The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
A modified Prony algorithm for exponential function fitting
SIAM Journal on Scientific Computing
Fuzzy Stochastic Automata for Reactive Learning and Hybrid Control
SETN '02 Proceedings of the Second Hellenic Conference on AI: Methods and Applications of Artificial Intelligence
Information and Computation
The Theory of Timed I/O Automata (Synthesis Lectures in Computer Science)
The Theory of Timed I/O Automata (Synthesis Lectures in Computer Science)
Hybrid modeling and simulation of genetic regulatory networks
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Verifying average dwell time by solving optimization problems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Spatial Networks of Hybrid I/O Automata for Modeling Excitable Tissue
Electronic Notes in Theoretical Computer Science (ENTCS)
Learning and Detecting Emergent Behavior in Networks of Cardiac Myocytes
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
StonyCam: A Formal Framework for Modeling, Analyzing and Regulating Cardiac Myocytes
Concurrency, Graphs and Models
An Exact Brownian Dynamics Method for Cell Simulation
CMSB '08 Proceedings of the 6th International Conference on Computational Methods in Systems Biology
Learning and detecting emergent behavior in networks of cardiac myocytes
Communications of the ACM - Being Human in the Digital Age
Modeling and simulation of cardiac tissue using hybrid I/O automata
Theoretical Computer Science
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We show how to automatically learn the class of Hybrid Automata called Cycle-Linear Hybrid Automata (CLHA) in order to model the behavior of excitable cells. Such cells, whose main purpose is to amplify and propagate an electrical signal known as the action potential (AP), serve as the "biologic transistors" of living organisms. The learning algorithm we propose comprises the following three phases: (1) Geometric analysis of the APs in the training set is used to identify, for each AP, the modes and switching logic of the corresponding Linear Hybrid Automata. (2) For each mode, the modified Prony's method is used to learn the coefficients of the associated linear flows. (3) The modified Prony's method is used again to learn the functions that adjust, on a per-cycle basis, the mode dynamics and switching logic of the Linear Hybrid Automata obtained in the first two phases. Our results show that the learned CLHA is able to successfully capture AP morphology and other important excitable-cell properties, such as refractoriness and restitution, up to a prescribed approximation error. Our approach is fully implemented in MATLAB and, to the best of our knowledge, provides the most accurate approximation model for ECs to date.