---
_id: '1314'
abstract:
- lang: eng
text: 'We derive a posteriori estimates for the modeling error caused by the assumption
of perfect incompressibility in the incompressible Navier-Stokes equation: Real
fluids are never perfectly incompressible but always feature at least some low
amount of compressibility. Thus, their behavior is described by the compressible
Navier-Stokes equation, the pressure being a steep function of the density. We
rigorously estimate the difference between an approximate solution to the incompressible
Navier-Stokes equation and any weak solution to the compressible Navier-Stokes
equation in the sense of Lions (without assuming any additional regularity of
solutions). Heuristics and numerical results suggest that our error estimates
are of optimal order in the case of "well-behaved" flows and divergence-free
approximations of the velocity field. Thus, we expect our estimates to justify
the idealization of fluids as perfectly incompressible also in practical situations.'
acknowledgement: The research of the author was supported by the Lithuanian-Swiss
cooperation program under the project agreement CH-SMM-01/0.
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Fischer JL. A posteriori modeling error estimates for the assumption of perfect
incompressibility in the Navier-Stokes equation. SIAM Journal on Numerical
Analysis. 2015;53(5):2178-2205. doi:10.1137/140966654
apa: Fischer, J. L. (2015). A posteriori modeling error estimates for the assumption
of perfect incompressibility in the Navier-Stokes equation. SIAM Journal on
Numerical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140966654
chicago: Fischer, Julian L. “A Posteriori Modeling Error Estimates for the Assumption
of Perfect Incompressibility in the Navier-Stokes Equation.” SIAM Journal on
Numerical Analysis. Society for Industrial and Applied Mathematics , 2015.
https://doi.org/10.1137/140966654.
ieee: J. L. Fischer, “A posteriori modeling error estimates for the assumption of
perfect incompressibility in the Navier-Stokes equation,” SIAM Journal on Numerical
Analysis, vol. 53, no. 5. Society for Industrial and Applied Mathematics ,
pp. 2178–2205, 2015.
ista: Fischer JL. 2015. A posteriori modeling error estimates for the assumption
of perfect incompressibility in the Navier-Stokes equation. SIAM Journal on Numerical
Analysis. 53(5), 2178–2205.
mla: Fischer, Julian L. “A Posteriori Modeling Error Estimates for the Assumption
of Perfect Incompressibility in the Navier-Stokes Equation.” SIAM Journal on
Numerical Analysis, vol. 53, no. 5, Society for Industrial and Applied Mathematics
, 2015, pp. 2178–205, doi:10.1137/140966654.
short: J.L. Fischer, SIAM Journal on Numerical Analysis 53 (2015) 2178–2205.
date_created: 2018-12-11T11:51:19Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:49Z
day: '01'
doi: 10.1137/140966654
extern: '1'
intvolume: ' 53'
issue: '5'
language:
- iso: eng
month: '01'
oa_version: None
page: 2178 - 2205
publication: SIAM Journal on Numerical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '5957'
quality_controlled: '1'
status: public
title: A posteriori modeling error estimates for the assumption of perfect incompressibility
in the Navier-Stokes equation
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2015'
...
---
_id: '1313'
abstract:
- lang: eng
text: We present an algorithm for the derivation of lower bounds on support propagation
for a certain class of nonlinear parabolic equations. We proceed by combining
the ideas in some recent papers by the author with the algorithmic construction
of entropies due to Jüngel and Matthes, reducing the problem to a quantifier elimination
problem. Due to its complexity, the quantifier elimination problem cannot be solved
by present exact algorithms. However, by tackling the quantifier elimination problem
numerically, in the case of the thin-film equation we are able to improve recent
results by the author in the regime of strong slippage n ∈ (1, 2). For certain
second-order doubly nonlinear parabolic equations, we are able to extend the known
lower bounds on free boundary propagation to the case of irregular oscillatory
initial data. Finally, we apply our method to a sixth-order quantum drift-diffusion
equation, resulting in an upper bound on the time which it takes for the support
to reach every point in the domain.
acknowledgement: This research was supported by the Lithuanian-Swiss cooperation program
under the project agreement No. CH-SMM-01/0.
author:
- first_name: Julian L
full_name: Julian Fischer
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: 'Fischer JL. Estimates on front propagation for nonlinear higher-order parabolic
equations: An algorithmic approach. Interfaces and Free Boundaries. 2015;17(1):1-20.
doi:10.4171/IFB/331'
apa: 'Fischer, J. L. (2015). Estimates on front propagation for nonlinear higher-order
parabolic equations: An algorithmic approach. Interfaces and Free Boundaries.
European Mathematical Society Publishing House. https://doi.org/10.4171/IFB/331'
chicago: 'Fischer, Julian L. “Estimates on Front Propagation for Nonlinear Higher-Order
Parabolic Equations: An Algorithmic Approach.” Interfaces and Free Boundaries.
European Mathematical Society Publishing House, 2015. https://doi.org/10.4171/IFB/331.'
ieee: 'J. L. Fischer, “Estimates on front propagation for nonlinear higher-order
parabolic equations: An algorithmic approach,” Interfaces and Free Boundaries,
vol. 17, no. 1. European Mathematical Society Publishing House, pp. 1–20, 2015.'
ista: 'Fischer JL. 2015. Estimates on front propagation for nonlinear higher-order
parabolic equations: An algorithmic approach. Interfaces and Free Boundaries.
17(1), 1–20.'
mla: 'Fischer, Julian L. “Estimates on Front Propagation for Nonlinear Higher-Order
Parabolic Equations: An Algorithmic Approach.” Interfaces and Free Boundaries,
vol. 17, no. 1, European Mathematical Society Publishing House, 2015, pp. 1–20,
doi:10.4171/IFB/331.'
short: J.L. Fischer, Interfaces and Free Boundaries 17 (2015) 1–20.
date_created: 2018-12-11T11:51:19Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:48Z
day: '01'
doi: 10.4171/IFB/331
extern: 1
intvolume: ' 17'
issue: '1'
month: '01'
page: 1 - 20
publication: Interfaces and Free Boundaries
publication_status: published
publisher: European Mathematical Society Publishing House
publist_id: '5956'
quality_controlled: 0
status: public
title: 'Estimates on front propagation for nonlinear higher-order parabolic equations:
An algorithmic approach'
type: journal_article
volume: 17
year: '2015'
...
---
_id: '1316'
abstract:
- lang: eng
text: In the present work we introduce the notion of a renormalized solution for
reaction–diffusion systems with entropy-dissipating reactions. We establish the
global existence of renormalized solutions. In the case of integrable reaction
terms our notion of a renormalized solution reduces to the usual notion of a weak
solution. Our existence result in particular covers all reaction–diffusion systems
involving a single reversible reaction with mass-action kinetics and (possibly
species-dependent) Fick-law diffusion; more generally, it covers the case of systems
of reversible reactions with mass-action kinetics which satisfy the detailed balance
condition. For such equations the existence of any kind of solution in general
was an open problem, thereby motivating the study of renormalized solutions.
acknowledgement: This research was supported by the Lithuanian-Swiss cooperation program
under the project agreement No. CH-SMM-01/0.
author:
- first_name: Julian L
full_name: Julian Fischer
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Fischer JL. Global existence of renormalized solutions to entropy-dissipating
reaction–diffusion systems. Archive for Rational Mechanics and Analysis.
2015;218(1):553-587. doi:10.1007/s00205-015-0866-x
apa: Fischer, J. L. (2015). Global existence of renormalized solutions to entropy-dissipating
reaction–diffusion systems. Archive for Rational Mechanics and Analysis.
Springer. https://doi.org/10.1007/s00205-015-0866-x
chicago: Fischer, Julian L. “Global Existence of Renormalized Solutions to Entropy-Dissipating
Reaction–Diffusion Systems.” Archive for Rational Mechanics and Analysis.
Springer, 2015. https://doi.org/10.1007/s00205-015-0866-x.
ieee: J. L. Fischer, “Global existence of renormalized solutions to entropy-dissipating
reaction–diffusion systems,” Archive for Rational Mechanics and Analysis,
vol. 218, no. 1. Springer, pp. 553–587, 2015.
ista: Fischer JL. 2015. Global existence of renormalized solutions to entropy-dissipating
reaction–diffusion systems. Archive for Rational Mechanics and Analysis. 218(1),
553–587.
mla: Fischer, Julian L. “Global Existence of Renormalized Solutions to Entropy-Dissipating
Reaction–Diffusion Systems.” Archive for Rational Mechanics and Analysis,
vol. 218, no. 1, Springer, 2015, pp. 553–87, doi:10.1007/s00205-015-0866-x.
short: J.L. Fischer, Archive for Rational Mechanics and Analysis 218 (2015) 553–587.
date_created: 2018-12-11T11:51:20Z
date_published: 2015-10-01T00:00:00Z
date_updated: 2021-01-12T06:49:50Z
day: '01'
doi: 10.1007/s00205-015-0866-x
extern: 1
intvolume: ' 218'
issue: '1'
month: '10'
page: 553 - 587
publication: Archive for Rational Mechanics and Analysis
publication_status: published
publisher: Springer
publist_id: '5955'
quality_controlled: 0
status: public
title: Global existence of renormalized solutions to entropy-dissipating reaction–diffusion
systems
type: journal_article
volume: 218
year: '2015'
...
---
_id: '1383'
abstract:
- lang: eng
text: In plants, vacuolar H+-ATPase (V-ATPase) activity acidifies both the trans-Golgi
network/early endosome (TGN/EE) and the vacuole. This dual V-ATPase function has
impeded our understanding of how the pH homeostasis within the plant TGN/EE controls
exo- and endocytosis. Here, we show that the weak V-ATPase mutant deetiolated3
(det3) displayed a pH increase in the TGN/EE, but not in the vacuole, strongly
impairing secretion and recycling of the brassinosteroid receptor and the cellulose
synthase complexes to the plasma membrane, in contrast to mutants lacking tonoplast-localized
V-ATPase activity only. The brassinosteroid insensitivity and the cellulose deficiency
defects in det3 were tightly correlated with reduced Golgi and TGN/EE motility.
Thus, our results provide strong evidence that acidification of the TGN/EE, but
not of the vacuole, is indispensable for functional secretion and recycling in
plants.
article_number: '15094'
article_processing_charge: No
article_type: original
author:
- first_name: Luo
full_name: Yu, Luo
last_name: Yu
- first_name: Stefan
full_name: Scholl, Stefan
last_name: Scholl
- first_name: Anett
full_name: Doering, Anett
last_name: Doering
- first_name: Zhang
full_name: Yi, Zhang
last_name: Yi
- first_name: Niloufer
full_name: Irani, Niloufer
last_name: Irani
- first_name: Simone
full_name: Di Rubbo, Simone
last_name: Di Rubbo
- first_name: Lutz
full_name: Neumetzler, Lutz
last_name: Neumetzler
- first_name: Praveen
full_name: Krishnamoorthy, Praveen
last_name: Krishnamoorthy
- first_name: Isabelle
full_name: Van Houtte, Isabelle
last_name: Van Houtte
- first_name: Evelien
full_name: Mylle, Evelien
last_name: Mylle
- first_name: Volker
full_name: Bischoff, Volker
last_name: Bischoff
- first_name: Samantha
full_name: Vernhettes, Samantha
last_name: Vernhettes
- first_name: Johan
full_name: Winne, Johan
last_name: Winne
- first_name: Jirí
full_name: Friml, Jirí
id: 4159519E-F248-11E8-B48F-1D18A9856A87
last_name: Friml
orcid: 0000-0002-8302-7596
- first_name: York
full_name: Stierhof, York
last_name: Stierhof
- first_name: Karin
full_name: Schumacher, Karin
last_name: Schumacher
- first_name: Staffan
full_name: Persson, Staffan
last_name: Persson
- first_name: Eugenia
full_name: Russinova, Eugenia
last_name: Russinova
citation:
ama: Yu L, Scholl S, Doering A, et al. V-ATPase activity in the TGN/EE is required
for exocytosis and recycling in Arabidopsis. Nature Plants. 2015;1(7).
doi:10.1038/nplants.2015.94
apa: Yu, L., Scholl, S., Doering, A., Yi, Z., Irani, N., Di Rubbo, S., … Russinova,
E. (2015). V-ATPase activity in the TGN/EE is required for exocytosis and recycling
in Arabidopsis. Nature Plants. Nature Publishing Group. https://doi.org/10.1038/nplants.2015.94
chicago: Yu, Luo, Stefan Scholl, Anett Doering, Zhang Yi, Niloufer Irani, Simone
Di Rubbo, Lutz Neumetzler, et al. “V-ATPase Activity in the TGN/EE Is Required
for Exocytosis and Recycling in Arabidopsis.” Nature Plants. Nature Publishing
Group, 2015. https://doi.org/10.1038/nplants.2015.94.
ieee: L. Yu et al., “V-ATPase activity in the TGN/EE is required for exocytosis
and recycling in Arabidopsis,” Nature Plants, vol. 1, no. 7. Nature Publishing
Group, 2015.
ista: Yu L, Scholl S, Doering A, Yi Z, Irani N, Di Rubbo S, Neumetzler L, Krishnamoorthy
P, Van Houtte I, Mylle E, Bischoff V, Vernhettes S, Winne J, Friml J, Stierhof
Y, Schumacher K, Persson S, Russinova E. 2015. V-ATPase activity in the TGN/EE
is required for exocytosis and recycling in Arabidopsis. Nature Plants. 1(7),
15094.
mla: Yu, Luo, et al. “V-ATPase Activity in the TGN/EE Is Required for Exocytosis
and Recycling in Arabidopsis.” Nature Plants, vol. 1, no. 7, 15094, Nature
Publishing Group, 2015, doi:10.1038/nplants.2015.94.
short: L. Yu, S. Scholl, A. Doering, Z. Yi, N. Irani, S. Di Rubbo, L. Neumetzler,
P. Krishnamoorthy, I. Van Houtte, E. Mylle, V. Bischoff, S. Vernhettes, J. Winne,
J. Friml, Y. Stierhof, K. Schumacher, S. Persson, E. Russinova, Nature Plants
1 (2015).
date_created: 2018-12-11T11:51:42Z
date_published: 2015-07-06T00:00:00Z
date_updated: 2021-01-12T06:50:18Z
day: '06'
department:
- _id: JiFr
doi: 10.1038/nplants.2015.94
external_id:
pmid:
- '27250258'
intvolume: ' 1'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4905525/
month: '07'
oa: 1
oa_version: Submitted Version
pmid: 1
publication: Nature Plants
publication_status: published
publisher: Nature Publishing Group
publist_id: '5827'
quality_controlled: '1'
scopus_import: 1
status: public
title: V-ATPase activity in the TGN/EE is required for exocytosis and recycling in
Arabidopsis
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2015'
...
---
_id: '1425'
abstract:
- lang: eng
text: 'In this work we aim at extending the theoretical foundations of lifelong
learning. Previous work analyzing this scenario is based on the assumption that
learning tasks are sampled i.i.d. from a task environment or limited to strongly
constrained data distributions. Instead, we study two scenarios when lifelong
learning is possible, even though the observed tasks do not form an i.i.d. sample:
first, when they are sampled from the same environment, but possibly with dependencies,
and second, when the task environment is allowed to change over time in a consistent
way. In the first case we prove a PAC-Bayesian theorem that can be seen as a direct
generalization of the analogous previous result for the i.i.d. case. For the second
scenario we propose to learn an inductive bias in form of a transfer procedure.
We present a generalization bound and show on a toy example how it can be used
to identify a beneficial transfer algorithm.'
alternative_title:
- Advances in Neural Information Processing Systems
author:
- first_name: Anastasia
full_name: Pentina, Anastasia
id: 42E87FC6-F248-11E8-B48F-1D18A9856A87
last_name: Pentina
- first_name: Christoph
full_name: Lampert, Christoph
id: 40C20FD2-F248-11E8-B48F-1D18A9856A87
last_name: Lampert
orcid: 0000-0001-8622-7887
citation:
ama: 'Pentina A, Lampert C. Lifelong learning with non-i.i.d. tasks. In: Vol 2015.
Neural Information Processing Systems; 2015:1540-1548.'
apa: 'Pentina, A., & Lampert, C. (2015). Lifelong learning with non-i.i.d. tasks
(Vol. 2015, pp. 1540–1548). Presented at the NIPS: Neural Information Processing
Systems, Montreal, Canada: Neural Information Processing Systems.'
chicago: Pentina, Anastasia, and Christoph Lampert. “Lifelong Learning with Non-i.i.d.
Tasks,” 2015:1540–48. Neural Information Processing Systems, 2015.
ieee: 'A. Pentina and C. Lampert, “Lifelong learning with non-i.i.d. tasks,” presented
at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol.
2015, pp. 1540–1548.'
ista: 'Pentina A, Lampert C. 2015. Lifelong learning with non-i.i.d. tasks. NIPS:
Neural Information Processing Systems, Advances in Neural Information Processing
Systems, vol. 2015, 1540–1548.'
mla: Pentina, Anastasia, and Christoph Lampert. Lifelong Learning with Non-i.i.d.
Tasks. Vol. 2015, Neural Information Processing Systems, 2015, pp. 1540–48.
short: A. Pentina, C. Lampert, in:, Neural Information Processing Systems, 2015,
pp. 1540–1548.
conference:
end_date: 2015-12-12
location: Montreal, Canada
name: 'NIPS: Neural Information Processing Systems'
start_date: 2015-12-07
date_created: 2018-12-11T11:51:57Z
date_published: 2015-01-01T00:00:00Z
date_updated: 2021-01-12T06:50:39Z
day: '01'
department:
- _id: ChLa
ec_funded: 1
intvolume: ' 2015'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://papers.nips.cc/paper/6007-lifelong-learning-with-non-iid-tasks
month: '01'
oa: 1
oa_version: None
page: 1540 - 1548
project:
- _id: 2532554C-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '308036'
name: Lifelong Learning of Visual Scene Understanding
publication_status: published
publisher: Neural Information Processing Systems
publist_id: '5781'
quality_controlled: '1'
scopus_import: 1
status: public
title: Lifelong learning with non-i.i.d. tasks
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 2015
year: '2015'
...