@Inbook{Berman_Halasz_Kumar_07,
	author="Berman, Spring
	and Hal{\'a}sz, {\'A}d{\'a}m
	and Kumar, Vijay",
	editor="Bemporad, Alberto
	and Bicchi, Antonio
	and Buttazzo, Giorgio",
	chapter="MARCO: A Reachability Algorithm for Multi-affine Systems with Applications to Biological Systems",
	title="Hybrid Systems: Computation and Control: 10th International Workshop, HSCC 2007, Pisa, Italy, April 3-5, 2007. Proceedings",
	year="2007",
	publisher="Springer Berlin Heidelberg",
	address="Berlin, Heidelberg",
	pages="76--89",
	isbn="978-3-540-71493-4",
	doi="10.1007/978-3-540-71493-4_9",
	url="http://dx.doi.org/10.1007/978-3-540-71493-4_9",
	abstract = "We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our previous 
        work on reachability analysis and that of our collaborators [1,2,3], we exploited the convexity of multi-affine 
        functions and the fact that the vector field in modes with rectangular invariants is uniquely determined by its 
        values at the rectangle vertices. In this paper, we explicitly calculate conical overapproximations of the reachable 
        set in the invariant of each mode. We describe our Multi-Affine Reachability analysis using Conical Overapproximations, 
        Marco, and show that it yields results that are superior to those obtained by existing methods for multi-affine hybrid systems. 
        Finally, we demonstrate the application of Marco to the analysis of an ant house hunting model that incorporates quorum sensing 
        [4] and the analysis of bi-stability of the lactose induction system regulated by glucose and lactose [5]."
}