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Approximate Bisimulations for Sodium Channel Dynamics [chapter]

Abhishek Murthy, Md. Ariful Islam, Ezio Bartocci, Elizabeth M. Cherry, Flavio H. Fenton, James Glimm, Scott A. Smolka, Radu Grosu
2012 Lecture Notes in Computer Science  
The technical basis for this result is the construction of an approximate bisimulation between the HH and IMW channel models, both of which are input-controlled (voltage in this case) continuous-time Markov  ...  (3) Exploring the sensitivity of the overall IMW model to the HH-type sodium-channel approximation.  ...  Conclusions and Future Work We constructed a two-state Hodgkin-Huxley-type model M H that can replace the 13-state continuous-time MDP model M I for sodium-channel dynamics, in the context of the IMW cardiac-cell  ... 
doi:10.1007/978-3-642-33636-2_16 fatcat:azmuhgvzqncpxcjqbun3stzc5q

Model-order reduction of ion channel dynamics using approximate bisimulation

Md. Ariful Islam, Abhishek Murthy, Ezio Bartocci, Elizabeth M. Cherry, Flavio H. Fenton, James Glimm, Scott A. Smolka, Radu Grosu
2015 Theoretical Computer Science  
(IMW) 67-variable cardiac myocycte model, it is possible to replace the detailed 13-state probabilistic model of the sodium channel dynamics with a much simpler Hodgkin-Huxley (HH)-like two-state model  ...  The basis of our results is the construction of an approximate bisimulation between the HH-type abstraction and the corresponding detailed ion channel model, both of which are input-controlled (voltage  ...  Consider the 13-state model for sodium-channel dynamics shown in Fig. 3 .  ... 
doi:10.1016/j.tcs.2014.03.018 fatcat:yot5xlpl7raszohwr6xthgfxky

Compositionality results for cardiac cell dynamics

Md. Ariful Islam, Abhishek Murthy, Antoine Girard, Scott A. Smolka, Radu Grosu
2014 Proceedings of the 17th international conference on Hybrid systems: computation and control - HSCC '14  
We show that this substitution of (approximately) equals for equals is safe in the sense that the approximation error between sodium-channel models does not get amplified by the feedback-loop context in  ...  To prove this feedback-compositionality result, we exhibit quadratic-polynomial, exponentially decaying bisimulation functions between the IMW and HH-type sodium channels, and also for the IMW-based context  ...  This substitution of (approximately) equals for equals is "safe" in the sense that, despite the feedback nature of the composition of the sodium-channel component and the rest of the IMW model, the approximation  ... 
doi:10.1145/2562059.2562138 dblp:conf/hybrid/IslamMGSG14 fatcat:5gefsiizzzgkzazgqfkttr6rxe

Specification, construction, and exact reduction of state transition system models of biochemical processes

Scott M. Bugenhagen, Daniel A. Beard
2012 Journal of Chemical Physics  
The application of the method to biochemical reaction systems is illustrated by models describing a hypothetical ion-channel at several levels of complexity.  ...  Here, we describe methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level  ...  Dependency graphs for the rate constants associated with the binding of Na + to a β subunit in the four component Na + sodium channel complex model.  ... 
doi:10.1063/1.4758074 pmid:23083149 pmcid:PMC3487925 fatcat:7yhkxkr2qndifer62hsa7zease

Models and emerging trends of concurrent constraint programming

Carlos Olarte, Camilo Rueda, Frank D. Valencia
2013 Constraints  
We also describe the current efforts to endow CCP with bisimulation reasoning techniques as standardly done in process calculi. Section 7 concludes the paper.  ...  In Section 6 we describe the elegant denotational semantics for CCP based on closure operators and the program analysis techniques developed for the language.  ...  We thank the anonymous reviewers for their detailed comments that helped us to improve this paper. Special thanks to Jorge A. Perez for his careful remarks and suggestions.  ... 
doi:10.1007/s10601-013-9145-3 fatcat:7mx6xnyfcjad7musa373vockne

From Biochemistry to Stochastic Processes

Cosimo Laneve, Sylvain Pradalier, Gianluigi Zavattaro
2009 Electronical Notes in Theoretical Computer Science  
This study also permits to reuse, in nanoκ, the theories and tools already developed for process calculi.  ...  Our implementation complies with the stochastic behaviors of systems, thus allowing one to use nanoκ as an intelligible front-end for a process-oriented simulator.  ...  Our correctness notion corresponds to the subcase of the strong stochastic bisimulation [3] where the bisimulation relation is a bijection.  ... 
doi:10.1016/j.entcs.2009.10.011 fatcat:33tq6kcdifaankofvoy25pb6hy

Combinatorics and Algorithmics of Strings (Dagstuhl Seminar 14111) Computational Complexity of Discrete Problems (Dagstuhl Seminar 14121) Computational Models of Cultural Behavior for Human-Agent Interaction (Dagstuhl Seminar 14131) Interaction and Collective Movement Processing (Dagstuhl Seminar 14132) Spatial reference in the Semantic Web and in Robotics (Dagstuhl Seminar 14142)

Johannes Fürnkranz, Eyke Hüllermeier, Cynthia Rudin, Scott Sanner, Roman Słowiński, Maxime Crochemore, James Currie, Gregory Kucherov, Dirk Nowotka, Pierre Dillenbourg, Claude Kirchner, John Mitchell (+25 others)
2014 unpublished
The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies  ...  This yields both an implicit characterization of polynomial time in terms of ordinary differential equations, and a completeness result on the reachability problems for the corresponding class.  ...  in which these sodium-channel models are placed.  ... 
fatcat:k3cugkqpf5btlba2hklfxyujdq