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Compositionality Results for delta-Bisimulations

Radu Grosu ( Vienna University of Technology )

By appealing to the small-gain theorem of one of the authors (Girard), we show that the 13-variable sodium-channel component of the IMW cardiac-cell model (Iyer-Mazhari- Winslow) can be replaced by an approximately bisimilar, 2-variable HH-type (Hodgkin-Huxley) abstraction. 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 feed-back-loop context in which it is placed. To prove this feed-back 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 in which these sodium-channel models are placed. These functions allow us to quantify the overall error introduced by the sodium-channel abstraction and subsequent substitution in the IMW model. To automate the computation of the bisimulation functions, we employ the SOSTOOLS optimization toolbox. Our experimental results validate our analytical findings. To the best of our knowledge, this is the first application of delta-bisimilar, feedback-assisting, compositional reasoning in biological systems.

Speaker bio

Radu Grosu is a full Professor, and the Head of the Institute of Computer Engineering, at the Faculty of Informatics, of the Vienna University of Technology. He is also the Head of the Cyber-Physical-Systems Group within the Institute of Computer-Engineering, and a Research Professor at the Department of Computer Science, of the State University of New York at Stony Brook, USA. He is the recipient of the National Science Foundation Career Award, the State University of New York Research Foundation Promising Inventor Award, the Association for Computing Machinery Service Award, and is an elected member of the International Federation for Information Processing, Working Group 2.2. Before receiving his appointment at the Vienna University of Technology, Radu Grosu was an Associate Professor in the Department of Computer Science, of the State University of New York at Stony Brook, where he co- directed the Concurrent-Systems Laboratory and co-founded the Systems-Biology Laboratory. He earned his doctorate (Dr.rer.nat.) in Computer Science from the Faculty of Informatics of the Technical University M√ľnchen, Germany, and was subsequently a Research Associate in the Department of Computer and Information Science, of the University of Pennsylvania, USA, and an Assistant Professor in the Department of Computer Science, of the State University of New York at Stony Brook, USA. His research interests include the modeling, the analysis and the control of cyber-physical systems and of biological systems. Applications include distributed automotive and avionic systems, autonomous mobility, green operating systems, mobile ad-hoc networks, cardiac-cell networks, and genetic regulatory networks.

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