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We present an approach to modeling complex biological systems that is based on Hybrid automata (HA). HA combine discrete transition graphs with continuous dynamics. Our goal is to efficiently capture the behavior of excitable cells previously modeled by systems of nonlin-ear differential equations. In particular, we derive HA models from the Hodgkin-Huxley(More)
Cycle-linear hybrid automata (CLHAs), a new model of excitable cells that efficiently and accurately captures action-potential morphology and other typical excitable-cell characteristics such as refractoriness and restitution, is introduced. Hybrid automata combine discrete transition graphs with continuous dynamics and emerge in a natural way during the(More)
We show how to automatically learn the class of Hybrid Au-tomata 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(More)
In order to characterize the action of androgen in skeletal muscle, we have investigated the effects of castration (GDX) and dihydrotestosterone (DHT) on global gene expression in mice. The serial analysis of gene expression method was performed in the muscle of male mice in six experimental groups: intact, GDX and GDX+DHT injection 1, 3, 6 or 24 h before(More)
We propose hybrid automata (HA) as a unifying framework for computational models of excitable cells. HA, which combine discrete transition graphs with continuous dynamics, can be naturally used to obtain a piecewise, possibly linear, approximation of a nonlinear excitable-cell model. We first show how HA can be used to efficiently capture the(More)
We introduce cycle-linear hybrid automata (CLHA) and show how they can be used to efficiently model dynamical systems that exhibit nonlinear, pseudo-periodic behavior. CLHA are based on the observation that such systems cycle through a fixed set of operating modes, although the dynamics and duration of each cycle may depend on certain computational aspects(More)
We present an efficient, event-driven simulation framework for large-scale networks of excitable hybrid automata (EHA), a particular kind of hybrid automata that we use to model excitable cells. A key aspect of EHA is that they possess protected modes of operation in which they are non-responsive to external inputs. In such modes, our approach takes(More)
  • H Y, L Y, Huanxing Yang, Bill Dupor, Eric Fisher, Howard Marvel +9 others
  • 2008
This paper considers a nonlinear pricing framework with both horizontally and vertically differentiated products. By endogenizing the set of consumers served in the market, we are able to study how increased competition affects nonlinear pricing, in particular the market coverage and quality distortions. We characterize the symmetric equilibrium menu of(More)
We present the Piecewise Linear Approximation Model of Ion Channel contribution (PLAMIC) to cardiac excitation. We use the PLAMIC model to conduct formal analysis of cardiac arrhythmic events, namely Early Afterdepolarizations (EADs). The goal is to quantify (for the first time) the contribution of the overall sodium (N a +), potassium (K +) and calcium (Ca(More)
—We present a novel approach to investigating key behavioral properties of complex biological systems by first using automated techniques to learn a simplified Linear Hybrid Automaton model of the system under investigation, and then carrying out automatic reachability analysis on the resulting model. The specific biological system we consider is the(More)