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Conference papers
A Case Study on the Parametric Occurrence of Multiple Steady States
Russell Bradford
1
James Davenport
1
Matthew England
2
Hassan Errami
3
Vladimir Gerdt
4
Dima Grigoriev
5
Charles Hoyt
6
Marek Košta
7
Ovidiu Radulescu
8
Thomas Sturm
9, 7
Andreas Weber
3
7
VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Russell Bradford 1
Mail :
Author
James H. Davenport 1
Mail :
Author Employer institution : University of Bath [Bath]
Matthew England 2
Author
Hassan Errami 3
Author
Vladimir Gerdt 4
Mail :
Author
Dima Grigoriev 5
Mail :
Author
Charles Hoyt 6
Mail :
Author
Marek Košta 7
Author
1
Department of Computer Science [Bath] (University of Bath, Bath, BA2 7AY, UK - United Kingdom)
- University of Bath [Bath] (laverton Down, Bath, North East Somerset BA2 7AY - United Kingdom)
2
Coventry University (UK) (United Kingdom)
- Coventry University (Coventry University Priory Street Coventry, United Kingdom CV1 5FB - United Kingdom)
3
Institut für Informatik II [Bonn] (Friedrich-Ebert-Allee 144
53113 Bonn - Germany)
- Rheinische Friedrich-Wilhelms-Universität Bonn (Regina-Pacis-Weg 3, 53113 Bonn - Germany)
4
JINR - Joint Institute for Nuclear Research (Joliot-Curie 6, 141980 Dubna, Moscow region - Russia)
5
LPP - Laboratoire Paul Painlevé - UMR 8524 (Université de Lille - Sciences et technologies
U.F.R. de Mathématiques 59 655 Villeneuve d'Ascq Cedex - France)
- Université de Lille (Lille - France)
- CNRS - Centre National de la Recherche Scientifique : UMR8524 (France)
6
B-IT - Bonn-Aachen International Center for Information Technology (Bonn - Germany)
- University of Bonn (D-53012 Bonn - Germany)
- RWTH - Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen Templergraben 55 52062 Aachen (Hausanschrift) 52056 Aachen (Postanschrift) - Germany)
- Fraunhofer-Gesellschaft - Fraunhofer (Hansastraße 27c, 80686 München - Germany)
- University of Applied Sciences Bonn-Rhein-Sieg (Grantham-Allee 20, D-53757 - Germany)
7
VERIDIS - Modeling and Verification of Distributed Algorithms and Systems (France)
- MPII - Max-Planck-Institut für Informatik (Campus E-1 4, 66123 Saarbrücken, Germany - Germany)
- Max-Planck-Gesellschaft (Jägerstrasse, 10-11, D-10117 Berlin - Germany)
- Inria Nancy - Grand Est (615 rue du Jardin Botanique 54600 Villers-lès-Nancy - France)
- Inria - Institut National de Recherche en Informatique et en Automatique (Domaine de Voluceau Rocquencourt - BP 105 78153 Le Chesnay Cedex - France)
- LORIA - FM - Department of Formal Methods (France)
- LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications (Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex - France)
- Inria - Institut National de Recherche en Informatique et en Automatique (Domaine de Voluceau Rocquencourt - BP 105 78153 Le Chesnay Cedex - France)
- UL - Université de Lorraine (34 cours Léopold - CS 25233 - 54052 Nancy cedex - France)
- CNRS - Centre National de la Recherche Scientifique : UMR7503 (France)
- LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications (Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex - France)
8
DIMNP - Dynamique des interactions membranaires normales et pathologiques (BT 24 CC 107 Place Eugène Bataillon 34095 MONTPELLIER CEDEX 5 - France)
- UM1 - Université Montpellier 1 (5, boulevard Henri IV - CS 19044 - 34967 Montpellier cedex - France)
- UM2 - Université Montpellier 2 - Sciences et Techniques (Place Eugène Bataillon - 34095 Montpellier cedex 5 - France)
- UM - Université de Montpellier (163 rue Auguste Broussonnet - 34090 Montpellier - France)
- CNRS - Centre National de la Recherche Scientifique : UMR5235 (France)
9
MPII - Max-Planck-Institut für Informatik (Campus E-1 4, 66123 Saarbrücken, Germany - Germany)
- Max-Planck-Gesellschaft (Jägerstrasse, 10-11, D-10117 Berlin - Germany)
Abstract : We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.
Document type :
Conference papers
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Complete list of metadatas
https://hal.inria.fr/hal-01648694
Contributor : Thomas Sturm <>
Submitted on : Wednesday, November 29, 2017 - 7:48:25 PM
Last modification on : Tuesday, June 16, 2020 - 11:42:22 AM
Contributor : Thomas Sturm <>
Submitted on : Wednesday, November 29, 2017 - 7:48:25 PM
Last modification on : Tuesday, June 16, 2020 - 11:42:22 AM
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- HAL Id : hal-01648694, version 1
- DOI : 10.1145/3087604.3087622
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CNRS | INRIA | LORIA-FM | LORIA | UNIV-LORRAINE | BS | UNIV-MONTPELLIER | UNIV-LILLE
Citation
Russell Bradford, James Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, et al.. A Case Study on the Parametric Occurrence of Multiple Steady States. ISSAC 2017 - International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.45-52, ⟨10.1145/3087604.3087622⟩. ⟨hal-01648694⟩
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