '1'
scopus_import: 1
status: public
title: On Gromov's method of selecting heavily covered points
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2014'
...
---
_id: '2155'
abstract:
- lang: eng
text: Given a finite set of points in Rn and a positive radius, we study the Čech,
Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete
Morse theory. We prove that the latter three complexes are simple-homotopy equivalent.
Our results have applications in topological data analysis and in the reconstruction
of shapes from sampled data. Copyright is held by the owner/author(s).
acknowledgement: This research is partially supported by ESF under the ACAT Research
Network Programme, and by the Russian Government under mega project 11.G34.31.0053
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations.
In: *Proceedings of the Annual Symposium on Computational Geometry*. ACM;
2014:484-490. doi:10.1145/2582112.2582167'
apa: 'Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay
filtrations. In *Proceedings of the Annual Symposium on Computational Geometry*
(pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167'
chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
Delaunay Filtrations.” In *Proceedings of the Annual Symposium on Computational
Geometry*, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167.
ieee: U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,”
in *Proceedings of the Annual Symposium on Computational Geometry*, Kyoto,
Japan, 2014, pp. 484–490.
ista: 'Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations.
Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium
on Computational Geometry, 484–490.'
mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
Filtrations.” *Proceedings of the Annual Symposium on Computational Geometry*,
ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167.
short: U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 484–490.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:01Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582167
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1312.1231
month: '06'
oa: 1
oa_version: Submitted Version
page: 484 - 490
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4851'
quality_controlled: '1'
scopus_import: 1
status: public
title: The morse theory of Čech and Delaunay filtrations
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2156'
abstract:
- lang: eng
text: We propose a metric for Reeb graphs, called the functional distortion distance.
Under this distance, the Reeb graph is stable against small changes of input functions.
At the same time, it remains discriminative at differentiating input functions.
In particular, the main result is that the functional distortion distance between
two Reeb graphs is bounded from below by the bottleneck distance between both
the ordinary and extended persistence diagrams for appropriate dimensions. As
an application of our results, we analyze a natural simplification scheme for
Reeb graphs, and show that persistent features in Reeb graph remains persistent
under simplification. Understanding the stability of important features of the
Reeb graph under simplification is an interesting problem on its own right, and
critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).
acknowledgement: National Science Foundation under grants CCF-1319406, CCF-1116258.
author:
- first_name: Ulrich
full_name: Bauer, Ulrich
id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
last_name: Bauer
orcid: 0000-0002-9683-0724
- first_name: Xiaoyin
full_name: Ge, Xiaoyin
last_name: Ge
- first_name: Yusu
full_name: Wang, Yusu
last_name: Wang
citation:
ama: 'Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: *Proceedings
of the Annual Symposium on Computational Geometry*. ACM; 2014:464-473. doi:10.1145/2582112.2582169'
apa: 'Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb
graphs. In *Proceedings of the Annual Symposium on Computational Geometry*
(pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169'
chicago: Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb
Graphs.” In *Proceedings of the Annual Symposium on Computational Geometry*,
464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.
ieee: U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in
*Proceedings of the Annual Symposium on Computational Geometry*, Kyoto, Japan,
2014, pp. 464–473.
ista: 'Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings
of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational
Geometry, 464–473.'
mla: Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” *Proceedings
of the Annual Symposium on Computational Geometry*, ACM, 2014, pp. 464–73,
doi:10.1145/2582112.2582169.
short: U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational
Geometry, ACM, 2014, pp. 464–473.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:02Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T06:55:39Z
day: '01'
department:
- _id: HeEd
doi: 10.1145/2582112.2582169
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1307.2839
month: '06'
oa: 1
oa_version: Submitted Version
page: 464 - 473
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '318493'
name: Topological Complex Systems
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4850'
quality_controlled: '1'
scopus_import: 1
status: public
title: Measuring distance between Reeb graphs
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2157'
abstract:
- lang: eng
text: 'We show that the following algorithmic problem is decidable: given a 2-dimensional
simplicial complex, can it be embedded (topologically, or equivalently, piecewise
linearly) in ℝ3? By a known reduction, it suffices to decide the embeddability
of a given triangulated 3-manifold X into the 3-sphere S3. The main step, which
allows us to simplify X and recurse, is in proving that if X can be embedded in
S3, then there is also an embedding in which X has a short meridian, i.e., an
essential curve in the boundary of X bounding a disk in S3 nX with length bounded
by a computable function of the number of tetrahedra of X.'
acknowledgement: ERC Advanced Grant No. 267165; Grant GRADR Eurogiga GIG/11/E023 (SNSF-PP00P2-138948);
Swiss National Science Foundation (SNSF-200020-138230).
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Eric
full_name: Sedgwick, Eric
last_name: Sedgwick
- first_name: Martin
full_name: Tancer, Martin
id: 38AC689C-F248-11E8-B48F-1D18A9856A87
last_name: Tancer
orcid: 0000-0002-1191-6714
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Matoušek J, Sedgwick E, Tancer M, Wagner U. Embeddability in the 3 sphere
is decidable. In: *Proceedings of the Annual Symposium on Computational Geometry*.
ACM; 2014:78-84. doi:10.1145/2582112.2582137'
apa: 'Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2014). Embeddability
in the 3 sphere is decidable. In *Proceedings of the Annual Symposium on Computational
Geometry* (pp. 78–84). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582137'
chicago: Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Embeddability
in the 3 Sphere Is Decidable.” In *Proceedings of the Annual Symposium on Computational
Geometry*, 78–84. ACM, 2014. https://doi.org/10.1145/2582112.2582137.
ieee: J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Embeddability in the
3 sphere is decidable,” in *Proceedings of the Annual Symposium on Computational
Geometry*, Kyoto, Japan, 2014, pp. 78–84.
ista: 'Matoušek J, Sedgwick E, Tancer M, Wagner U. 2014. Embeddability in the 3
sphere is decidable. Proceedings of the Annual Symposium on Computational Geometry.
SoCG: Symposium on Computational Geometry, 78–84.'
mla: Matoušek, Jiří, et al. “Embeddability in the 3 Sphere Is Decidable.” *Proceedings
of the Annual Symposium on Computational Geometry*, ACM, 2014, pp. 78–84, doi:10.1145/2582112.2582137.
short: J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, in:, Proceedings of the Annual
Symposium on Computational Geometry, ACM, 2014, pp. 78–84.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:02Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2021-01-12T07:55:36Z
day: '01'
department:
- _id: UlWa
doi: 10.1145/2582112.2582137
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1402.0815
month: '06'
oa: 1
oa_version: Submitted Version
page: 78 - 84
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4849'
quality_controlled: '1'
related_material:
record:
- id: '425'
relation: later_version
status: public
scopus_import: 1
status: public
title: Embeddability in the 3 sphere is decidable
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...
---
_id: '2158'
abstract:
- lang: eng
text: Directional guidance of migrating cells is relatively well explored in the
reductionist setting of cell culture experiments. Here spatial gradients of chemical
cues as well as gradients of mechanical substrate characteristics prove sufficient
to attract single cells as well as their collectives. How such gradients present
and act in the context of an organism is far less clear. Here we review recent
advances in understanding how guidance cues emerge and operate in the physiological
context.
acknowledgement: This effort was supported by the Intramural Research Program of the
Center for Cancer Research, NCI, National Institutes of Health and the European
Research Council (ERC).
author:
- first_name: Ritankar
full_name: Majumdar, Ritankar
last_name: Majumdar
- first_name: Michael K
full_name: Sixt, Michael K
id: 41E9FBEA-F248-11E8-B48F-1D18A9856A87
last_name: Sixt
orcid: 0000-0002-6620-9179
- first_name: Carole
full_name: Parent, Carole
last_name: Parent
citation:
ama: Majumdar R, Sixt MK, Parent C. New paradigms in the establishment and maintenance
of gradients during directed cell migration. *Current Opinion in Cell Biology*.
2014;30(1):33-40. doi:10.1016/j.ceb.2014.05.010
apa: Majumdar, R., Sixt, M. K., & Parent, C. (2014). New paradigms in the establishment
and maintenance of gradients during directed cell migration. *Current Opinion
in Cell Biology*. Elsevier. https://doi.org/10.1016/j.ceb.2014.05.010
chicago: Majumdar, Ritankar, Michael K Sixt, and Carole Parent. “New Paradigms in
the Establishment and Maintenance of Gradients during Directed Cell Migration.”
*Current Opinion in Cell Biology*. Elsevier, 2014. https://doi.org/10.1016/j.ceb.2014.05.010.
ieee: R. Majumdar, M. K. Sixt, and C. Parent, “New paradigms in the establishment
and maintenance of gradients during directed cell migration,” *Current Opinion
in Cell Biology*, vol. 30, no. 1. Elsevier, pp. 33–40, 2014.
ista: Majumdar R, Sixt MK, Parent C. 2014. New paradigms in the establishment and
maintenance of gradients during directed cell migration. Current Opinion in Cell
Biology. 30(1), 33–40.
mla: Majumdar, Ritankar, et al. “New Paradigms in the Establishment and Maintenance
of Gradients during Directed Cell Migration.” *Current Opinion in Cell Biology*,
vol. 30, no. 1, Elsevier, 2014, pp. 33–40, doi:10.1016/j.ceb.2014.05.010.
short: R. Majumdar, M.K. Sixt, C. Parent, Current Opinion in Cell Biology 30 (2014)
33–40.
date_created: 2018-12-11T11:56:03Z
date_published: 2014-10-01T00:00:00Z
date_updated: 2021-01-12T06:55:40Z
day: '01'
department:
- _id: MiSi
doi: 10.1016/j.ceb.2014.05.010
external_id:
pmid:
- '24959970'
intvolume: ' 30'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4177954/
month: '10'
oa: 1
oa_version: Submitted Version
page: 33 - 40
pmid: 1
publication: Current Opinion in Cell Biology
publication_status: published
publisher: Elsevier
publist_id: '4848'
quality_controlled: '1'
scopus_import: 1
status: public
title: New paradigms in the establishment and maintenance of gradients during directed
cell migration
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2014'
...