@article {,
	title = {Probabilistic reachability for multi-parameter bifurcation analysis of cardiac alternans},
	journal = {Theoretical Computer Science},
	year = {2018},
	month = {02/2018},
	abstract = {<p>Using a probabilistic reachability-based approach, we present a multi-parameter bifurcation analysis of electrical alternans in the two-current Mitchell{\textendash}Schaeffer (MS) cardiac-cell model. Electrical alternans is a phenomenon characterized by a variation in successive Action Potential Durations generated by a cardiac cell or tissue. Alternans are known to initiate re-entrant waves and are an important physiological indicator of an impending life-threatening arrhythmia such as ventricular fibrillation. The multi-parameter bifurcation analysis we perform identifies a bifurcation hypersurface in the MS model parameter space, such that a small perturbation to this region results in a transition from highly likely alternans to highly likely non-alternans behavior. Our approach to this problem rests on encoding alternans-like behavior in the MS model as a five-mode, multinomial hybrid automaton. To perform multi-parameter bifurcation analysis of cardiac alternans, we first treat the parameters in question as bounded random variables. We then apply a sophisticated guided-search-based probabilistic reachability analysis to compute a bounded bifurcation region (possibly very tight) that contains the bifurcation hypersurface (BH). Our probabilistic reachability analysis uses a technique that combines a δ-decision procedure with statistical tests. In the process of computing the bifurcation region, we further partition the parameter space into two more regions such that any valuation chosen from one of the regions will either produce alternans or non-alternans behavior with a probability greater than a user-defined threshold.</p>
},
	keywords = {Bifurcation analysis, Cardiac alternans, Cardiac modeling, Formal methods, Hybrid systems, Probabilistic reachability},
	issn = {0304-3975},
	doi = {https://doi.org/10.1016/j.tcs.2018.02.005},
	url = {http://www.sciencedirect.com/science/article/pii/S0304397518300823},
	author = {Md. Ariful Islam and Rance Cleaveland and FLAVIO H. FENTON and Radu Grosu and Paul L. Jones and Scott A. Smolka}
}
@conference {,
	title = {Lagrangian Reachabililty},
	booktitle = {Computer Aided Verification - 29th International Conference, {CAV} 2017 Proceedings, Part {I}},
	year = {2017},
	abstract = {<p>We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.</p>
},
	doi = {10.1007/978-3-319-63387-9_19},
	author = {Jacek Cyranka and Md. Ariful Islam and Greg Byrne and Paul L. Jones and Scott A. Smolka and Radu Grosu}
}
