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Efficient Modeling of Excitable Cells Using Hybrid Automata
The goal is to efficiently capture the behavior of excitable cells previously modeled by systems of nonlinear differential equations by derive HA models from the Hodgkin-Huxley model of the giant squid axon, the Luo-Rudy dynamic model of a guinea pig ventricular cell, and a models of a neonatal rat ventricular myocyte. Expand
Modelling excitable cells using cycle-linear hybrid automata.
It is shown that the CLHA closely mimics the behaviour of several classical highly nonlinear models of excitable cells, thereby retaining the simplicity of Biktashev's model without sacrificing the expressiveness of Fenton-Karma. Expand
Learning Cycle-Linear Hybrid Automata for Excitable Cells
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 and provides the most accurate approximation model for ECs to date. Expand
Hybrid Automata as a Unifying Framework for Modeling Excitable Cells
This work shows how hybrid automata can be used to efficiently capture the action-potential morphology and reproduce typical excitable-cell characteristics of the dynamic Luo-Rudy model of a guinea-pig ventricular myocyte. Expand
A Cycle-Linear Approach to Modeling Action Potentials
It is shown how cycle-linear hybrid automata can be used to efficiently model the action potential of various types of excitable cells and their adaptation to pacing frequency. Expand
Efficient Event-Driven Simulation of Excitable Hybrid Automata
An efficient, event-driven simulation framework for large-scale networks of excitable hybrid automata (EHA) and a five-fold improvement in the simulation time required to produce spiral waves in a 400-times-400 cell array is demonstrated. Expand
Formal Analysis of Abnormal Excitation in Cardiac Tissue
The PLAMIC model is used to conduct formal analysis of cardiac arrhythmic events, namely Early Afterdepolarizations (EADs), and the goal is to quantify the contribution of the overall sodium, potassium, potassium and calcium currents to the occurrence of EADs during the plateau phase of the cardiac action potential. Expand
Modeling excitable cells using hybrid automata
This work designs a specific kind of hybrid automata: Cycle-Linear Hybrid Automata (CLHA), to model multiple physiological properties of excitable cells including action potential, restitution and hyper-polarization and presents how machine learning techniques are applied to automatically learn the parameters of CLHA from existing data. Expand
Symbolic Analysis of the Neuron Action Potential
The results obtained reveal the precise conditions under which bifurcation manifests, when taking into consideration an infinite class of input stimuli of arbitrary shape, amplitude, and duration within given respective intervals and demonstrate that Linear Hybrid Automata, as a formal language, is both expressive enough to capture interesting excitable-cell behavior, and abstract enough to render formal analysis possible. Expand
A note on paratopological groups with an ωω-base
Abstract In this paper, paratopological groups with an ω ω -base are investigated. The following results are obtained, which generalizes some conclusions in literature. (1) Every Frechet-UrysohnExpand